Sc1- What factors affect the stopping distance of a car?

1.) Speed

My prediction is that the more speed the car is travelling with, the longer the stopping distance will be after applying the brake.

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The velocity of the car is related to the kinetic energy of the car. The equation for finding the kinetic energy is = 1/2 � mass � velocity2. To remove the kinetic energy of the car wheels, i.e. applying the brakes on, the brakes do work, which can be calculated with the equation W=Force � distance (m). In order to stop the car completely, the brakes have to convert all the kinetic energy to heat energy, sound energy and other kinds of energy. According to the Principal of Conservation of Energy, energy can be changed from one form to another, but it cannot be created nor destroyed. In this case,

Kinetic Energy (of car) = Work done (by brakes)

1/2mv2 = Fd

Using this balanced equation, we can find out if my prediction is right. Here we take away any constant terms, which are ‘1/2’, mass and force, which leaves ‘v2’ and ‘d’, making the equation:

v2 = d

v2 ? d

This is exactly what I am predicting -the velocity2 is proportional to the stopping distance.

2.) Braking Force

My prediction is that the more braking force applied on the wheels, the shorter the stopping distance is. What I think is that as the brakes convert the kinetic energy of the car into heat sound and other energies, the greater the braking force is, the more kinetic energy is converted, therefore gradually the car has less and less kinetic energy for travelling, hence it has a shorter stopping distance.

Again, because of the Principal of Conservation of Energy, the kinetic energy of the car should be the same as the work done by the brakes:

1/2mv2 = Fd

Now the constant terms are taken away to find out what is proportion to what. In this case, 1/2′, the mass and the velocity2 are constant, leaving:

1 = Fd

F ? 1/d

This is my prediction -the braking force applied is inversely proportional to the stopping distance.

Method

To set up the standard of measuring the stopping distance, the distance is measured from the point where the brake is applied to the back of the trolley. Three results are taken for each to give an average.

To obtain results to prove my predictions, the following methods are used:

1.) Speed

To find out the relationship between the speed and the stopping distance, we have to apply different speeds on an object to see how the stopping-distance changes. In this experiment this is done by placing a three-wheeled trolley on different staring positions marked on a slope. The higher the starting position is, the faster the speed the trolley gets, when the mass of the trolley is kept constant.

Before we start anything, I have to convert the starting positions to velocity2 so that I can plot the results onto the s.d./v2 graph. This is done by releasing the trolley (with an extra mass of 10N on it since it is used for keeping a constant braking force) from each starting positions and, without applying brake on, use the light-gate to measure its velocity (this is done three times for more accurate results; more can be obtained to replace any results which have a great difference from the others).

Here is the method:

1. Place a crossbar lying horizontally (which should be in line with the side of the slope) at a height, clamped with two stands standing at the end of the slope;

2. We then mark down the point where we start measuring from. This has to be where the brake is triggered just after the back wheels of the trolley has landed on the floor, which ensures that the trolley has gone up to its full speed before the brake is applied, keeping the results accurate;

3. To do this, we slowly push the trolley down until the back wheels land on the floor, then position the stands accurately where it triggers the brake just after the trolley has completely landed on the floor, and then we use a marker pen to mark the point down (where the back wheels touch the ground);

4. Now, one person is in charge of releasing the trolley: this is done by using a finger to hold the front of the trolley just before the position line on the slope. It is important that the person doesn’t push the trolley back and then let it go; he or she must make sure that it is done by just lifting off his or her finger so that the trolley is actually setting off just before the starting position;

5. Another person is in charge of measuring the stopping distance. In this experiment we used several 1m rulers to measure the distance. The stopping distance is then measured from the marked line to the back wheels of the trolley (where it is touching the ground) in a straight line (as the rulers do no good if we measure the distance with one ruler bending to a different angle, making the measurement inaccurate);

6. The result is recorded after each run, and then once the person in charge of the trolley gets the trolley back, he or she then either do another run on the same starting position for more results, or do a new run on another position up;

7. If the three results have a great difference between each other, then we can always take some more results to replace the funny-looking ones.

2.) Braking Force

This experiment has to be done with a constant velocity, which is actually the starting position on the slope. This experiment is similar to the previous one, but the constant terms are different, i.e. in this case, v2. The braking force is increased by moving a mass from the body of the cart onto the rod on the brake, which keeps the mass of the cart unchanged:

Apart from that, the apparatus is the same as the previous one, e.g. the crossbar for pushing the brake trigger, and the slope with the same markings.

Here is the method:

1. First, set up exactly the same apparatus that was used for the previous experiment;

2. Two people would be required for the same job as before;

3. The result is recorded after each run, and then once the person in charge of the trolley gets the trolley back, he or she then either do another run with the same braking force for more results, or do a new run with a greater braking force (+1N);

4. If the three results have a great difference between each other, then we can always take some more results to replace the funny-looking ones.

To avoid the trolley going too far away in the above experiments, I have to do a preliminary experiment to find out the best constant braking force and best constant starting position:

Starting PositionBraking Force

0 N

5 N

10 N

1

Brake doesn’t engage

0.56 m

0.53 m

5

Hits bench

1.76 m

1.28 m

10

Hits bench

Hits bench

2.55 m

Here I have decided to use 10 N as the constant braking force for the speed experiment, since at the top starting position on the slope (10), it is the only force which can stop the trolley before it hits the bench.

As for the braking force experiment, I think starting position number 3 would be the best constant starting position since the trolley, with no braking force, hits the bench when released from position no. 5, and the brake doesn’t work properly when no braking force is applied and released from position no. 1, so position no. 3, which is in between no. 1 and no. 5, should work well as a constant starting position.

