Investigation into factors affecting the speed of a car rolling down a ramp

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The following investigation that I am going to embark on will involve the transfer of energy from one form to another. Usually when there is a transfer of energy from one component to another, these constituents are parts of machines or mechanisms, which are collectively classed as systems. In any one system there could be just one energy transfer or numerous transfers of energy. However, when we are dealing with systems, we must remember that there is no system that is absolutely perfect, in other words there is no system that can transfer energy 100% efficiently.

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There are several different types of energy. One would be elastic energy, which is a form of stored energy, e.g. found in a taut rubber band or spring. Another type would be chemical energy, which we as humans are in contact with everyday - it is the energy we get from in food, the energy used by our muscles and energy in batteries etc. Some systems involving energy transfers are:

* Torches: they use batteries to power them.

This power source provides electrical energy from the chemical energy in the batteries. The electrical energy then goes round the circuit powering the bulb and supplying light energy. In addition the bulb also emits heat energy. The torch's main function is to provide light, however, the heat energy also given of is in effect the "leak" in the system that makes it less than 100% efficient. In actual fact the desired light energy that is obtained is only about 5% of the initial chemical energy and the rest is wasted heat energy.

So a torch if a very inefficient system. Below is a diagram that shows the transfer of energy in a torch: -

In order to carry out this investigation, I first have to define the terms of the objectives so that an understanding is present and a clear process to acquire the answer can be devised.

Factors affecting speed

Speed is a measure of the rate at which something is moving, so:

Speed = distance travelled ? time taken

Sir Isaac Newton stated in Newton's First Law of Motion that:

If the forces on a mass are balanced (no resultant force), then

* if it is at rest, it stays at rest

* if it is moving, it keeps on moving at a constant speed in straight line

In the case of this coursework, I am going to be investigating the factors that affect the speed of a toy car rolling down a ramp. So I will need to outline which dynamics are going to influence the speed in this situation. Below are some important keywords that will be of significance on this investigation:

Two forms of energy relating directly to the car rolling down the ramp are potential and kinetic energy. Gravitational potential energy (GPE) will be present because the car will be starting above the ground. On Earth the force of gravity pulls down on all objects so the GPE would be the force that moves the car. However, as it rolls down the ramp the GPE will decrease because its height off the ground is decreasing. At the same time, kinetic energy (KE) will be increasing as the car goes down the ramp. At the top when the car is stationary, it will have no kinetic energy because it will not be moving. However, it will gain kinetic energy when it goes down the ramp because it will go from being motionless to moving and increasing in speed. So this system of a toy car rolling down the ramp will

Still on the lines of energy, there is still the problem of energy being lost as the car travels down the ramp. The GPE turns to KE as the car goes down, however, all the energy may not be converted into KE. Some energy may be lost to the atmosphere by heat and sound, although I doubt there will be much lost and so it would not be worthwhile including it in the investigation as a primary consideration. The car will probably accelerate as it goes down the ramp so the length of the ramp will have an effect on the speed of the car, that is, if the car does not reach its top speed by the time it has gone down the ramp. More importantly is the influence of the height of the ramp. GPE = mass x gravity x height so if the height of the ramp is increased then so will the GPE. This in turn will affect the KE.

Another main factor is the friction that will occur when the car rolls down the ramp. If there was no air resistance or friction then all objects would accelerate downwards at the same rate. This can be proved by a famous experiment by Galileo, which he is supposed to have done from the leaning tower of Pisa. He dropped a heavy stone and a light stone simultaneously and they both accelerated at the same rate and landed at the same time. However, the car will have friction acting on it - between the wheels of the car and the ramp. The car will only be able to move if the force pushing it overcomes the friction acting against it. This means that some of the GPE will be lost towards countering the friction and so the KE will be reduced as friction increases. Since friction is acting on the car then the mass of the car will have an effect too. Increasing the mass of the car would increase the GPE, however, the increased mass at the same time would also increase friction since the pressure between the car wheels and the ramp will be greater. Since these two opposite forces are increasing all at once they may even cancel each other out, therefore the effect of the mass on energy lost being neutralised, but still increasing the net speed of the car.

