Chapter1

=__**Chapter 1: Driving the Roads**__=

=__**First Inquiry Lab Writeup**__=
 * 1) What does the object do?
 * 2) How does the object work?
 * 3) Who can use this object?
 * 4) The object is probably designed to do something specific. Think of something else that the object may be used for.

__**6.**__ 1. It can hold liquid. 2. It contains the liquid and stops the liquid from moving. 3. All people can use these. 4. It can also be used as a decoration.

__**5.**__ 1. This object is used as a balancing tool. 2. Two differently weighted objects are placed at separate ends of string with a holder in the middle. 3. Anyone trying to determine which of two objects is heavier. 4. It can also be used as a wind chime or a toy.

__**4.**__ 1. The smoke shows the path of the laser going through the glass block. 2. When the smoke is sprayed in the path of the laser it shows the beam of the laser. 3. Anyone can use this object. 4. It can be used at parties or if you are robbing a bank and do not want to walk into a laser and set of an alarm.

__**3.**__ 1. The slinky is used to stop the weight from hitting the bottom. 2. The slinky springs up and down to keep the weight from hitting. 3. Anyone can use this. 4. If it was larger it could be used like a bungee jump.

__**2.**__ 1. It measures the weight in newtons. 2. Hook the metal hook into the metal rod the spring inside measures the weight. 3. Anyone trying to weigh an object in newtons. 4. It can be used by an engineer or a scientist to measure heavy objects that are too large to measure on a scale.

__**1.**__ 1. It measures the distance and speed the car travels. 2. The further back you pull the car the faster and farther it will go forward when you let go. 3. Race car drivers can use this. 4. It can also be used as a toy or a game.

toc

**__Learning Objectives__**

 * Measure- reaction time using one of two different methods.
 * Compare- the different methods of measuring reaction time.
 * Compare- the reaction times of your classmates.
 * Investigate- how distractions affect reaction time.

__**What do you see?**__
The orange car is flipped over and the yellow car is on top of it. The blue car is trying to stop before it crashes into the two car pile up that is in front of it. The man in the blue cars hat is flying off. The tires are smoking. There is a puddle in the middle of the road. The blue car was speeding. The man in the blue car is driving around a turn.

__**What do you think?**__
The speed you were going. Your reaction time. How soon you realize you need to stop? The size of your car. Is there anything around you? The weather; if the ground is wet or not. Car condition (breaks) Visibility If you are on your cell phone. (distractions) How tired you are. The distance between you and what is in front of you.

__1.1 Investigate__
36.3 29.3 21.3
 * Pre-lab**
 * Aubrey || Aaron || Cory ||
 * .53 || .65 || .52 ||
 * Method A**
 * Aubrey || Aaron || Cory ||
 * .34 || .32 || .21 ||
 * .32 || .28 || .32 ||
 * .22 || .49 || .11 ||
 * Average:**
 * Average:**


 * Method B (in cm)**

.26 .28 .31
 * Aubrey || Aaron || Cory ||
 * 33 || 21 || 19 ||
 * 38 || 27 || 18 ||
 * 46 || 17 || 14 ||
 * Average:**


 * Average:** 0.22

__**Compare Methods of Measuring Reaction Time**__


 * __1.)__**
 * a.** They were not all the same because everyone has a different reaction time.
 * b.** I think that Method B most accurately measures your reaction time. I think that having to react fast enough in order to catch the ruler before it hits the floor is a much better test then stopping the stop watch.

__**2.)**__
 * a.** The average time for Method A was 36.3, 29.3, and 21.3. The average reaction time for Method B was .22. Method B had a faster reaction time than Method A. Method A was tested by starting two stop watches at the same time and seeing how long it takes for the second person to stop it once the first is stopped. Method B was tested by dropping ruling and seeing how long it takes for you to realize it is falling and grab it.
 * b.** I think that reaction times vary a little for every person, but i think that it varies more when it comes to ages. That as you grow up your reaction time gets better, but as you start to age your reaction time tends to slow down.

__**Reaction Time with Distractions**__

dropping the ruler (red= catch the ruler + green= drop the ruler) .40 cm .42 cm .26 cm .48 cm .50 cm
 * Method C.**
 * average:** 41.2 cm

dropping the ruler (pretend to text or change the radio) (red= catch the ruler + green= drop the ruler) .93 cm .42 cm .86 cm .34 cm .24 cm
 * Method D.**
 * average:** 55.8 cm

__**1.)**__
 * a.** The average reaction time when you need to make a decision is longer then when you do not need to make a decision.
 * b.** If you are having a serious conversation and become sucked in while driving it can significantly slow down your reaction time. If you were not on your phone you may have been able to avoid an accident. Since you were paying more attention to your call then to your driving you might end up apart of an accident you could of easily avoided.

__**2.)**__
 * a.** The reaction time for Method D is even longer then it was for Method C. This test showed that thinking about when to catch the ruler while trying to do something else can slow your reaction time even more.
 * b.** 10 things that can distract you while driving:
 * 1) talking on a cell phone
 * 2) texting
 * 3) changing the radio station
 * 4) talking to someone else in the car
 * 5) singing along to the radio
 * 6) staring at something outside of the car
 * 7) putting on makeup
 * 8) fixing your hair
 * 9) dialing a phone number
 * 10) driving while under the influence

__**Homework: Cell Phones vs. Drunk Driving**__
The : are going to test if driving drunk is just as dangerous as driving while talking on a cell phone. First they are going to do a test drive without using a phone or while under the influence. What they have to do on the course (both passed the test)
 * First accelerate to 30 and stop at the stop sign
 * Second you must parallel park
 * Then they have to follow a course and go the exact speed that the driver instructs (in 45 seconds)
 * Accident Avoidance Test

Cell Phone (both failed the test)
 * Repeat a sentence
 * Verbal Puzzle
 * Have to list five things about a specific topic

Driving Drunk (both failed the test)
 * They had to remain under the legal limit

They did worse on the cell phone test even though they failed both tests. Although you can stop talking on the phone, but you can not stop being drunk. Also they were just under the legal limit.

__**Physics Talk Summary**__

 * **Reaction Time-** the time that it takes to respond to a situation
 * The reaction was longer when there was a distraction, but imagine how much slower it would be if you were not expecting to have to react.
 * Reaction time can increase or decrease the amount of collisions you have.
 * While a person is driving they might need to take their eyes off the road for a second like when they sneeze. But other times it is a fault of theirs like if they are talking, texting, or doing another task while they are driving.
 * Every US state has a law against drunk driving because it can lower your reaction time significantly. Alcohol is not the only thing that can do that. Drugs (prescription and not) can also slow your reaction time. That is why some medications tell you not to operate any machinery while taking it.
 * A persons reaction time can also vary based off of:
 * age
 * gender
 * practice
 * fatigue
 * exercise
 * attentiveness
 * personality

__**Checking Up Questions**__
1.) How do distractions affect reaction time? A distraction can significantly lower a persons reaction time.

2.) Why is driving under the influence of alcohol or drugs illegal? Driving under the influence of alcohol or drugs is illegal because it can slow your reaction time even more.

3.) Name three factors in addition to distractions and drugs or alcohol that can affect reaction time? Things like age, gender, or fatigue can also affect a persons reaction time.

__**Physics Plus #1 and #2**__
Calculating Reaction TIme d=1/2at 2 d= the distance the ruler falls (measured in cm) a= the acceleration due to gravity on Earth (980 cm/s 2) t= the time of fall (in seconds) __ **1.)** __
 * Time(s) || Distance(cm) ||
 * 0.00 || 0 ||
 * 0.02 ||  ||
 * 0.04 || 0.784 ||
 * 0.06 || 1.764 ||

Both charts show the same thing.

__**2.)**__ 16 cm. with the thumb and index finger of your right hand 19 cm. with the thumb and index finer of your left hand 17 cm. with the thumb and middle finger of your more dominant hand

The reaction time of catching the ruler with your left hand was slower than the reaction time of your right hand.

Trying to catch the ruler with the your thumb and index (left hand) takes longer than catching the ruler with your thumb and middle finger of your more dominant hand.

__**3.)**__ Using the second equation I converted the the distance into time 16 cm = 0.03265 19 cm = 0.03878 17 cm = 0.03469

__**What Do You Think Now?**__
What factors affect the time you need to react to an emergency situation while driving? I think that there are many different factors that affect a person's reaction time in an emergency situation while they are driving
 * age
 * gender
 * practice
 * fatigue
 * exercise
 * attentiveness
 * personality
 * if they are sober
 * if they are texting
 * if they are talking on the phone
 * if they are talking to someone in the car

__**Section 1 Essential Questions**__
What is reaction time? Reaction time is the time it takes for a person to respond to a situation.

How did you measure reaction time in this section? What was the range of reaction times obtained by other students in your class? In this section we measured reaction times by having two people stop two stopwatches at the same time and by having one person drop a ruler and see how long it takes for the other person to catch it. We also took the ruler dropping challenge and made it more difficult by only being able to catch it when the person said red and letting it fall when they say green. Now that the person had to think about what color was being said and when to catch the ruler they also would have pretend to be texting.

Describe how reaction time is a measure of change over time. Reaction times measures the amount of time that it takes for a person to react to an urgent situation or not.

What relevance does reaction time have to driving safely? Having a fast reaction time can help you to be a better and safer driver. It can also help you to not get into an accident or from crashing into something that jumps out in-front of your car.

__**Reflection on Section 1 and the Challenge**__

 * In section 1 we learned all about reaction times and their importance.
 * Having a quick reaction time can keep you from becoming apart of an accident.
 * Knowing my personal reaction time will help me with my driving.

__**Physics to Go**__
1. Method B 2. There was a small difference, but not a big difference. I think this was because I asked my siblings who are older than me, but not that much. So we had similar reaction times.
 * 1 || 2 || 3 ||
 * 20cm || 19cm || 19cm ||
 * 28cm || 16cm || 24cm ||
 * 23cm || 15cm || 20cm ||

3. a. It is difficult to catch the piece of paper with your index and middle finger because it is awkward to catch the piece of paper as it slips through your fingers. b. When you catch it with your thumb and index finger it is easier because you have opposable thumbs and you can pinch it as it falls. The piece of paper was 15 cm in total. c. No, there is not a large range of values for the reaction time because both numbers are very close to each other. d. I think that your reaction time would improve after repeating this same task several times. Because you will know when its coming and it will not be a surprise. Also the more you practice the something the better you get a it.
 * 1) index and middle finger = 9 cm
 * 2) thumb and index finger = 13 cm

4. I think that a race car driver needs a faster reaction time because they are going at much higher speeds. The race car driver will have to see the problem and react very fast otherwise it could end horribly. When your driving through a school zone you have to be very careful because there a students running across the street and could jump right out in front of your car. That is why school zones have lower speeds when students are present. Even if you are not speeding in a school zone you must be very careful and pay attention to everything around you so that way if you need to stop you can.

5. Alcohol, changing radio stations, and talking on a cell phone are all different types of distractions that can greatly slow down a persons reaction time.