Results

Results for converting starting position to velocity2

Starting Position

Stopping Distance (m)

Average Velocity (m/s)

v2

1st Try

2nd Try

3rd Try

1

0.82

0.833

0.802

0.818

0.669

2

0.992

0.991

1.02

1.001

1.002

3

1.11

1.07

1.11

1.097

1.203

4

1.27

1.24

1.27

1.26

1.588

5

1.33

1.32

1.35

1.33

1.769

6

1.50

1.53

1.50

1.51

2.280

7

1.64

1.69

1.70

1.677

2.812

8

1.81

1.77

1.70

1.76

3.098

9

1.85

1.84

1.78

1.823

3.323

10

1.92

1.93

1.89

1.913

3.650

Results for the Change of Stopping Distance affected by the Speed

Starting Position

Stopping Distance (m)

Average Stopping

1st Try

2nd Try

3rd Try

Distance (m)

1

0.48

0.48

0.48

0.48

2

0.65

0.65

0.69

0.66

3

0.84

0.82

0.84

0.83

4

1.10

1.16

1.12

1.13

5

1.37

1.40

1.38

1.38

6

1.61

1.63

1.63

1.62

7

1.89

1.84

1.82

1.85

8

2.14

2.06

2.13

2.11

9

2.32

2.28

2.26

2.29

10

2.59

2.54

2.57

2.57

Results for the Change of Stopping Distance by the Braking Force

Braking Force (N)

Stopping Distance (m)

Average Stopping

1/d

1st Try

2nd Try

3rd Try

Distance (m)

1

2.91

2.90

2.90

2.903

0.344

2

2.36

2.34

2.40

2.367

0.422

3

1.98

1.93

1.88

1.930

0.518

4

1.54

1.65

1.68

1.623

0.616

5

1.35

1.30

1.33

1.327

0.754

6

1.18

1.16

1.19

1.177

0.850

7

1.10

1.14

1.12

1.12

0.893

8

1.03

0.96

1.02

1.003

0.997

9

0.95

0.94

0.94

0.943

1.060

10

0.90

0.89

0.90

0.897

1.115

Analysing Evidence

1.) Speed

The graph is very close to the line of best fit crossing through the origin, showing that v2 is proportional to the stopping distance, which is not surprising as my prediction was that the velocity2 is proportional to the stopping distance.

2.) Braking Force

The graph is surprisingly above the line going through the origin, this may be due to the fact that we did not add the mass of the piece of wood and the metal rod on it into the braking force, therefore when the braking force was actually about 3N, we thought it was only 1N, so the graph was shifted to the left. but still it is very close to the line of best fit, so my prediction -the braking force is inversely proportional to the stopping distance- is probably right.

Evaluation

Quality of Evidence

1.) Speed

The plotting on the graph is very close to the line of best fit. There aren’t any anomalies, maybe it is because of how we took a number of results and chose the best three results. The graph is so close to the line of best fit that it is good enough to prove that my prediction -speed2 is proportional to the stopping distance- is right.

2.) Braking Force

The graph is close to the line of best fit, but it was a bit further from the origin. This may be due to the fact that we did not add the mass of the piece of wood and the metal rod on it into the braking force, therefore when the braking force was actually about 3N, we thought it was only 1N, so the graph was shifted to the left. But still, as the graph is so close to the line of best fit, it is good enough to prove that my prediction -the braking force is inversely proportional to the stopping distance- is probably right.

Suitability of Procedure

During the experiment we experienced many problems and inaccuracies-

* The trolley did not go in a straight line for most of the time, because they were not level; this cannot be improved unless we can get a better trolley.

* We used 3 1m rulers to measure the stopping distance from the marked line to the back wheel of the trolley in a straight line. The reason for us measuring the stopping distance in a straight line was because that we didn’t have the trolley’s trail. To solve this problem we can paint the wheels of the trolley with some paint, and the when the trolley runs it leaves a trail on the ground, then we can use a piece of string to measure the exact stopping distance of the trolley, which is far more accurate than what we have done.

* The trolley was released by a person with a finger. This makes the results inaccurate as we don’t know if the trolley did set off just before the starting positions, or the person might have pushed the trolley back when he or she was releasing it. These are normally affected by human factors, e.g. tiredness, mood, etc. This problem can be solved by using an electric magnet to hold the steel trolley instead of using a finger. To release the trolley just simply cut off the power supply to the magnet and then the trolley will set off without being affected by human factors.

* The stands which hold the crossbar for triggering the brake were not stable and often moved away from where they were supposed to be. This can be improved by holding the stands together with the ramp once they are positioned from a right distance from the end of the slope, so that the stands are always in the right place to trigger the brake.

* The brake kept becoming loose off the main body of the trolley. This can be improved by sellotaping the brake firmly onto the trolley, but make sure that this is one before we weigh the trolley as it will increase the mass of the trolley.

Sufficiency of Results

I have 10 results for each experiment, which is enough to make my graph clear, so having 10 results is plenty, but, of course, more would be good as they make the graph more reliable.

Further Work

Additional relevant evidence can be found with some further work. This is to be done with a totally different experiment, but should be much more better.

For the speed, we can use a car being driven on a road built with the same material (tarmac) staying flat all the way through so that the road surface would be the same all the way down. The braking force would always be the same if we press the brake footpad all the way down, so it is constant. The speed can be read inside the car, so when it reaches to the right speed, the driver can then brake the car, and the stopping distance can be measured from the tyre skid mark (therefore the car has to be fairly fast). This will be quite dangerous and requires a large amount of space (only if we can use the whole of M1…).

As for the braking force, I honestly don’t have any ideas apart from using a trolley, as it is very complicated (or impossible) to control the braking force of a vehicle, unless they can be digitally controlled, then we can do this experiment on a flat road by increasing the braking force with a constant speed all the way through the experiment.

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