Investigating how the height of a runway affects the average speed of a trolley

GPE = mass x g x height

Where g = acceleration due to gravity

= 10m/s2

However when the object begins to fall its GPE is converted gradually into kinetic energy (KE).

KE = 1/2 x mass x (velocity)2

Therefore at the top of the ramp the GPE is at its maximum and at the bottom of the ramp the KE is at its maximum, this is because the energy is being converted as it cannot be destroyed. Moreover I can therefore presume that as the height of the ramp is increased the velocity of the trolley will also increase.

So if Max GPE = Max KE

Then mxgxh max = 1/2 x m (v max)2

I can now work out the velocity by using the following formula:

gh = 1/2 x v

2gh = v2

velocity = 2gh

The table below shows as the height of the ramp is increased the changes in the GPE and the KE

Height (m) Calc. (hxgxm) Max GPE(J) Calc. (1/2xmxv2) Max KE(J)

0.0 0.0x10x0.86 0.5x0.86x0

0.1 0.1x10x0.86 0.5x0.86x

0.2 0.2x10x0.86 0.5x0.86x

0.3 0.3x10x0.86 0.5x0.86x

0.4 0.4x10x0.86 0.5x0.86x

0.5 05x10x0.86 0.5x0.86x

This table shows how we can calculate the average velocity:

Height Calc. (2gh) Average velocity (m/s)

0.0 20x0.0 0.00

0.1 20x0.1 0.45

0.2 20x0.2 0.89

0.3 20x03 1.34

0.4 20x0.4 1.79

0.5 20x0.5 2.24

However as correct as my predicted results are my actual results will not be exactly like these due to friction. They may be quite similar to the results I get when the ramp is set at a low incline as the alacrity will be slower meaning less friction will be acting on the trolley. However as the height is raised the trolleys velocity increases and the friction will exert a stronger force on the object and will act as a resistance slowing the trolley down causing some of the energy which I have predicted to be "lost".

Therefore I predict my results to be slightly lower than the ones displayed in the table above and that as the height increases the results will even out and wont be as far spaced apart.

The graph below illustrates what my results should look like:

Apparatus

In the duration of the experiment I will use the following apparatus:

 2 x 1m rulers;

 A ramp;

 Clamp;

 Scales;

 Trolley;

 Tickertape Vibrator;

 Ticker Tape;

 Powerpack;

 Files and paper;

Method:

To perform this experiment, we will work in pairs as this will make the experiment less complex. Setting up the apparatus will be one of the hardest parts of the experiment. The first thing we will do, is set our board at an incline carefully adjusted so that no force will change the speed of our trolley. This will be set-up by clamping the ramp securely at each height we measure so that we can be ensured accurate results. As I discovered in the preliminary that if I set the ramp at a height which was too low it would not travel at a fast enough velocity to enable it to reach the end of the 1m run off, therefore my starting height will be 0.1m. However I also realised that the most elevated height possible would have to be 0.5m otherwise the speed at which the trolley runs off would be too fast and could result in an accident being caused. I decided to use a large range of heights all at the same size interval to prevent confusion when plotting my results and also consequently so that I could be assured a good degree of accuracy in my results. I will then place my file at the end of the ramp as this will prevent the trolley from "jumping" off the end of the ramp consequently affecting its velocity.

We will then take a power adapter to power our ticker timer dispenser and will connect them using plugs and when the time is right, power it to the correct voltage inorder for it to record dots onto the ticker timer paper. We will then cut some self-marking ticker timer paper and thread it into the ticker timer machine assuring us that there is carbon paper in the ticker timer device and we will then selotape the other end of the tickertape to the back of the trolley. We will then complete setting up our apparatus by hooking the back wheels of the trolley onto the end of the ramp as we have decided that we will measure everything in regard to the trolley in accordance to the rear of it. We will then, be ready.

Diagram to show how I will set up the apparatus:

Once I have set up my apparatus like so, I will switch the ticker timer on and release the trolley so that it can accelerate down the ramp. I will measure its velocity from the very point it leaves the ramp for 1m. I chose 1m as it is a suitable distance, if I was to have a number any smaller the trolley may not have yet reached its average speed.

Once I have carried out the investigation, by doing each height 2 times to ensure accuracy I will plot a rough graph. This is so that I can facilely distinguish any anomalous results that may need repeating, rather than having to make a presumption as to which results are erroneous in a table.