6. If you are driving and you have a slow reaction time there are more consequences because it will take you longer to see the problem and even longer to react than someone with a fast reaction time. Some consequences could be getting into an accident or hitting something or someone.

7. Auto insurance if more expensive for teenagers than older more experienced drivers because teenagers are new driver just learning. Even if thy have a faster reaction time. We are still learning and are a bigger risk on the road than the average experienced driver.

__**Section 2**__

 * Measurement: Erros, Accuracy, and Precision**

__**Learning Outcomes**__

 * Calibrate the length of a stride
 * Measure a distance by pacing it of and by using a meter stick
 * Identify sources in errors of measurements
 * Evaluate estimations of measurements reasonable or unreasonable

__**What Do You See?**__

 * The man is walking fast
 * They are measuring the stride of a teenage boy vs. a little girl
 * A woman and a cat in the background
 * They are in a school

__**What Do You Think?**__

 * If two students measurements come up 3m and 10m. Who made the mistake?
 * If the students reported measurements of 3m and 3.01m. Who made a mistake?
 * Precision- how repeatable the measurements are
 * Accuracy- how close the measurement is to the true value

__**Investigate**__
35 strides 51 length of stride total 1,785 meterstick: 2253 cm
 * 35 x 51 = 1,785**


 * Group || Stride (#5) || MeterStick (#7) || TapeMeasure (7d) ||
 * **1** || 2006cm || 2253 cm || 2261 cm ||
 * 2 || 1100cm || 1369 cm || 1370 cm ||
 * 3 || 900 cm || 1369 cm || 1370 cm ||
 * 4 || 867 cm || 1369 cm || 1370 cm ||
 * **5** (my group) || 1598cm || 2253 cm || 2261 cm ||
 * 6 || 759 cm || 1370 cm || 1372 cm ||

__**5.)**__ An error could have been made in...
 * a.**No even though it was the same distance, the number of strides varied. Group 1 and group 5 walked the same amount, but group 1 took more strides than group 5 did.
 * b.** There are differences among the measurements made by the different groups because of errors that could have been made.
 * counting the number of strides
 * the size of the stride could have varied
 * calculating the numbers
 * c.** The measurements can be improved if you repeat this step a few times and average them together. If all groups do this i think that the range will be smaller and closer, but there will still be a gap.

__**7.)**__
 * a**. All of the measurements agree exactly. (Except group 6 is 1 cm more than group 2, 3, and 4)
 * b.** I think there are differences in the measurements between the groups because errors were made in measuring. The difference in measurement is very small and is a small mistake because it is only 1 cm off.
 * c.** Re-emeasuring the same length a few times and taking the number that you get the most, could improve the measurements. Do this as a way of double checking your measuring skills. If all groups do this hopefully there will be no range and they will all be the same.
 * d.** I think if every group was to measure with a very long tape measure the measurements would be much more exact. All of the groups measured the same exact amount except for group 6. I think that each group has a better chance of getting the same measurement while measuring with a tape measure rather than with a meter stick.
 * e.** No there is always a chance of difference in measurements because there is no way to rule out all errors completely.

__**8.)**__
 * a.** A systematic error is an error that can be corrected by a calculation. There were probably a couple systematic errors made when measuring the hallway because that is a common mistake.
 * b.** A random error is an error that cannot be corrected by a calculation. When measuring with a meter stick even time you pick up the meter stick and put it back down again and read off the measurement you run the risk of having a random error. That is why using a tape measure will give you a smaller range of making an error. Although a random error can still be made when using a tape measure.

__**Physics Talk: Erros in Measurement**__
Random Errors Systematic Errors Accuracy and Precision
 * Random Errors- errors that cannot be corrected by calculating (random error can be lowered by using a more precise ruler, but it can not be completely eliminated.
 * If you are using a meter stick with only centimeters you will have a larger chance of random error. The chance will be lowered if the meter stick has millimeters, as long as it is lined up exactly.
 * an error that can not be corrected
 * can be avoided or corrected by calculating (it can happen if you accidentally measure with a yardstick if you think it is a meter stick, 4yd when it should be 4m) can be corrected using a calculation
 * Precision (can be repeated)- an indication of the frequency with which a measurement produces the same result (getting the arrows all in the same area)
 * Accuracy- an indication of how close a series of measurements are to an accepted value (hitting the bull's-eye)
 * accurate and precise (all darts on the bull's-eye)
 * precise, but not accurate (all in the same place, but not accurate)
 * not accurate and not precise- all in different places and none where you were aiming


 * SI System: International Units**
 * **Quantity** || **Unit** || **Symbol** ||
 * length || meter || m ||
 * mass || kilogram || kg ||
 * time || second || s ||
 * temperature || kelvin || K ||
 * current || ampere || A ||

1m=0.001km || 1m=100cm || 1m=1000mm ||
 * Meter**: Base unit of length
 * **Prefix** || **Symbol** || **Multiple of ten by**
 * which base unit is**
 * multiplied** || **Example** ||
 * **kilo** || k || 10^3=1000 || 1km=1000m
 * **centi** || c || 10^-2=0.01 || 1cm=0.01m
 * **milli** || m || 10^-3=0.001 || 1mm=0.001m

__**Driving the Roads and United States Units of Measurement**__
 * Road distances are measured in feet, yards, or miles
 * Speed limits are posted in miles per hour (not kilometer per hour)
 * 12 inches=1 foot
 * 3 feet= 1 yard
 * 5280 feet (1760 yards)= 1 US mile

__**Checking Up Questions**__
1.) Explain the difference between systematic and random errors. A systematic error is an error that can be corrected when using a calculation. A random error can never be completely eliminated, but can be lowered by using a more specific measurement.

2.) Explain why there will always be uncertainty in measurement. There is always an uncertainty in measurement because when you are measuring and the object falls in between two tick marks. Rounding to one of the tick marks is creating the uncertainty in measurement.

3.) What would the positions of arrows on a target need to be to illustrate measurements that are neither accurate nor precise? If the arrows are spread out completely randomly and not where you were aiming.

__**Do Now 9/22/11**__
1.) 6.789, 6.784, 6.781. **___random__** __error.__ __2.) Using inches to measure a length instead of cm.__ **_systematic__** error.

__**Section 2 Notes: Uncertainty (plus or minus (1000,100,10,1,.01,.001,.0001)**__
26.7 cm. (what is the measure of uncertainty) 510 cm. plus or minus __10__cm. (513 cm. it would be plus or minus 1cm. ) 10.250 cm. (plus or minus .001) 7.34 cm. (plus or minus .01) .90 plus or minus .01 .09 plus or minus .01 2,000,000 plus or minus 1,000,000 (first non zero and put 6 zeros behind it) 2,000,000.00 plus or minus .01 cm.
 * The 7, not so far off; close
 * + over - 0.1 cm.
 * 5,000. cm. + over - 1 cm
 * 5,000 cm. plus or minus 1,000 cm. (first real number)
 * 5000.0 cm. the uncertainty is .0 (plus or minus .1 cm.)
 * go to the first non-zero before the decimal 510 (it would be 10 because the first is zero and that does not work)

__**Physics Plus: Precise Measurements and Olympic Records**__
1m plus or minus 10cm 90cm to 110 cm or .9m to 1.1m

1.) What is the range of lengths for 50 m. pools that have an uncertainty of plus or minus 10cm? plus or minus 1cm? plus or minus 1mm? 50m would be plus or minus 10m. 50m = 50.00m 49.90-50.10 49.99-50.01 49.999-50.001

plus or minus 10cm .1 plus or minus 1cm .01 plus or minus 1m .001

2.) How much extra time does it take to swim 50.01m than 49.99m (a difference of 2 cm)? Assume a good swimmer can swim 50m in 25 seconds. 50m/25s (50m in 25 seconds) 2m/s x 100= 200cm/s 2cm/200cm/s= 1/100=.01 seconds

speed=distance/time time=distance/speed

3.) Estimate how long it takes to swim 60cm. Assume a good time for the 1500-m. race is 15 minutes. .006 minutes .36 seconds 1500m/15m=.60/x (cross multiply) 9/1500=1500x/1500 x=.006 minutes x=.36 seconds

4.) In watching the Olympic Games, you hear that someone just broke the record for the 1500m swim by 1/1000 of a second. Explain how it is possible that this person may actually be slower than the previous record holder. (Can it be that the new record holder is swimming in a shorter 50m pool than the prior record holder?) Yes, this is possible due to uncertainty in measurements because the record could have first been made in a pool that is 51m. So the original record holder swam an extra meter. The new record holder could have swam in a pool that was 40 meters. So really the first record holder still holds his title.

__**What Do You Think Now?**__
Yes because 3m and 10m have too big of a gap the be uncertainty. There must have been a mistake made while one of the students was measuring. This was probably just random error or uncertainty. As long as it was in the range of 2.9m, 3m, 3.01m.
 * Two students measure the length of the same object. One reports a length of 3m, the other reports a length of 10m. Has one of them made a mistake?
 * If the students reported measurements of 3m and 3.01m, do you think one of them has made a mistake?

__**Essential Questions**__
This is systematic error because you can fix your mistake by using an equation. Precision is how repeatable something is and accuracy is how close you get to where you were aiming.
 * What does it mean?**
 * Suppose your friend mistakes a yardstick for a meter stick and measures the length of an intersection in your neighborhood. Is this error random or systematic? Which of these types of errors affect precision or accuracy?**

The jeweler can not be completely sure that it is 1 oz. of gold because of random error. It could be 0.9 oz, 1oz., 1.01 oz.
 * How do you know?**
 * Suppose you want to buy some gold jewelry. The jeweler tells you that the jewelry contains exactly 1 oz. of gold. How do you know that the jeweler cannot be sure that it is exactly 10z?**

You can trust experiments even though they have uncertainties because the numbers have been measured and remeasured also they use the most precise method of measurement. Also their measurements are backed up with modes and theories to prove that their numbers are correct.
 * Why do you believe?**
 * All physics knowledge is based on experimentation. All experiments require measurements. How can you trust experiments if all measurements have uncertainties?**

If you are driving and are not accurate with your stopping distance you could hit the car in front of you or stop too far past a stop sign and be out too far in the road. If you misjudge the amount of space between your car and the car in front of you and they stop short or you do then someone can get rear-ended.
 * Why should you care?**
 * What are the consequences of not estimating stopping distances accurately, or the width of a space between your vehicle and other vehicles while driving?**

1000 plus or minus 1000

__**Physics To Go**__
(#5,6,7,8a) The measurements on the labels of these food products like all other food products are close to how much it says, but it is never exactly what it says on the label. Some cans may have the exact amount while others have extra and some have less. if it is 1.4 oz plus or minus .1 oz (it could be 1.3-1.5) 16 oz. (15-17 oz.)
 * 5.) Choose five food products. How accurate are the measurements on labels.**
 * 1) soup
 * 2) pasta
 * 3) jello
 * 4) cereal
 * 5) juice

6. No probably 2 or 3 2L bottles of soft drink. Yes, you can drive from Boston to New York City on one tank of gas.
 * a. A 2-L bottle of soft drink is enough to serve 12 people at a meeting.**
 * b. A mid-sized automobile with a full tank of gas can travel from Boston to New York City without having to refuel.**


 * 7.** No because measuring the distance from me school to my house is a much larger amount than the size of my room. If I am buying flooring for my room and I am off by 1m, I would be missing a lot of flooring. But if I am saying how many meters it is to walk from my school to my house and if I am off by 1 meter it will not make much of a difference.