What I am Going To Do

Out of all the factors that I have discussed regarding their effect on the speed of the car rolling down the ramp I will investigate the following:

* Height of Ramp:

The height of the ramp will directly affect the speed and kinetic energy because as the height is increased, so the GPE of the car increases and the force powering the car increases. Raising one end of the ramp to the desired height can easily alter the height of the ramp and the height that the car starts at. This variable can also be easily changed.

* Gravitational Potential Energy:

I have already identified the fact that a stationary object requires a positive force in order to start it moving and increase its velocity as outlined in Newton's First Law of Motion. With help from the results from my experiment I will develop my investigation of the GPE, which is the force behind the car.

* Kinetic Energy:

I have also established that the GPE is converted into kinetic energy, which increases as the car accelerates. I will also develop my investigation of KE through the results I obtain from the experiment.

Following these I have also determined my fixed variables in the investigation. They are:

* Mass of Car and Length of Ramp:

I will keep the mass of the car and the distance that the car travels constant so that I can focus directly on the effect that the height of the ramp has on the speed. The mass of car can affect the force pushing the car and the distance travelled would affect the average speed. If I alter the mass of the car then I will not to be able to distinguish which factor between that and the height of the ramp

are the cause of the change in the force behind the car. Similarly if I change the distance that the car has to travel each time then additional limiting factors may be introduced such as deceleration owing to friction.

Prediction

Based on the facts that I know regarding the factors affecting a car rolling down a ramp, I believe that as the height of the ramp increases, so the speed of the car rolling down it will increase. This prediction has been derived from the theory that the kinetic energy of the car at the bottom of the ramp (when it is at its fastest) will be inversely proportional to the gravitational potential energy of the car (at the top of the ramp to begin with). In other words, as the GPE decreases as the car rolls further down the ramp, so the kinetic energy will be increasing, and resultantly the speed of the car increases. If the car starts at a height of x then the GPE will be:

mass of car x force of gravity x height (x)

The KE will be equal to the GPE because the energy will have been transferred through the system. With this in mind, if the height of the ramp is then increased to 2x then the GPE will be doubled, and so the kinetic energy will double. In addition to this I can make a prediction mathematically using the following formula:

GPE = m x g x h

KE = 1/2 x m x v2

? m x g x h = 1/2 x m v2

g x h = 1/2 x v2

2 x g x h = v2

v = ?2gh

Subsequently I can now say that the speed of the car will be proportional to the square root of the height of the ramp. However, as I discussed in my introduction, no system is perfect, which means that energy can be lost from the system. So the KE is most likely to be very slightly lower than the GPE. It will only be slightly lower because energy can only be lost through heat produced from friction and through sound. The sound energy will be very low and friction may not be too great because the smooth wheels will be rolling down a smooth surface reducing the friction than if there were rubber wheels on a textured surface.

Preliminary Experiment

Aim: To find the optimum conditions required to carry out the main experiment in order to return accurate and reliable results.

Apparatus: Retort stand; 2x boss + clamps; ramp; toy car; ticker timer; ticker tape; ruler; plasticine.

Diagram:

Method: Set up the apparatus as shown so that one end of the ramp is elevated to the desired height (which can be measured with the ruler) using the clamp on the retort stand, and so that the other end is in contact with the table. Also fix the ticker timer to the retort stand too, using another clamp, so that it is positioned parallel to the top of the ramp. Attach a length of ticker tape (that is sufficiently longer than the length of the ramp) to the toy car using the plasticine provided. Then feed the other end of the tape through the ticker timer. Making sure that the car and the tape are aligned with the ticker timer, place the car at the top of the ramp. Then release the car allowing it to roll all the way down to the end of the ramp. Repeat the same test again with the ramp set at different heights.

Results: These are the results returned from the preliminary experiment:

Height (cm)

Result

Car remained stationary

Car rolled down ramp

Car rolled too fast

Ticker tape became detached from car

Analysis: In order to try and get the most accurate and reliable results when I perform the main experiment, I will need to be able to monitor the outcomes of the experiment easily. Therefore, as shown by the preliminary experiment, it is recommended that I keep the height of the ramp to values between 0cm and 40cm exclusive. The ramp should not be kept at 0cm because at this height the car does not roll at all so it would be a pointless test since the aim is to find factors affecting speed. From 5cm to 30cm high, the car rolls down at a satisfactory speed for adequate results to be obtained. However, after these heights, at 40cm, the car rolls too fast with the ticker tape even becoming separated from the car at 60cm.