To work out my average speed from my ticker timer paper I will use the following formula:

Average Speed = Distance / Time

Safety

There are no real safety issues to worry about, however to be certain that there are no injuries, we will make sure everyone's ramps are well spaced apart, to prevent any trolleys colliding into anyone. And that our ramp is very stable to prevent it collapsing and hurting someone.

Factors to make it a fair test

I am very anxious to keep all the factors of the experiment fair and by doing this I will have only one variable element which will be the height as this is what we are investigating. The components which we will keep consistent throughout are:-

 Mass of the Trolley; -As the force which will be acting on the ramp must stay the same throughout, and the mass is what will determine this. To control this quandary we will use the same trolley each time.

 Friction will slow down the speed at which the trolley travels. A way of reducing the amount of friction is by having a smoother surface and keeping the superficies of the wheels the same.

 Air resistance; -we cannot control this to a great extent however we will keep the aerodynamics of the trolley the same each time.

 The length of the ramp must remain the same otherwise we will not be able to know whether the acceleration was influenced by the height of the ramp or something else and if the ramp were too be extended further this would cause there to be a different velocity.

Obtaining Evidence

In the duration of the investigation I kept everything constant except for the heights which were accurate to the nearest 0.5mm so that our final results would not be affected.

We kept the following factors constant, for the same reasons as I said in the plan

 Mass of the Trolley; -As the force that acted on the ramp must stay the same throughout the experiment, and the mass is what will determine this. To control this quandary I used the same trolley each time.

 Friction will slow down the speed at which the trolley travels. A way I reduced the amount of friction was by having a smoother surface and keeping the superficies of the wheels the same.

 Air resistance; -we could not control this to a great extent however we kept the aerodynamics of the trolley the same each time.

The length of the ramp had to remain the same otherwise we would not have been able to know whether the acceleration was influenced by the height of the ramp or something else. If the ramp were to have been extended further this would have caused there to be a different velocity.

Analysing Evidence

Looking at my graph in obtaining evidence I am able to make a conclusion, which proves my prediction to be correct. That the greater the height, the faster the velocity. However as the height doubles the velocity does not.

For example when the height was 10cm the average speed was 51.95cm/second, yet when the ramp was set at an incline of 20cm the velocity was 0.72

My results display that the higher the ramp the faster the velocity of the trolley will be. This is because an object, which is a certain distance above the ground, has gravitational potential energy (GPE), and when the trolley rolls down the ramp this energy is converted gradually into Kinetic Energy (KE). By the time the trolley reaches the end of the ramp all the GPE will have converted to KE.

In contrast with my prediction, I think I have been fairly correct by what I said. I predicted that my average speed would be slightly less than the results I plotted on the table due to the friction acting on the trolley, especially when the ramp was suspended at 0.5m. And that my results wouldn't be as far spread out as the height increased and my graph proves this as it evens out at the end.

Evaluation

In conclusion to the investigation, I believe that the experiment went very well, I did not overcome any major difficulties, and feel that I achieved the best of my abilities. However given more time and better apparatus to measure the velocity of the trolley I think it could have been more accurate. Possibly a centisecond timer or millisecond timer which have the sensitivities to be able to measure the velocity of the trolley upto 1/1000s would have guaranteed better accuracy. Nevertheless I am pleased I chose to use the tickertimer over the stopwatch as even though the tickertape timer caused friction on the trolley, compared to the human reflex actions which would be working the stopwatch it proved to be very reliable and rectified.

Taking 2 sets of results on each height proved the tickertimer to be dependable as both the readings were practically the same each time. By taking 2 sets of results also ensured myself that I should not get any anomalous results, which I didn't, I know this as the line of best fit went through my plotted results on my graph. And by plotting a rough graph as I carried out the experiment simplified things as I was able to keep track of my results and be sure no mistakes were being made. Even though all my results were fine, they showed that even though my prediction was correct, I had prognosticated that my results would be only slightly lower than the ones I wrote in the table, when actually it turns out that they weren't.

The file I placed on the end to smoothen out the main ramp to prevent the trolley "jumping" confirmed that my results were not altered due to any change in speed, which could have occurred.

Given more time I would have repeated the whole experiment and maybe taken 5 or more readings of each height to guarantee that my results were reliable. Furthermore, I am still sure that my results are of a high degree of accuracy and are dependable enough to draw a reliable conclusion.