Your speedometer should read 60mph to guarantee that you are not driving over the speed limit.
 * 8. You are driving on a highway that posts a 65 mph speed limit. The speedometer is accurate within 5mph.**
 * a. What speed should you drive as shown on the speedometer to guarantee that you will not exceed the speed limit?**

__**Section 3**__

 * Average Speed: Following Distance and Models of Motion**

__**Learning Objectives**__

 * Define: and contrast average speed and instantaneous speed
 * Use: strobe photos, graphs, and an equation to describe speed.
 * Use: a motion detector to measure speed.
 * Construct: graphs of your motion.
 * Interpret: distance-time graphs.
 * Calculate: speed, distance, and time using the equation for average speed.

__**What Do You See?**__

 * The three cars are bumper to bumper.
 * The car in the the back of this picture is going fast because her hair is flying and smoke is coming out of her car.
 * The blue car stopped short and the red and yellow car all got into an accident.
 * The yellow car was speeding and hit the red car which hit the blue car.
 * The cars in front do not have space between the cars.
 * The cars in back have enough space in between them.
 * The bunny ran through the street causing the cars to stop short.

__**What Do You Think?**__
What is a safe following distance between your automobile and the vehicle in front of you? Any distance depending on your speed and reaction time. If you are driving an older car you should have more space because your brakes are older.

How do you decide what a safe following distance is? Enough space to stop without hitting the car in front of you if they stop short. Speed, Reaction Time, Weather

__**Investigate**__
1a. (top 3 rectangles) 2a. 45 mph 2b. The cars are further apart when the cars are traveling at 30 mph. The cars closer together when the car is going 45 mph.Each car goes about 0.5 miles per minute. 2c. 60 mph; the cars would have to be the closest together because they are traveling the quickest. The faster the car is going, the less space there is between the cars.

3a. In the diagram the cars going the slowest are in diagram A, the cars going a medium speed are in diagram B, and the cars going the fastest are in diagram C. I know this because pictures of these cars are being taken at the same time. So the cars with the most space in between are gong the slowest. When there is the most space in between cars they are going the slowest. b. Yes, you can tell that all of the cars are traveling at a steady speed because the distance between each car equal.
 * Speed is the distance traveled in a given amount of time*

4a. a person walking toward the motion detector at a normal steady speed

4b. a person walking away from the motion detector at a normal speed

4c. a person walking away from the motion detector then toward it at a very slow speed

4d. a person walking in both directions at a fast speed

4e. Graph a and Graph b ascend and descend at the same pace, but in opposite directions. When you walk towards the motion detector the line descends, but as you walk closer to the motion detector the line ascends. Graph c and Graph d form the same shape. Except Graph c is formed in about 18 seconds while Graph d is formed in about 8 seconds.

5.) a. sketch predicting #5 I think that the graph will slowly descend from a higher distance and that it will ascend quickly because the person is walking fast towards it.

5b. walk toward the motion detector at a slow speed and away from it at a fast speed My prediction turned out to be accurate after it was tested. The graph below shows that.

6a. trial 1: walk slowly away from the detector trial 2: walk quickly away from the detector 6b. The line on the graph that is shorter will be trial 2 because the person had to walk quickly. The longer line will be trial 1 since they would be walking slower.

7. **Average Speed** of an object: the total distance traveled by an object during a given time

7a. In the trials for number 4 the total distance was 6 feet, but we did the trials for 5 and 6 in a different room the next day and their measurements were 5.5 feet for trial 5 and about 5 feet for trial 6.

7b. It took about 12 seconds for trials 4a and 4b, 18 seconds for 4c, and 8 seconds for 4d. Trial 5 lasted 11 seconds. Trial 6a was about 6 seconds and 6b was 3.5 seconds.

7c. **distance/time** =average speed in meters per second (m/s) 4a and 4b = 6/12= **0.5 m/s** 4c = 6/18= .3(repeating)= **0.3 m/s** 4d = 6/8= **0.75 m/s** trial 5 = 5.5/ 11= **0.5 m/s** 6a = 5/6= .83 (repeating 3) = **0.83 m/s** 6b = 5/3.5= **1.43 m/s**

7d. You would be walking about 7 feet. It is possible to extrapolate data from this question because you can rearrange the given equation in three different ways to where they are equivalent.So you can solve for time or distance if you need to find them and you already have the average speed.

8a. v=d/t 60 ft/s = d/0.5 s d=v*t d=60*0.5 d= 30 ft.

8b. v=d/t 60 ft/s =d/1.5 s d=v*t d=60*1.5 d=90 ft

8c. 1.) v=d/t 50 ft/s = d/0.5 s d=v*t d=50*0.5 d= 25 ft.

2.) v=d/t 50 ft/s =d/1.5 s d=v*t d=50*1.5 d=75 ft

8d. 1.) v=d/t 70 ft/s = d/0.5 s d=v*t d=70*0.5 d= 35 ft.

2.) v=d/t 70 ft/s =d/1.5 s d=v*t d=70*1.5 d=105 ft

8e. v=d/t 40 ft/s=d/0.5 s d=v*t d=40*0.5 d= 20 ft

8f. v=d/t 60 ft/s=15 ft/t t-d/v t=15/60 t= 0.25 s

**__Physics Talk__**

 * Understanding Motion:** describe the motion of a vehicle while you are driving and explain what affects distance, braking distance, and the total stopping distance (speed affects all of this)
 * **speed**: the distance traveled per unit time; speed is a scalar quantity, it has no direction
 * **constant speed**: speed that does not change over a period of time.
 * **average speed**: the total distance traveled divided by the time it took to travel that distance
 * Model 1: Describing Motion and Speed Using Strobe Photos**
 * Motion can be showed by using strobe photos; which is a multiple-exposure photo where a moving object is photographed multiple times at regular time intervals.
 * An object traveling at a slow speed will have a smaller distance between each car rather than a car traveling faster. If a car is driving slow it will not travel far before the picture is taken again.
 * **Strobe Photos** are used to illustrate the velocity of an object by the distance between the object in each picture.
 * Model 2: Describing Motion and Speed Using an Equaiton**
 * average speed = distance traveled /time elapsed (used to describe speed)
 * v=d/t= distance/time= triangle d/tringle t
 * Triangle before something means change in
 * v av = average speed
 * triangle d = the change in position or the total distance traveled
 * triangle t = the change in time or elapsed time
 * the triangle which means delta stands for a change in
 * Sample Problem
 * Before your car starts moving the speed is 0 mi/h and when your car stops at the end of your trip is is once again 0 mi/h.
 * instantaneous speed: the speed at a given moment


 * Using the Equation for Speed toFind Other Quantities**
 * the average speed equation can be used to find
 * can solve for speed
 * can find the distance you traveled in that time if you know the average speed and the time it took you to travel that speed
 * can find the time traveled if you know the distance traveled and the average speed
 * 1) v= d/t
 * 2) d= v * t
 * 3) t= d/v


 * this one equation that is used to find average speed can be written in three equivalent ways
 * m/s


 * Sample Problem 2**


 * In your calculations do not forget your units***


 * Sample Problem 3**


 * Speed and Velocity**
 * **velocity**: is the speed in a given direction; always includes both speed and direction


 * Model 3: Describing Motion and Speed Using a Distance-Time Graph**
 * Another way to represent motion is by using graphs
 * Graphs are a visual way to represent data
 * This graph shows a car traveling at a constant speed of 50 mi/h
 * x-axis is time
 * y-axis is distance
 * 50 mi after 1 hour, 100 mi after 2 hours, 150 mi after 3 hours


 * whatever the slope is equals the speed
 * speed=slope* (in a distance-time graph)
 * Graph A: the person is standing still
 * Graph B: the person is walking slow (same speed)
 * Graph C: the person is walking fast
 * Graph D: the person is traveling in an opposite direction (towards and at a constant pace)
 * Graph E: the person is changing speed (shown as a slope) it is not linear


 * Speed and the Slope of a Distance-Time Graph**
 * **slope of a line:** is the rise (change along the y dimension) divided by the run (change along the x dimension)
 * **rise**: is the distance covered
 * **run**: is the time taken
 * **slope = rise/run** or distance/time


 * Kilometers and Miles**
 * miles per hour are used when driving
 * meters is used in collecting data
 * mathematical conversions can be used to convert miles per hour to kilometers per hour

__**Checking Up**__
1.) Explain how the average speed of a vehicle is different from instantaneous speed. The average speed of a vehicle is the speed that it is going over the total period of time. Instantaneous speed is the speed taken at one instance.

2.) How are the speed and velocity of an object different? Velocity is the speed and direction and speed is the rapidity of a movement or action.

3.) If the distance-time graph shows a straight, inclined line, what does the line represent? It shows that the person is standing still.


 * a curve on the distance-time graph shows that the speed is constantly changing*

4.) How does reaction time affect reaction distance? Reaction time is the amount of time it takes a person to react and reaction distance is the distance that it takes for a person to react.

__**Physics Plus**__
v=d/t=80/3=27 miles per hour

1.)

2.) 80 mile trip flip the dots close together and then farther apart 100 mile trip very close dots and then one dot

3a. 50mi at 50mi/h 50mi at 25mi/h 50mi at 10mi/h 85/3= an average of about 29 mi/h

3b. v=d/t (50+50+50=150) (1hour+2hours+5hours= 8 hours) v=150/8 v=18.75mi/h My estimate was off because in my estimate i found the average speed by averaging the three speeds together. When really those three speeds were each driven for different amounts of time.

? || 150mi || 8h || v(av)=150/8=18.75mi/h v(av) total distance/total time
 * speed || distance || time ||
 * 50mi/h || 50mi || 1h ||
 * 25mi/h || 50mi || 2h ||
 * 10mi/h || 50mi || 5h ||
 * total

4. 1st half: 20miles at 20mi/h 2nd half: 20 miles at 60mi/h total: 40mi/h 60mi/h to have a total of 40mi/h

__**What Do You Think Now?**__
What is a safe following distance between your automobile and the vehicle in front of you?
 * A safe following distance between your automobile and the vehicle in front of you is a big enough space so that you have enough time to see the problem and react. Before you hit the car in front of you.
 * Be outside of the reaction distance: the distance that a vehicle travels in the time it takes the driver to react.

How do you decide what a safe following distance is?
 * A safe following distance is different for everyone if you know that you have a slow reaction time you should keep more room in front of your car. If you have a fast reaction time you could stay a little closer.
 * Depends on the individuals reaction time and reaction distance(which relies on other distractions)
 * Your speed does not react your reaction time, but it does react your reaction time.