Hence in the main experiment the heights at which the car should be when released will be:

5cm; 10cm; 15cm; 20cm; 25cm; 30cm; 35cm.

In order to keep a fair test I have to make sure that the car is always released from the same point on the ramp so that it travels the same distance to the end of the ramp each time. Also to keep it fair, I must make sure that the ticker tape is always equidistant from the sides of the ticker timer as the car rolls down the ramp. If it is not, or the tape touches the sides of the timer, then there will be involuntary friction introduced into the system and will invalidate the reliability of the experiment. To keep this from happening I have to position the car at the top so that the tape is free from friction, then take care that the car rolls down in a straight line parallel to the sides of the ramp. In addition to these adjustments, the most basic way of getting accurate results is to repeat the test a few times; this way I can dampen anomalous results too.

Main Experiment

Aim: To investigate the effect of height on the speed of a car rolling down a ramp.

Apparatus: Retort stand; 2x boss + clamps; ramp; toy car; ticker timer; ticker tape; metre ruler; plasticine, electrical leads, electronic balance, power pack.

Diagram:

Method: Set up the apparatus as shown so that one end of the ramp is elevated to the desired height (which can be measured with the metre ruler) using the clamp on the retort stand, and so that the other end is in contact with the table. Fix the ticker timer to the retort stand too using another clamp then connect it to the power pack using the leads, so that the top of the timer is positioned level with the top of the ramp. Mark out where the start point of the car is going to be then measure the distance from the point to the bottom of the ramp in centimetres. Attach a length of ticker tape (that is sufficiently longer than the length of the ramp) to the toy car using the plasticine provided. Measure the combined mass of the car and the plasticine using the electronic balance in grams. Then feed the other end of the tape through the ticker timer. Making sure that the car and the tape are aligned with the ticker timer so that there is no contact, place the car at the top of the ramp on the mark indicated previously. Switch on the ticker timer and then release the car allowing it to roll all the way down in a straight line to the end of the ramp. Repeat the test again for a second and third time before moving on to repeat the whole thing with the ramp set at the different heights as necessary. Remember to replace the ticker tape for each test. After completing all the experiments, crop all the tapes so that they are the same length as the distance travelled by the car. Then count the number of dots on each length of tape.

Results: Below are the results obtained from the main experiment.

Height of ramp (cm)

Length of tape (cm)

Number of dots

Avg. No. of dots

With the knowledge that the ticker timer marks a dot onto the tape every 0.02 seconds, I know that every second there will have been 50 dots made. This information can be used to find the time taken for the car to roll down the ramp:

Time taken (seconds) = No. of dots ? 50

After I have found the time taken for the car to roll down the ramp I can find its average speed, which can be calculated by the equation:

Average Speed (m/s) = Distance Travelled (m) ? Time taken (s)

Using these equations I have now been able to draw up a modified set of results:

Height of ramp (cm)

Number of dots

Time taken (s)

Distance travelled (m)

Avg. Speed (m/s)

1.40

0.58

0.41

1.44

0.58

0.40

1.42

0.58

0.41

0.98

0.58

0.59

0.98

0.58

0.59

1.04

0.58

0.56

0.78

0.58

0.74

0.76

0.58

0.76

0.82

0.58

0.71

0.68

0.58

0.85

0.64

0.58

0.91

0.68

0.58

0.85

0.62

0.58

0.94

0.60

0.58

0.97

0.58

1.00

0.54

0.58

1.07

0.56

0.58

1.04

0.52

0.58

1.12

0.48

0.58

1.21

0.46

0.58

1.26

0.48

0.58

1.21

There has obviously been acceleration while the car was rolling down the ramp. This is blatant because the car went from stationary (at the top of the ramp) to moving (at the bottom) so I am assuming that the car was travelling at the greatest velocity at the bottom of the ramp since it had been accelerating on its decline. It is the velocity of the car at the bottom of the ramp that is important because at this point there would have been no potential energy. So if I find the greatest velocity, it will allow me to calculate the greatest amount of kinetic energy in the system, therefore permitting me to analyse the transfer from GPE to KE. Using the equations of motion I can find the final velocity of the car.