__**Essential Questions**__
What does it mean to say that the speed of a vehicle is 40mi/h? It means that the average speed that the car is traveling is 40mph.
 * What does it mean?**

How would you go about measuring the speed of a vehicle? What measurements would you have to take? What calculations would you have to preform? You can measure the speed of a vehicle by finding the average speed. You can use the equation average speed=distance/time. It can be written in three different, but still equivalent forms. You need at least two of the three to solve it.
 * How do you know?**

Physicists use models to better understand the world. Speed can be modeled with a strobe photo, an equation, or a graph. How can all three models represent a car moving at 20m/s? -A strobe photo can show a car moving at 20m/s at a constant speed with equal spaces in between each photo. -An equation can show how you found out that the car was traveling at 20m/s. Use the equation v=d/t. -A graph can show a steady increase of speed and time.
 * Why do you believe?**

When driving you have to leave room between your car and the car in front of you. The reaction distance is the distance that a vehicle travels in the time it takes the driver to react. A person's reaction time is the amount of time that it takes for a person to react to a situation, it can depend on if they are being distracted, their age, and many other reasons. Your speed is the only thing that does not affect your reaction time although it does affect your reaction distance. The person might react by stepping on the gas, but that does not mean the car is instantly going to stop. It will take a few moments to slow down and stop.
 * Why should you care?**

__**Physics To Go**__
1a. In picture a the car is traveling at a constant slow speed because the amount of space in between each car is equal and large enough to show a slow speed. 1b. It shows that the car starts out slow, then speeds up, to then slow down again. (closer=slower) (faster=further)

2a. (on top) an automobile starting from rest and reaching a final constant speed. 2b. (the bottom) an automobile traveling at a constant speed then coming to a stop.

3. 350ft/s (almost 250 mph) in 20 seconds distance ? v=d/t 350=d/20 (20)(350)=d(20)(20)cancels d=7000 ft

4. 215mi from NYC to DC in 4.5 hours 4a. average speed? v=d/t v=215/4.5 v=47.7 (repeating 7) v= 48 mi/h 4b. Do you know how fast she was going when she passed through Baltimore? No, because you can only find an average from the information that was given. She could have gone different speeds throughout the trip, but the average from the given information was 48mi/h. Do not have the instantaneous speed when they are driving through Baltimore.

5. d=5 mi t=15 minutes (1/4 of an hour) v=? v=d/t v=5/.25 v=20mi/h

6. 6a. The automobile is traveling at a fast and constant speed and at the straight line they stop 6b. The automobile is traveling very fast, stops (straight line), and goes in the opposite direction slower than the original direction. (back to the original point) going back 6c. The automobile is going slow at a constant pace and then continues going constant a little faster. 6d. The speed is never constant always increasing.

.53 v=d/t 25m/s=d/.53 (.53)(25)=d(.53)(.53)cancels d=13.25 meters v=d/t 16m/s=d/.53 (.53)(16)=d(.53)(.53) cancels d=8.48 meters If you are traveling 25m/s it will take you an extra 4.77 meters to stop. If you are driving at 16m/s you can stop that much quicker. v=d/t 25m/s=d/1.06 (1.06)(25)=d (1.06)(1.06) cancels d= 26.5 meters
 * 7.** (answer in meter/seconds)
 * 7a.** How far does your automobile travel in meters during your reaction time if you are moving at 55mi/h (25m/s)?
 * 7b.** How far does your automobile travel during your reaction time if you are moving at 35 mi/h (16m/s)? How does the distance compare with the distance at 55mi/h?
 * 7c**. Suppose you are very tired and your reaction time is doubled. How far would you travel at 55mi/h during your reaction time?


 * 8.** (three second rule only works if you follow it exactly and if you are following the speed limit
 * 8a.** Traffic experts can be sure that this a safe following distance because they probably looked at the average reaction time and used that in the v=d/t formula. This might be too large or not enough space for some people, but it is a good rule to use as you drive.
 * 8b**. Yes, as long as you are following the 3 second rule exactly it will not matter what type of road you are on. (interstate highway or rural road)

v= 70mi/h (100 ft/s) d=? t=1/3 of a second v=d/t 100=d/.20 (.20)(100)=d(.20)(.20) cancels d= 20 feet 9b. No my classroom is about 45 feet not 20 feet long.
 * 9.** A sneeze requires you to close your eyes for one third of a second.
 * 9a.**

v=d/t 88 ft/s=d/.5s (.5)(88)=d (.5)(.5) cancels d=44 feet
 * 10.** Imagine you are driving your automobile at 60 mi/h (88ft/s) moving in a straight line and your reaction time is 0.5 seconds.
 * 10a.**

44/15= 2.93 (3 repeating) About 2.9 distances (about 3)
 * 10b.** How many automobile spaces is this for an automobile that is 15ft long?

30 miles * 5280= 158400 158400/3600(hours to minutes to seconds 60*60)= 44 feet/seconds 44ft/s=d/.5s (.5)(44)=d (.5)(.5) d= 22 feet About 1.47 spaces of the automobile (about 1-1.5 car spaces)
 * 10c.** 30mi/h
 * v=d/t
 * 22/15= 1.46 (6 repeating)

90*5280=475200 475200/3600=132 132 ft/s v=d/t (.5)(132)=d (.5)(.5) d= 66 ft About 4.4 spaces of the automobile The fraction would be 60/11
 * 10d**. 90 mi/h
 * 132 ft/s=d/.5
 * 66/15= 4.4
 * 360ft/66ft= 5.45 (45 repeating)

158400/3600(hours to minutes to seconds 60*60)= 44 feet/seconds v=d/t 44 ft/s=d/1.06 (44)(1.06)=d (1.06)(1.06) d= 46.64 feet
 * 10e.** Find distance for 30mi/h, 60mi/h, and 90mi/h (if your reaction speed is doubled)
 * 30 miles * 5280= 158400

316800/3600= 88ft/s 88ft/s v=d/t 88=d/1.06 (88)(1.06)=d(1.06)(1.06) d= 93.28 feet
 * 60 miles * 5280= 316800

475200/3600=132 132 ft/s v=d/t 132 ft/s=d/1.06 (1.06)(132)=d(1.06)(1.06) d= 139.92 feet
 * 90 miles * 5280=475200

316800/3600= 88ft/s 88ft/s
 * 11.** Consider an automobile traveling at 60 mi/h. Sketch a graph showing distance traveled versus reaction time, with reaction times of 0.25 s, 0.50 s, 0.75 s, and 1.00 s.
 * 60 miles * 5280= 316800

88=d/.25 (.25)(88)=d (.25)(.25) cancels d=22 feet 88=d/.50 (.50)(88)=d(.50)(5.0) d=44 feet 88=d/.75 (.75)(88)=d(.75)(.75) d=66 feet 88=d/1 (1)(88)=d(1)(1) d=88 feet
 * v=d/t
 * v=d/t
 * v=d/t
 * v=d/t

(should be a straight line 60 should be 66)

__**Section 4: Graphing Motion: Distance, Velocity, and Acceleration**__

 * __Learning Objectives__**
 * **Measure**: a change in velocity (acceleration) of a cart on a ramp using a motion detector.
 * **Construct**: graphs of the motion of a cart on a ramp.
 * **Define**: acceleration using words and an equation.
 * **Calculate**: speed, distance, and time using the equation for acceleration.
 * **Interpret**: distance-time and velocity-time graphs for different types of motion.

__**What Do You See?**__

 * the red car is accelerating because there is smoke, the front of the car is up, and the hat and scarf are flying off
 * the car is rear wheel drive because only the back wheels are spinning
 * the yellow car is still stopped
 * the light just turned green
 * the man and dog are running away from the red car which is speeding up

__**What Do You Think?**__
An auto and a bus are stopped at a traffic light. What are some differences and similarities of the motion of these two vehicles as each goes from a stop to the speed limit of 30 mph?

Similarities Differences
 * they will both start at the same time
 * both vehicles
 * by the time the bus gets to 30mph the car will be further in front of it

__**Chapter 1 Section 4 Investigate**__
__**Graphing Motion: Distance, Velocity, and Acceleration**__

__**Objective:**__ To produce and explain distance versus time and velocity versus time graphs for a cart as it moves up and down an incline; to use a tangent line to show instantaneous velocity; to calculate accleration.

__**Materials:**__ Ramp, ring stand, clamp, motion detector, usb, cart

__**Procedure:**__ In one of them the car moves at a constant velocity away from zero In another the car moves at constant velocity towards zero In another, the car travels faster at the beginning and slows toward the end. In another, the car travels slower at the beginning and speeds up.
 * 1) If you were to place the cart at the top of the ramp and release it to freely move down the ramp would it move through the first half of the distance in the same amount of time as the second half of the distance? Why or why not?
 * 2) Below are four different distance vs time graphs.



At 0.5 seconds velocity is maintained, until it starts to increase at about 1 second. At 1.5 seconds the velocity has greatly increased and is about to stop. speed rise/run=8/10= 0.8m/s
 * Run 1: Motion Detector at top, Cart released from top, stopped at bottom.**
 * Predict:**
 * Push:**
 * Tangent Line:**

acceleration=(final velocity-initial velocity)/time final velocity= 0.9 m/s initial velocity= 0m/s time= 1.6 seconds a=(.9-0)/1.6 a=.9/1.6 a= 0.5625 m/s2
 * Velocity Time Graph:**
 * Calculate Acceleration:**

speed rise/run=8/20= 0.4m/s
 * Run 2: Motion Detector at top, Cart released from top, stopped at bottom.**
 * Predict:**
 * Push:**
 * Tangent Line:** At 0.5 seconds the velocity has not changed, but at 1.5 seconds the velocity has already dropped and is beginning to level out again.

acceleration=(final velocity-initial velocity)/time final velocity= 0 m/s initial velocity= -0.8 m/s time= 2.2 seconds a=(0- -0.8)/2.2 a=-0.8/2.2 a= -0.036 (36 repeating) a= -0.036 m/s2
 * Velocity Time Graph:**
 * Calculate Acceleration:**

speed rise/run=8/20= 0.4m/s
 * Run 3: Motion Detector at the bottom, car released from top stopped at bottom.**
 * Predict:**
 * Push:**
 * Tangent Line:** At 0.5 seconds the velocity is not changing. At 1.5 seconds the velocity has slowed down and is about to stop.

acceleration=(final velocity-initial velocity)/time final velocity= .2 m/s initial velocity= 0 m/s time= 2 seconds a=(.2-0)/2 a=.2/2 a= 0.1 m/s2
 * Velocity Time Graph:**
 * Calculate Acceleration:**

speed rise/run=7/10= 0.7m/s
 * Run 4: Motion Detector at the bottom, car pushed from bottom stopped at top.**
 * Predict:**
 * Push:**
 * Tangent Line:** At 0.5 seconds the velocity has not changed, but at 1.5 seconds the velocity is beginning to straighten out again after there is an upward curve.

acceleration=(final velocity-initial velocity)/time final velocity= 0 m/s initial velocity= 0.8 m/s time= 2 seconds a= (0-.8)/2 a= -0.8/2 a= -0.4 m/s2
 * Velocity Time Graph:**
 * Calculate Acceleration:**

__**Run 5 Part 2 from 10/17**__
 * Run 5: Motion Detector at the bottom, car pushed from bottom, stopped at bottom.**
 * Predict:**
 * Push:**
 * Tangent Line: At 0.5 seconds the velocity is on an upward curve. At 1.5 seconds the velocity is at the curve and will be begin to curve down again in about 0.5 to 1 second.**
 * Velocity Time Graph:**

acceleration=(final velocity-initial velocity)/time final velocity= -1 m/s initial velocity= 1 m/s time= 4 seconds a= (-1-1)/4 a= -2/4 a= -0.5 m/s2
 * Calculate Acceleration:**

__**Explanation Why:**__ Velocity is the slope of a distance vs. time graph

Why acceleration is the slope of a velocity vs. time graph

Why you need to use tangent lines to find instantaneous speed

__**Physics Talk**__
Can change speed and direction at the same (driving on a mountain road with curves)
 * Changing Speed**
 * Acceleration:** the change in velocity with respect to a change in time.
 * a cart traveling down an incline plane has a constant acceleration, so the velocity of the cart changes at a regular rate and is represented by a straight line on the velocity vs. time graph.
 * Acceleration is a Vector Quantity**
 * a bus can go from 0 to 60 mph and from 60 mph to 0 mph
 * an automobile can also do this, but faster and with greater acceleration
 * Difference of Speed and Velocity
 * when driving on a curvy road you might maintain the same speed, but changing direction will be a change in velocity
 * Ways to change an automobiles velocity:**
 * to speed up (increasing the speed, or magnitude of velocity)
 * to slow down (decreasing the speed, or magnitude of velocity)
 * turn (change the direction of velocity)


 * vector:** a quantity that has both **magnitude** (size) and **direction**.
 * negative acceleration:** a decrease in velocity with respect to time. The object can slow down (20m/s to 10 m/s) or up (-20 m/s to -30 m/s).
 * positive acceleration:** an increase in velocity with respect to time. The object can speed up (20 m/s to 30 m/s) or slow down (-20 m/s to -10m/s).
 * Velocity:** the speed and direction of an object
 * Vector Quantity:** a quantity that involves both direction and size **like velocity**
 * Scalar Quantity:** a quantity that has size, but not direction **like speed**


 * Describing Accelerated Motion Using Strobe Pictures**
 * the automobile is moving greater distances during each second of travel


 * Describing Acceleration Using an Equation**
 * Units for Measuring Acceleration**
 * acceleration is when you divide a change in velocity by a change in time
 * velocity can be m/s or km/h
 * acceleration could be (m/s)/s (meters per second every second) or (km/h)/s (kilometers per hour every second)
 * Using the Equation for Acceleration to Find Other Quantities**
 * acceleration, velocity, time (if you know 2 you can find the third)
 * Sample Problem**

Can determine the general motion of an automobile by looking at
 * Describing Acceleration Using Graphs**
 * tangent line: a straight line that touches a curve in only one point
 * if you imagine tangents at different points you can see the slopes of the tangent increase as the time increases
 * increasing speed during a time interval is an acceleration
 * y-axis=velocity
 * x-axis=time
 * acceleration=value of the slope of the velocity-time graph
 * if the slope of a velocity time graph is constant you can conclude that the acceleration is constant
 * Describing Types of Motion Using Graphs**
 * a distance vs. time graph
 * velocity vs. time graph
 * acceleration vs. time graph
 * Comparing distance vs. time graphs, velocity vs. time graphs, and acceleration vs. time graphs

__**Checking Up**__
1.) Give the defining equation for acceleration in words, and by using symbols. Acceleration= Change in velocity/Change in time a=v/t

2.) What is an SI unit for measuring acceleration? Use words and unit symbols to describe the unit. acceleration= (m/s)/s (meteres per second every second) or (km/h)/s (kilometers per hour every second) velocity= m/s (meters per second) or km/h (kilometers per hour) time= s (seconds)

3.) What is the difference between a vector and a scalar quantity? A vector is a quantity that has both magnitude (size) and direction like velocity. While scalar quantity is a quantity that has size, but not direction like speed.

4.) Sketch a distance-time graph for 5.) What does the slope of a velocity-time graph represent? The slope of a velocity-time graph represents the rate of acceleration or the rate of deceleration.
 * a.) constant velocity
 * b.) constant acceleration

__Physics Plus 10/19/11__


__**Extra Questions**__ Why is velocity the slope of a distance vs. time graph? Velocity is the slope of a distance time graph because when you are trying to find the velocity of something the equation that you use is v=d/t. Finding slope on a distance time graph is just like dividing distance by time.
 * -slope=rise/run=distance/time=velocity**

Why is acceleration the slope of a velocity vs. time graph? Acceleration is the slope of a velocity time graph because when you are finding slope you divide rise over run. Which is just like velocity by time when finding acceleration.
 * -slope=rise/run=velocity/time=acceleration**

Why do you need to use tangent lines to find instantaneous speed? Tangent lines are used to find instantaneous speeds because it picks out one point out of the whole graph. So this way you can know the exact speed at any specific time. -slope is will not find instantaneous speed but a tangent line will because it will find the one point

__**Homework 10/19/11**__

vector: magnitude and direction

__**Section 5**__

 * Negative Acceleration: Braking Your Automobile**

__**Learning Outcomes**__

 * Plan: and carry out an experiment to relate braking distance to initial speed
 * Determine: braking distance
 * Examine: accelerated motion

__**What Do You See?**__

 * the car is stopping short
 * the tires are smoking
 * the moose is standing in front of the car
 * the car is braking
 * negative acceleration

__**What Do You Think?**__

 * What factors must you consider to determine if you will be able to stop in the distance between you and the animal to avoid hitting it?
 * speed
 * braking distance
 * reaction time
 * condition of your brakes
 * reaction distance

__**Investigate**__
In this Investigate, you will plan and carry out an experiment to determine the relationship between the initial speed and the braking distance of an automobile. 1.)Knowing how far your automobile will travel after you have stepped on the brake pedal is important. One factor that may have an impact on braking distance is the initial speed of the automobile. a.) What would a graph of braking distance vs. initial speed look like? Sketch a graph that shows what you think the data would show. (Place the initial speed on the x-axis and the braking distance on the y-axis.) While sketching the graph, imagine what would happen to the braking distance for a slow-moving vehicle, a faster-moving vehicle, and a very fast moving vehicle. __**Prediction Sketch**__ **(Run #1 in red)**
 * The **initial speed** is the speed at which you begin to apply the brakes.
 * **Braking distances** is the distance required to bring the vehicle to rest once the brakes are applied.
 * In your investigation, the initial speed will be the speed at the point at which you begin your measurement of baking distance. You will collect data to study the relationship between initial speed and braking distance.

__**Why we drew the sketch this way**__ b.) We drew the prediction the way we did because the speed of the car would continue to increase until it eventually slowed down enough that it would come to a complete stop. We had the correct curve of, but we though that it would go slower than it went.

2.) Your teacher will provide your group with equipment similar to the equipment shown in the illustration below. Discuss with your group how you could use the equipment to study the relationship between initial speed and braking distance.


 * How will you vary the initial speed of the cart (that is, the velocity the cart has at the bottom of the hill when the brakes are applied)?
 * You can vary the initial speed of the cart by raising and lowering the the ramp. Changing the slope of the ramp will make the car change the initial speed of the cart because if there is not a large slope the cart will brake sooner, than if there is a larger slope.
 * The cart does not really have brakes applied by a driver, but the cart will stop on its own. **Friction plays the role of brakes in the cart.**
 * How will you determine the initial speed of the cart just before it begins braking?
 * The motion detector will record the cart the entire time. So look at the highest point on the graph to find find the initial speed, it will be the highest point because it is right before the cart begins to brake.
 * How will you measure the braking distance? (What tool should you use? Should you measure from the front or the back of the cart? How accurate will you make your measurements?)
 * The braking distance can be measured by using a meter stick. You should start measuring from the back of the cart at the top of the ramp and stop measuring at the front of the cart wherever it came to a complete stop. The measurements should be very accurate as long as you are careful when measuring, although you can never be error free.
 * How many different initial speeds will your group need to examine to find a pattern?
 * We should test about six or seven different initial speeds. You can change the initial speeds by changing the height of the ramp.
 * How many trials should you preform at each initial speed?
 * You only need to preform each trial once unless you make a mistake during the trial.
 * What will each group member be responsible for?
 * Each group member will be responsible for participating in the lab, organizing the data, and recording it all in our physics wiki spaces.
 * How will you organize your data?
 * Our data will be organized in graphs and our lab (including these graphs) will be on our wiki spaces.

3.) After discussing these questions in your group, develop a plan for what your group will do. Your teacher may ask you to wither draw a flowchart or an outline showing the steps you will take.

4.) Set up your equipment and preform your experiment. a.) Record numerical data and observations in your Active Physics log.

5.) Use data yout collected to complete the following: a.) Draw a graph showing how the braking distance depends on the initial speed. Place the initial speed on the horizontal axis and the braking distance on the vertical axis. b.) How does the braking distance change with initial speed? A car with a faster initial speed will have a longer braking distance than a car with a slower initial speed because it will take longer for the car to slow down if it is traveling faster. c.) How does your graph compare to the graph you sketched in Step 1.a)? In our prediction we drew the correct curve in the line, but we thought that the car was going to travel slower than it did. d.) Compare your graph with those of other groups. What are some similarities and some differences? When we compared our graphs to graphs from the other groups we saw some similar slopes and curves. The initial speeds and breaking distances varied, but that is because we all tried different angles on the ramp. But the overall look of the graph was similar. e.) Does looking at the other groups' graphs make you feel more confident or less confident about your data? Explain your answer. After comparing my graphs to the graphs that the other groups made I feel confident because our graphs had similar curves. The slope of the line was was close to ours.

__**Graph:**__
 * **Distances**
 * run 4: 345 cm.
 * run 5: 170 cm.
 * run 6: 281 cm.
 * run 7: 140 cm.

__**Graph with slope found at 1.2 meters**__



6.) Select two values of initial speed from your graph, with one value approximately twice the value of the other. Note the braking distance which corresponds to each initial speed. Run 3 had an initial speed of 0.2m and a braking distance of 170 cm. Run 5 had an initial speed of 0.5m and a braking distance of 281 cm. a.) What is the effect of doubling the initial speed on the distance traveled during braking? When the initial speed was almost doubled the distance greatly increased because the faster the car goes the longer it takes for the car to slow down.

7.) select two values of initial speed from your graph, with one value approximately three times as fast as the other. Note the braking distance which corresponds to each initial speed. Run 2 has an initial speed of 0.4m and a braking distance of 345 cm. Run 6 has an initial speed of 0.1m and a braking distance of 140 cm. a.) What is the effect of tripling the initial speed on the distance traveled during braking? When the initial speed is tripled the distance traveled is almost tripled too. b.) Predict how going four times faster will affect the braking distance. If the initial speed is about four times faster than the braking distance will also be about four times the amount of the braking distance.