Avg speed = u + v

Avg speed = 0 + v

2 x Avg speed = 0 + v

Final velocity = 2 x Avg speed

Thus the final velocity can be found by doubling the average speed, which I already have.

Height of ramp (cm)

Avg. speed (m/s)

Final velocity (m/s)

0.41

0.83

0.82

0.40

0.81

0.41

0.82

0.59

1.18

1.16

0.59

1.18

0.56

1.12

0.74

1.49

1.48

0.76

1.53

0.71

1.41

0.85

1.71

1.74

0.91

1.81

0.85

1.71

0.94

1.87

1.93

0.97

1.93

1.00

2.00

1.07

2.15

1.04

2.07

1.12

2.23

1.21

2.42

2.44

1.26

2.52

1.21

2.42

With these results I can now plot a suitable scatter graph to show how the height of the ramp affects the speed of the car:

Analysis

From the graph plotted directly from the results as shown above, you can see that there is a strong positive correlation, which implies that as the height of the ramp increases, so the final velocity of the car increases in proportion.

However, I want to go further into detail be analysing the energy transfer in the system. We already know that the main energy transfer being made is from GPE to KE. Although, I don't how efficient the energy transfer is. As I explained in the introduction, all systems are less than 100% perfect, in that there are "leakages" of energy throughout. I aim to find how much energy is actually being transferred in this case. I can now compare these results to theoretical values in order to see the difference between them.

In theory the GPE should equal the KE:

GPE = KE

Therefore I can use the following equation to find theoretical values for the velocity of the car at the different heights:

GPE = m x g x h

KE = 1/2 x m x v2

? m x g x h = 1/2 x m v2

g x h = 1/2 x v2

2 x g x h = v2

v = ?2gh

Height of ramp h (m)

2gh

Velocity (m/s)

0.05

0.98

0.99

0.10

1.96

1.40

0.15

2.94

1.71

0.20

3.92

1.98

0.25

4.90

2.21

0.30

5.88

2.42

0.35

6.86

2.62

I can plot these values alongside my results to see the difference between them:

The inefficiency of the system can be seen more clearly when comparing theoretical and actual values. My results are slightly lower than those that were calculated. The difference between the two plots is the energy that has been lost.

If this was to be a perfect system where all the energy is conserved then appropriately the KE would be equal to GPE since all the energy would have been transferred. However, it isn't so I want to find the actual values for GPE and KE and find the difference between them. This difference will be the energy lost. The formula for GPE is as follows:

GPE = mgh

GPE = mass x gravitational force x height

The values relevant to this experiment can be substituted into the formula. The mass of the car was 0.0892 kilograms and the force of gravity on Earth can be rounded to 9.8N.

GPE (j) = 0.0892 x 9.8 x height of ramp(m)

GPE (j) = 0.87416 x height of ramp(m)

The formula for kinetic energy is:

KE (j) = 1/2mv2

KE (j) = 1/2 x mass x velocity2

The values relevant to this experiment can also be substituted into this formula.

KE (j) = 0.0446 x final velocity2

Height of ramp (cm)

GPE (joules)

Final velocity (m/s)

KE (joules)

0.044

0.82

0.030

0.087

1.16

0.060

0.131

1.48

0.098

0.175

1.74

0.135

0.219

1.93

0.166

0.262

2.15

0.206

0.306

2.45

0.267

With the values for the GPE and KE at each height I can now find the energy lost in the system as the car rolls down the ramp.

Height of ramp (cm)

GPE (joules)

KE (joules)

Energy lost (joules)

0.044

0.030

0.014

0.087

0.060

0.027

0.131

0.098

0.033

0.175

0.135

0.040

0.219

0.166

0.053

0.262

0.206

0.056

0.306

0.267

0.039

I have plotted a graph below that shows the energy lost as the height of the ramp increases.