8.) Use the data on the sports car provided at the end of this chapter on page 116-117 to answer the following: a.) Where is the braking data located? b.) The braking distance is shown for two speeds. The ratio of the two speeds is 80 mi/hr : 60 mi/hr. This ratio is 80/60 = 1.33. This is an increase of 133 percent. Do you expect the ratio of the braking distances to also be in the ratio of 80/60 = 1.33? What is the ratio of the braking distances? How does it compare with the ratio of the two speeds? c.) How does this data correspond to what you found in your experiment?



__**Physics Talk/Notes**__

 * 10/27/11**

__**Checking Up Questions**__
1.) If a vehicle is traveling at constant velocity and then comes to a sudden stop, has it undergone negative acceleration or positive acceleration? Explain your answer. The vehicle has undergone a negative acceleration because it is still a positive speed, but since the velocity has stopped it gives the car a negative acceleration.

2.) Explain how you know that increasing the velocity of an automobile increases the braking distance. If you increase the velocity you are also increasing the braking distance because it will take longer for a car to stop if it is traveling at a faster speed.

3.) Why is the term negative acceleration used instead of deceleration? In this case negative acceleration and positive acceleration are explaining the direction that the car is moving not the speed.

__**Physics To Go**__




__**Total Stopping Distance**__

 * reaction distance+braking distance**

__**Section 6**__

 * Using Models: Intersections with a Yellow Light**

__**Learning Outcomes**__

 * Investigate: the factors that affect the STOP and GO Zones at intersections with traffic lights.
 * Investigate: the factors that result in an Overlap Zone or a Dilemma Zone at intersections with traffic lights.
 * Use: a computer simulation to mathematically model the situations that can occur at an intersection with traffic lights.

__**What Do You See?**__

 * The red car is stopping short because the front tires are smoking and the back of the car is in the air.
 * The green car is speeding up to go through the red light.
 * The light is just turning red.
 * The dog is being flung out of the red car because the car is stopping short.

__**What Do You Think?**__
Some traffic lights stay yellow for three seconds. Others stay yellow for six seconds.
 * If all traffic lights stayed yellow the same amount of time, how would this affect drivers' decisions at intersections?
 * All yellow lights are timed differently because roads are all different speed limits.
 * different speed limits will cause different stopping distances.
 * Going faster you will need a longer light because you will not be able to stop in time and end up running the red light.
 * How could an intersection with a traffic light be dangerous?
 * If the person behind you thinks you are accelerating through the light and you decide to brake then you will rear-end the in front of you.
 * there could be a malfunction (if everyone decides to go and everyone goes there is an accident)
 * 4 way stop the first person goes

__**Investigate**__
3. a. Yes b. Yes, automobile B is in the GO Zone because it is close enough to the light where it can make it through the light before it turns red. c. Yes d. No, automobile C is not in the GO Zone if they try to drive through the light will be red when they go through.

4. a. Yes, automobile E is in the STOP Zone because they would never make it through the light in time. b. No, automobile F is in the GO Zone so if he decides to stop there is a chance that car D could rear-end him if car D thinks that car F is going through the light. c.

5. In order to study the yellow-light problem, transportation engineers use a computer simulation to model how various factors affect the GO Zone and the STOP Zone. In the yellow-light model shown at the right, there are five input variables that can affect the two output variables. a. Five Variables that affect if a car is in the GO Zone or the STOP Zone b. (ty) || -the GO Zone will become larger || 7b. || (ty) || -the GO Zone will shrink || 7b. || time || increase (tr) || -the GO Zone will be larger || 7b. || time || decrease (tr) || -the GO Zone will shrink || 7b. || (v) || -More of a chance at making it through the GO Zone || 7b. || (v) || -Less of a chance of being in the GO Zone || 7b. || acceleration || increase (a) || -Will not make it to the GO Zone || 7b. || (a) || -Will have a better chance of making it to the GO Zone || 7b. || (w) || -More lanes so the GO Zone will have more cars in it || 7b. || (w) || -Less lanes so the GO Zone will have less cars in it || 7b. ||
 * 1) yellow-light time (ty)
 * 2) driver response time (tr)
 * 3) speed of vehicle (v)
 * 4) negative acceleration (a)
 * 5) width of intersection (w)
 * Variable || Change ||  || Predicted effect of change onGOZone || Actual affect of change onGOZone ||
 * ty || yellow-light time || increase
 * ty || yellow-light response || decrease
 * tr || response
 * tr || response
 * v || speed limit || increase
 * v || speed limit || decrease
 * a || negative
 * a || negative acceleration || decrease
 * w || width of intersection || increase
 * w || width of intersection || decrease

6. a. What is the distance of the GO Zone if the yellow-light time is 3s? 53 meters b. What happens to the GO Zone when the yellow-light time is increased to 3.5s? 63 meters c. Would increasing the yellow-light time allow you to get though the intersection from a further distance away? Explain your answer in your log. Yes because if you are further away from the light you will need more time to reach the light so if the light is yellow longer is will give you a better chance at making the light. d. Record the effect of changing the yellow-light time in your log. Changing the time of the yellow-light will change the GO and STOP Zone. Either increasing it or decreasing it based on if they make the light yellow for more time or less.

7. a.Yes, because if you change one of the variables it automatically changes the output. b. If you increase the yellow-light time then the GO Zone increases. If you increase human response then the STOP Zone increases. If the speed of the vehicle increases then both the STOP and Go Zone increase. If you increase the negative acceleration then the STOP Zone decreases. If you increase the width of the intersection the GO Zone decreases and the STOP remains the same. c. The GO Zone and STOP Zone are able to be calculated by entering an equation, so they instantly change. d. If you increase the yellow-light time the GO Zone increases so if you the yellow-light time is decreased then the GO Zone is also decreased. The width of the intersection has a different result though. If the width is decreased then the GO Zone increases rather than also decreasing. e. The reaction time and negative acceleration do not appear in the equation because they have no effect on the GO Zone. This is because the time it takes for a person to react to something will not change the size of the GO and STOP Zone. Neither does the negative acceleration of a car.

8. STOP Zone a. predictions on STOP Zone: The yellow-light time being decreased the STOP Zone is increased in space. If the human response time is decreased the STOP Zone is decreased. If the speed of the vehicle is decreased the STOP Zone increases. If the Negative acceleration is decreased it does not effect the STOP Zone. If the Width of intersection is decreased the STOP Zone increases. b. results on STOP Zone: If the yellow-light time is being decreased the STOP Zone is not affected If the human response time is decreased the STOP Zone is decreased. If the speed of the vehicle is decreased the STOP Zone is decreased. If the negative acceleration is decreased the STOP Zone is increased. If the width of the intersection is decreased the STOP Zone is no affected. c. Explanation: I thought that the yellow-light time would increase the STOP Zone when it really does not effect it. I thought that the speed of the vehicle would increase the STOP Zone, but it really decreases it. I said that the negative acceleration does not effect the STOP Zone when it increases it. The width of the intersection has no effect on the STOP Zone.

9. a. STOP Zone formula: (Speed of vehicle * Human response time) + (Speed of vehicle^2) / (2*Negative acceleration) STOP=(B5*B4)+(B5^2)/(2*B6) reaction distance+braking distance=stopping distance stopping distance= (vtr)+v^2/2a

b. The yellow-light time and the width of the intersection do not appear in the equation for the STOP Zone because the timing of the light and the width of the intersection do not relate to the size of the STOP Zone. c. Reaction time, velocity, and negative acceleration all appear in the formula to find the STOP Zone. Reaction time is how the person reacts when the light is changing. Velocity of the car as the driver approaches the light. The negative acceleration is if the car will make it in time.

1. Automobile A: stop Automobile B: go Automobile C: go Automobile D: stop
 * Part B: Yellow-Light Dilemma**

2. Automobile E: stop Automobile F: stop Automobile G: go Automobile H: go

3. Automobile J: stop Automobile K: go Automobile L: stop Automobile M: stop

4.Compare the GO Zone and the STOP Zone for intersections I, II, and III. a. How are the intersections different? Intersection I is just a stop and go zone. Intersection II has a stop, go, and an overlap zone. Intersection III has a stop, go, and dilemma zone. b. In intersection II, if the light turned yellow when you were between the GO Zone and the STOP Zone, what would your choices be? Which choices would be safer? Explain your answer. I would go because if i was in the overlap zone you are still apart of the go zone technically even though it contains parts of both zones. c. In intersection III, if the light turned yellow when you were in the space between the STOP Zone and the GO Zone, what woudl your choices be? WHich choices would be safe? Explain your answer. I would stop because I would not feel comfortable speeding up and risk going through a red light. If you try I am sure you could make it through if you speed up, but not if you are driving slowly. d. When both choices are safe, the space between the GO and STOP Zones is called the Overlap Zone. WHen neither choice is clearly safe, it is called the Dilemma Zone. Intersections with a Dilemma Zone are not safe. Which intersection has an Overlap Zone and which has a Dilemma Zone? Intersection II is an overlap zone and Intersection III is a dilemma zone. The overlap zone is safe if you stop or go and the dilemma zone is dangerous if you stop or go.

5. a. What is the relationship between the GO Zone and the STOP Zone at an unsafe intersection? At an unsafe intersection there is an area of 25 meters that are unsafe to be in. In this area it can be dangerous to stop or to go. b. There is an overlap if the speed of the vehicle is at 20m/s because the GO and STOP Zone both change to 64 meters. c. What happens to the GO Zone and the STOP Zone when the speed is increased to 30m/s? Is there still an Overlap Zone or Dilemma Zone. It becomes a Dilemma Zone d. Now lower the speed to 10 m/s. Is the intersection safer now? Explain your answer? The intersection is safest at 20m/s. At 30 m/s it is the most dangerous because the dilemma zone is 25 meters. At 10 m/s the dilemma zone is dangerous, but not as dangerous as 30 m/s because the dilemma zone is only 5 meters.

6.Continue your investigation by resetting the speed to its original value of 20m/s. Adjust the yellow-light time and determine its effect on the Dilemma and Overlap Zones. a. At 3.7 seconds there is a 0 meter overlap zone. At 1.5 seconds there is a 44 meters overlap zone. At 6.8 seconds there is a 62 meters overlap zone

7. What effect do reaction time, negative acceleration, and width of the intersection have on the safety of the intersection? Does changing any of these variables create a Dilemma Zone? Conduct investigations with your spreadsheet. a. Reaction Time: 1.2 seconds= 25 meters 0.5 seconds=4 meters 2.4 seconds=64 meters

Negative Acceleration: 5m/s/s= 25 meters 2m/s/s= 160 meters 6m/s/s= 10 meters

Width of the Intersection : 10 meters=25 meters 5 meters=20 meters 15 meters=30 meters

8. More than one variable change can eliminate a Dilemma Zone and replace it with an Overlap Zone. a. Of the five variables, explain the ease of difficulty in changing each one to make the intersection safer. yellow-light time: increasing the number of seconds increases the number of meters in the overlap zone human response time: decreasing the amount of time decreases the number of meters that are unsafe speed of vehicle: decreasing the speed increases the number of safe meters negative acceleration rate: increasing the negative acceleration rate decreases the number of meters in the unsafe zone width of intersection: decreasing the number of meters decreases the number of unsafe meters

9. The yellow-light problem is based on a simple model and only provides approximate calculations. It does not include other factors such as whether the road is flat or the length of the automobile. a. How does the length of the automobile affect the model? Which outputs are affected by the length of the automobile? The length is a factor because it will take more time for the car to travel through the intersection and the car will take up more room in the stop and go zone. Both GO and STOP Zones are affected by the length of the car.

**__Physics Talk__**
Using Models: model was excel What are models Mathematical Models:
 * something you can use
 * mathematical formulas or equations that are used to help us understand something that is in the real world
 * __**But**__ they do not need to relate to real objects (the excel file had nothing to do with an intersection)
 * it helps us to understand (computer on its own has nothing to do with it, but can be used to understand

Yellow-light Model: different variables to determine whether to stop or go through a yellow light
 * 1) determine the stop zone and the go zone
 * 2) determine safety (through dilemma zone or overlap zone)

__**Go Zone**__
 * includes all positions where you can safely go through a yellow light at an intersection
 * 3 variables impact the GO Zone
 * velocity of the car (v) :if v increases, the GO Zone increases
 * yellow-light time (ty) :if ty increases, the GO Zone increases
 * width of the intersection (w) :if w increases, the GO Zone decreases
 * Equation of find the Go Zone is
 * GO Zone = vty - w

__**Stop Zone**__
 * stop zone = vtr + v^2/2a
 * vtr=reaction distance
 * v^2/2a= braking distance
 * together it makes the total stopping distance
 * all the positions where you can safely stop at a yellow light
 * 3 variables that impact the stop zone
 * velocity :if v increases, then stop zone increases
 * reaction time : if tr decreases, then stop zone decreases
 * negative acceleration : if a increases, then stop zone decreases

__**Dilemma vs. Overlap zones**__
 * Zones help determine the safety of the intersection
 * Dilemma Zone: the intersection **is not** safe (creates an area where stopping and driving is not safe)
 * speeding creates unsafe situations
 * Overlap Zone: the intersection **is** safe (this creates an area where stopping or driving are both safe)

__**Limitations of the Yellow-light Model**__ input/output table based on model Input output
 * values for speed of the vehicle
 * width of the intersection
 * the yellow-light time
 * the braking acceleration
 * the reaction times
 * values for the GO Zone and the STOP Zone

The STOP and GO Zone model allows you to analyze the intersection. This model is used by traffic engineers to determine if an intersection is safe or dangerous and if it could be made safer.

LIMITATIONS
 * the stop and go zone models do not take into account the length of the vehicle
 * color has no impact on a stop and go zone
 * do not consider slowing down for safety vehicles

__**Checking Up Questions**__
1. In this section, the spreadsheet is referred to as a model. What makes it a model? A model is a mathematical formula or equation that is used to help you understand something about the real world. They do not need to relate to what they are modeling. 2. In your own words, describe what is meant by the GO Zone. The go zone is the area where it is safe for you to drive through the intersection when the light is yellow. 3. In your own words, describe what is meant by the STOP Zone. The stop zone is the area where it is not safe for you to drive through the intersection when the light is yellow. 4. Describe what is meant by the Overlap Zone. The overlap zone is the area where the go and stop zone overlap so it is safe to go or stop. 5. Describe what is meant by the Dilemma Zone. The dilemma zone is neither the stop or go zone. It is not safe to stop or go when you are in this area.

__**Physics Plus**__
Speed and the Yellow-Light Model As a driver, you have control over the speed of your automobile. How does that speed affect the GO and STOP Zones for a yellow light? 1. Predict how increases or decreases in speed will affect the GO Zone and STOP Zone. If you increase the speed of your car the go zone will increase (the stop zone would decrease). If you decrease the speed of your car then the go zone will decrease (the stop zone would increase). 2. Using a spreadsheet program or a graphing calculator, graph the relationship of the GO Zone vs. different speeds. 3. Graph the relationship of the STOP Zone vs. different speeds. 4. Using a graphing calculator or a spreadsheet program, graph the STOP Zone and the GO Zone vs. speed on the same set of axes. Try different values for the other variables from your earlier work. 5. Indicate the Overlap or Dilemma Zones on your graph. The overlap Zone is on the first chart and the Dilemma Zone is shown on the second chart. 6. In the investigate, you analyzed how decreasing the speed of the automobile can eliminate the Dilemma Zone. Your graph may indicate that there is a new Dilemma Zone at very low speeds. Explain how this can be. There can be a Dilemma Zone at very low speeds because if you are driving too slow that is also unsafe. The cars around you might not know if you are slowing down or if you are going to drive through the light because you are not letting them know based on how you are driving. 7. In the scenario for this chapter, the teenager jokes that a yellow light means "step on it." Would accelerating help you get through a yellow light? Calculate how much it may help. If you are in the GO Zone or the Overlap Zone then "stepping on it", would actually help you get through the light unharmed. But this would be very dangerous if you are in the STOP Zone or the Dilemma Zone.

**__What Do You Think Now?__**
If all traffic lights stayed yellow the same amount of time, how would this affect drivers' decisions at intersections? If traffic lights stayed yellow the same amount of time at all intersections then people would try to race through the intersection thinking they had enough time. Also all roads are different speed limits.

How could an intersection with a traffic light be dangerous? An intersection with a traffic light can be dangerous if you are in the dilemma zone. The dilemma zone is the area where it is dangerous for you to stop and dangerous for you to go.

__**Essential Questions**__
What does it mean? What factors determine the size of the GO Zone, the STOP Zone, and whether an intersection has a Dilemma Zone?
 * The yellow-light time, driver response, speed of vehicle, negative acceleration, and width of intersection.

How do you know? What measurements can you make to test your understanding of the GO, STOP, Overlap, and Dilemma Zones? In this section, you used equations and calculations on a computer model (spreadsheet) to determine these zones. How could you verify the conclusions from your spreadsheet to determine the zones? GO Zone=(speed*yellow light) - width STOP Zone=(speed*response time)+(speed^2)/(2*negative acceleration rate) The overlap and dilemma zone is found by subtracting the go and stop zone.
 * To make a model spreadsheet you need the GO Zone formula and the STOP Zone formula

Why do you believe? Physics uses mathematical models to describe physical situations. How do the GO Zone and STOP Zone models help you to improve your understanding of traffic at a yellow-light intersection?
 * These models allow you to test what will happen at different speeds, different time intervals, and different distances.

Why should you care? How can understanding the physics behind the GO, STOP, Overlap, and Dilemma Zones make you a better, more aware, and more informed driver?
 * Understanding the physics behind the go, stop, overlap, and dilemma zone can help improve my driving and make me more aware because now when I come to an intersection with a yellow light I will know whether to stop or go through. I can judge what zone I am in and my decision based on where I am.

__**Physics To Go**__
1. a. GO Zone GZ=(velocity*yellow light time) - width of intersection GZ=(15m/s)(4s) -15m GZ=60-15 GZ= 45 meters b. STOP Zone SZ=(velocity*reaction time) + velocity^2/(2*negative acceleration) SZ=(15m/s)(1s) + (15m/s^2)/(2*5) SZ=(15)+(225)/(10) SZ=(15)+(22.5) SZ=37.5 meters c. overlap because go zone is from edge of intersection so is the stop zone so if the stop zone is less than the go zone it will overlap. dilemma the stop zone must be higher.

2. a. GO Zone GZ=(velocity*yellow light time) - width of intersection GZ=(30m/s)(4s) -15m GZ=120-15 GZ= 105 meters STOP Zone SZ=(velocity*reaction time) + velocity^2/(2*negative acceleration) SZ=(30m/s)(1s) + (30m/s^2)/(2*5) SZ=(30)+(900)/(10) SZ=(30)+(90) SZ= 120 meters b. GO Zone GZ=(velocity*yellow light time) - width of intersection GZ=(10m/s)(4s) -15m GZ=40-15 GZ= 25 meters STOP Zone SZ=(velocity*reaction time) + velocity^2/(2*negative acceleration) SZ=(10m/s)(1s) + (10m/s^2)/(2*5) SZ=(10)+(100)/(10) SZ=(10)+(10) SZ= 20 meters The GO Zone is larger than the STOP Zone. 3. The increase in their response time will not effect the GO Zone because it is not in the equation to find the GO Zone. It would increase the STOP Zone though because it is in the equation.

4. Worn tires and bad brakes will cause the driver to decide further back what they are going to do. They need more time to brake if they are not going to go through the intersection because their brakes do not work. Increasing stop zone, which will cause a dilemma zone.

5. The delayed green is so that cars driving through a yellow light that just changed do not get hit by cars driving through do not hit them.

6. Having a countdown on a stop light is very dangerous because people will try to race through the light thinking they have enough time and speeding when there is not enough time to make it through. The stop zone will increase because the car will race to get through and step on the brakes when they realize they can not make it through.

7.
 * do not put -7 put positive 7

Unsafe because there is about 4 meters of a dilemma zone. GO=48 meters STOP= 52.6 unsafe dilemma

go=72 meters stop- 52.6 meters overlap safe Unsafe because there is about 8 meters of a dilemma zone. go 48 stop 48.6 not safe Safe about 7 meters of an overlap zone. go 48 stop 64.6 not safe Safe about 2 meters of an overlap zone 40.5 34.1 safe

8. No painting go and stop boundary lines at all intersection would not work because they are different all the time. It depends on... NO
 * speed of vehicle
 * time of the yellow light
 * response time
 * negative acceleration rate
 * width of intersection

__**Section 7**__
__**Centripetal Force: Driving on Curves**__

__Learning Outcomes__

 * **Recognize**: the need for a centripetal force when rounding a curve
 * **Predict**: the effect of an inadequate centripetal force
 * **Relate**: speed to centripetal force

__What Do You See?__

 * the car is speeding around the turn
 * the car is out of control
 * if he continues like this he will get in an accident with the car in front of him or drive off of the mountain
 * car is on two wheels

__**What Do You Think?**__
You are driving along a road at the posted speed limit of 50 mph (80 km/h). A road sign warns that you are approaching a curve and tells you to slow down to 25 mi/hr (40 km/h). A gradual curve you can drive faster, but if it is a very sharp curve you must go much slower Determined by the turn if you are going to the left your side of the car lifts up a little if you are going too fast
 * Why is the sign indicating to slow down?
 * How is the amount you should slow down determined?

**__Investigate__**
1. a. Imagine that you have a toy car at the end of a string, and it is moving in a circle. If you let go of the string. which way would the car travel? The diagram on the following page show several possibilities. In which direction do you think the car will travel? Write your choice and how you made your decision in your log. B. I think that if you let go of the string that keeps the car traveling in a circle it will look like letter B because it is traveling in a circular motion and once you let go it form a straight line.