As you can see the energy lost also increases as the height of the ramp increases, with the exception of the last point where the energy lost is lower than if it followed the trend. However, the increase in the loss of energy is so small that on a zoomed-out scale the whole plot would look very close to a horizontal line. The range of values is within 0.05 joules, which is of a minute proportion. The main cause of the energy lost is through friction. Friction in itself is a force acting against the car rolling down the ramp. So some of the energy in the system is being used towards overcoming the opposing force of friction therefore allowing the car to move. I can calculate the force of friction using the equation below:

Work done = distance moved x force

This can be re-written as follows and then applied to my results:

Energy lost = distance moved x force

Force of friction (N) = energy lost (j)___

distance moved (m)

I am assuming that the force of friction will be a uniform value because in each experiment it is the same surfaces in contact with each other (the wheels on the car and the ramp) and the same mass acting downwards.

Height of ramp (cm)

Energy lost (j)

Distance moved (m)

Force of friction (N)

0.014

0.58

0.024

0.027

0.58

0.047

0.033

0.58

0.057

0.040

0.58

0.069

0.053

0.58

0.091

0.056

0.58

0.097

0.039

0.58

0.067

These results give the average force of friction to be 0.065 Newtons.

I also want to find the efficiency of the system. As seen from the comparison between the actual and theoretical results, the efficiency is going to be somewhat lower than 100% (the perfect system). Efficiency in terms of energy transfer can be easily worked out by the following equation:

Efficiency = useful energy output x 100%

total energy input

Height of ramp (cm)

GPE (j)

KE (j)

Efficiency (%)

0.044

0.030

68.2

0.087

0.060

69.0

0.131

0.098

74.8

0.175

0.135

77.1

0.219

0.166

75.8

0.262

0.206

78.6

0.306

0.267

87.3

The average efficiency rate in the system is 75.8%. This is a relatively decent value showing that approximately 3/4 of the energy from GPE is useful in moving the car to the bottom of the ramp.

With regard to my prediction I stated that as the height of the ramp increases, so the speed of the car will increase in direct proportion. If this was true then it could be graphically represented by a graph with a straight line continuing up to the origin. However, the results do not comply because by prediction only applies when there is no friction or any other force opposing the system or if the system was 100% efficient. Secondly I stated that due to this inevitable inefficiency, the results would seem to be slightly lower than theoretical values. This prediction was correct because as you can see from the graph on page 14 the two lines are almost exactly the same shape except that my values are lower down.

Evaluation

The actual method of executing the experiment required for this investigation in itself was potentially troublesome. In undertaking the process I did encounter minor difficulties, however, to my relief there were no substantial intricacies involved and on the whole the operation ran smoothly. The most significant problem that I had was trying to keep the car from straying off its course, which ideally should be a perfectly straight line down the ramp. This obstruction could have played some part in influencing the results. If when the car did not roll down in a straight line then there could have been a chance that there was convergence between the ticker tape and the ticker timer. Any contact with the sides of the machine can succumb to an increase in the overall friction in the system and therefore subsequently decreasing the kinetic energy and slowing down the speed of the car.

With this in mind there could be inaccuracies amongst the results and that could be the cause of the very slight deviations seen in the graph plotting the height of ramp against the speed of the car (page 14). The reliability of the experiment to deliver conclusive results is also questionable. The set-up involves numerous analogue readings and outputs that could be substituted with more precise solutions with a revised experimental method. Our main instrument indirectly recording speed of the car is the ticker timer. As explained the ticker timer can possibly augment the amount of friction acting against the system. The timer can be replaced by an arrangement of light gates and in turn this alternative would directly measure the speed of the car. So, as well as eliminating one external cause of friction this method can also rule out the blatant imprecision and human error made when if the ticker tape had to be analysed to find the speed. With a light gate it would not matter if the car didn't roll down parallel to the ramp so that awkward dilemma would cease to exist.

In extension to this investigation, I could explore the effects that other factors have on the speed of the car. They would probably all tie in with the theory of GPE changing to KE such as varying the mass of the car or carrying out the experiment in a vacuum if possible. Also to give a more extensive view of application in reality I could explore different materials and the friction caused by them. Eg. The use of rubber tyres or even different surfaces.