2. a. The string makes the car travel in a circle. In which direction does the string pull on the car? This pull is referred to as a force in physics. Understanding the forces is a topic that you will return to many times in this course and every future physics course. The string pulls the car in a circle because of the centripetal force of the string. b. Now release the string. Which way does the car travel when it is released? When the piece of string is released then the car will travel in a straight line.

3. a. Draw a diagram of an automobile traveling north and making a right turn. On your diagram, draw the direction of the frictional force that keeps the car moving in a circular curve.

4. a. The distance from the washer to the center of the turntable. 17 cm.

5. Spin the turntable. As it spins, the washer is held on the spinning surface by friction. (In other words, the washer is prevented from sliding off the turntable by friction. If friction suddenly disappeared while the washer was rotating, it would be similar to letting go of the string of the motorized toy car.) This friction between the washer and the surface of the turntable is not identical to the friction that holds an automobile on the road, but it is similar to the friction between the surface of the road and an automobile’s tires.

6. a. Use a stopwatch to measure and record the time it takes for 10 revolutions. 25 seconds b. Use the data in a to determine the speed of the turntable in revolutions per minute (rpm). Outline your calculations i detail in your wiki. 24 revolutions per minute

c. Use the information in b to determine how much time goes by during one revolution. Calculate it - don't measure it directly! Show your calculations in your wiki. d. In step 6c you measured the time of 10 revolutions and then calculated the time of one revolution. In terms of your understanding of scientific error (recall section 2) explain why measuring 10 revolutions is a better technique. *Easier to calculate because since you multiply by 10 all you need to do is move a decimal point.

e. How fast is the turntable moving in revolutions per second (rps). Convert the information in b from __**rpm to rps**__. Show your work in your wiki.

__**Calculate the Maximum Safe Speed of the Washer**__ 7. Speed = distance/time.

To calculate the speed of the block in m/s, divide the circumference of the circle (the distance the washer travels) by the time it takes to make one revolution. Circumference = 2** πr ** What is the speed of the washer when it stayed on the turntable? Show your calculations in your wiki.

__ **Effect of Friction on Velocity** __ 8. Now repeat steps 4-7, but this time, place the washer on the sandpaper surface. a. Predict the effect the sandpaper will have on the results overall? (Place the washer near the edge of the disk on the sandpaper and then gradually increase the rotational speed of the turntable until the washer just begins to slide. Placing the washer on the sandpaper causes the washer to stay in place because the sandpaper creates friction.

b. Use a stopwatch to determine the time of a single revolution using the same technique you used previously. Show calculations in wiki.

c. What is the speed of the washer when it stayed on the turntable? Show your calculations in your wiki.

__**Effect of Radius on Velocity**__ 9. In addition to the speed and the road surface, you will also explore the effect of the curvature of the road. "Curvature" refers to how tight the turn happens to be. The simplest curve is an arc of a circle. A large circle (large radius) has a gentle curve, while a small circle (small radius) has a tight curve. In this step, you will explore the effect of the curve on the safe speed of the washer. (Remember, the washer represents a car on a road surface). a. Predict the effect the radius of the circular path has on the maximum safe speed of the car. b. Create a table in your wiki notebook that is similar to the one below: c. Select three different radii (near the edge, middle and nearer the center) and determine the maximum safe speed for each radius. Complete three trials by measuring the time of one revolution (using the 10 revolution technique used earlier). Use the average time to calculate the speed for each radius. Summarize your data and calculations in the table. You do not have to show your calculations this time. (cm) || Time of 1 rev. (s) || Time of 1 rev. (s) || Time of 1 rev. (s) || Average Time of 1 rev. (s) || Circumference (cm) || Maximum Safe Speed (m/s) ||
 * The longer the radius the larger of a circular path the car can go around the center of the circle. The smaller the radius, the smaller the circular path will be.
 * Radius
 * 6 || 2.67 || 2.36 || 2.56 || 2.53 || 37.70 cm || 1.49 ||
 * 12 || 2.08 || 1.96 || 1.82 || 1.95 || 75.40 cm || 3.86 ||
 * 18 || 2.3 || 2.34 || 2.17 || 2.27 || 113.10 cm || 4.98 ||

d. As the radius decreases (becomes tighter) what happens to the maximum safe speed? As the radius decreases and becomes smaller the maximum safe speed also decreases. For example if the radius is 18 cm the maximum safe speed is 4.98m/s and if the radius is 6 cm the maximum safe speed is 1.49m/s.

__**Effect of Mass on Maximum Safe Speed**__ Does the mass of a vehicle affect how fast it can move through a curve in a road? This may be a complex question, since there are many variables that may contribute to the mass of a vehicle including how tall the vehicle or how the mass is distributed. 10. a. Consider two identical pickup trucks. Identical in every way - same model and same type of tires, but one truck is empty, while the other is loaded with bricks. Predict if the extra mass of the heavier truck affects how fast it can move through a curve in a road (compared to the lighter truck)? -If a truck that is weighted down with bricks drives through a curve it can go at the same speed, but has a higher chance of driving off road. A truck that is not carrying any bricks can go at a higher speed without having to slow down as much as the heavier truck.

b. Place a thicker washer mid way between the edge and center of the turntable. Select the same position you used in one of the trials in step 9. Determine the velocity of heavier disk and compare it to the velocity of the lighter disk you found step 9. Show your calculations in your wiki. c. Does the mass of a vehicle affect how fast it can move through a curve in a road? Explain how you know. Yes the heavier the vehicle, the slower it must be when it goes through the curve because if it goes through the curve to quickly it will go off the road. The more weight there is the longer it will take to slow down. You should slow down before the curve, then go slowly through it.

__**Physics Talk**__
-the force of the string keeps the car moving in a circle, if you let go of the string then the car will move in a straight line
 * Circular Motion:Centripetal Force**
 * force:** a push or a pull
 * centripetal acceleration:** a change in the direction of the velocity with respect to time
 * acceleration associated with a car changing direction

Newtons first law of motion: an object in motion will stay in motion at a constant speed and travel in a straight line unless a force act on it. -any time an object is moving along a curved path, there must be a force acting on it -the force of friction is always near the center of the circle -the force of friction between the road and tires keeps the car moving in a circle when it makes a turn -an icy road takes away the friction not allowing the car to turn so it continues straight, the force of friction is toward the center of this curve -the centripetal force can be
 * centripetal force:** a force directed toward the center to keep an object in a circular path
 * the tension in the string
 * friction between the block of wood and surface of the turntable
 * friction between a car and the road
 * gravity is the centripetal force for the earth moving around the sun

The toy car -the speed remains the same -velocity does not change -changing direction
 * changes in **velocity** with respect to **time** is __**acceleration**__


 * Acceleration is the change in velocity with respect to time
 * Velocity can change when an object speeds up, slows down, or changes direction



__**Checking Up Questions**__
1. What is the direction of the force that keeps an object moving in a circle? The force is directed towards the center.

2. What is the name of the force that keeps an object moving in a circle? Centripetal force: a force directed toward the center to keep an object in a circular path.

3. Name the force that keeps an automobile moving in a circular path on a road? Centripetal Force

4. Explain how the velocity of an object can change even if the speed is not changing. Velocity can change if the the object speeds up, slows down, or if the **direction changes**. -if the direction is changing then the velocity is also changing the speed does not have to

5. Describe three situations in which acceleration can take place. acceleration is the change in velocity with respect to time -car speeds up -slow down direction change

6. What is the force that keeps Earth moving in a circle around the Sun? The centripetal force is gravity.

__**Physics Plus Questions a-c**__
Calculating Centripetal Acceleration and Centripetal Force

centripetal force centripetal acceleration F= force v= velocity m= mass r= radius of the curve

a. What is the frictional force of an automobile that is driving the speed limit? F= mv^2/r F= (1000)(14^2)/40 F=(1000)(196)/40 F= 196000/40 F= 4900 N

b. How much additional frictional force does the automobile need if the driver decides to exceed the speed limit and travel at 20m/s. F= mv^2/r F= (1000)(20^2)/40 F= (1000)(400)/40 F= 400000/40 F= 10000 N

c. If the frictional force were reduced by half due to wet leaves and water on the road, what speed would you recommend for drivers? F=mv^2/r 4900=(1000)v^2/40 (40)(4900)=(1000)v^2 196000=1000v^2 196000/1000=196 196=v^2 v=14 v= 14 m/s

__**Physics To Go**__
(1-5, 7-9, 11, 12)

1. F= mv^2/r 24=(1000)(v^2)/6400 (6400)(24)=(1000)(v^2) 153600=(1000)(v^2) 153.6= v^2 v= 12.4

2. r= 1.5x10^8 r=1500000000 24=(1000)(v^2)/6400 (6400)(24)=(1)(v^2) 153600=(1)(v^2) 153600= v^2 v= 391.9 km/h
 * speed in km/h**

24=(1000)(v^2)/6400 (6400)(24)=(1000)(v^2) 153600=(1000)(v^2) 153.6= v^2 v= 12.4 m/s
 * speed in m/s**

3. 60 revolutions per second r= 15 cm Fc=mv^2/r Fc=(60^2)/150 Fc=3600/150 Fc=24 m/s

4. Friction can hold an automobile on the road when it is traveling at 20 m/s and the radius of the turn is 15 m. What happens if: a.) the curve is tighter? When the curve is tighter it increases the chance of the car tipping over and the friction is what keeps the tires on the ground. b.) the road surface becomes slippery? When the road becomes slippery then the friction is cut in about half. c.) both the curve is tighter and the road is slippery? If the curve is tighter and the road is slippery the car has to drive at a much lower speed because there is less friction and you need more control of where you are going.

5. Think about other examples in which objects travel in curved paths, such as the clothes in a spin dryer, or the Moon traveling around the Earth. For each example, explain what produces the force that is constantly being applied to the object toward the center of the curve. Centripetal Force is the force that keeps the object moving in a circular path, even if it is clothes spinning in a dryer or if it is the Moon traveling around the Earth.

7. Explain the following statement: "The driver may turn the wheels but it is the road that turns the automobile." The driver is in control of steering the wheel, but the road has traction which the car needs in order to not drive off of the road. The turn is like the circular path that the car is following, but is released to go straight.

8. ac=v^2/r v= 270 m/s r= 1000m ac=72900/1000 ac=72.9 m/s^2

9.
 * In the first explanation I do not think that the person was wearing their seatbelt because they would not have smashed into the car door if they were belted.
 * I think that in the second explanation the person is wearing their seatbelt because the belt keeps them still where they are. The seat belt represents centripetal force.

11. Why are highway curves that have radii that decreases as you go into them especially dangerous? In other words, curves that start out as gentle turns but become tighter and tighter as you get into them. They are more dangerous because the driver is still driving at the same speed but when the curves get tighter they are still driving at the same speed. So they are taking these curves too fast.

12. In the US, vehicles drive on the right-hand side of a two-lane road. If the curve bends to the right and you lose traction in the turn, would you end up in the ditch on your side of the road, or into the lane of oncoming traffic? What if the curve bends to the left?

If the curve bends to the right you will end up in the ditch on your side, but if the curve bends left and you lose traction then you will end up in upcoming traffic.