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Trolly Experiment

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Introduction

Data Analysis Coursework

I am going to investigate the relationship between the velocity of a moving object, and the distance it travels down a ramp, using secondary data obtained by a class experiment.

image00.png

The apparatus was set up as shown above and illustrates a runaway vehicle down a hill. The light gate was placed at several points along the slope and measured the velocity of the card passing through it.

The trolley, of mass 1000g (1kg), was released 126cm up the slope from front of the card. The palm top then measured the time it took for the whole piece of card to pass through the light gate.

Once this was done the light gate was moved down the slope by 10cm at a time and again recorded the time it took for the card to pass through the light gate. This was carried out for 8 different locations. Each location’s time was repeated to end up with 3 readings. The average of these could then be taken and used as the time it took for the card to pass through the light gate.

To reduce the fiction of the wheel axis on the trolley, I have sprayed it with a lubricant (WD40).

The results I have been given are as follows:

Distance to Light Gate (m)

Velocity (m/s)

1st go

2nd go

3rd go

Mean Velocity

0.8

0.565

0.556

0.556

0.559

0.7

0.532

0.518

0.525

0.525

0.6

0.487

0.484

0.481

0.484

0.5

0.449

0.436

0.437

0.441

0.4

0.395

0.390

0.393

0.393

0.3

0.339

0.338

0.339

0.339

0.2

0.277

0.277

0.274

0.276

0.1

0.186

0.191

0.190

0.189

I have decided to make a preliminary graph to show my expected results.

image05.png

The graph above shows that as the slope distance increases the velocity of the trolley must increase.

...read more.

Middle

As well as this I can use Newton’s Second Law to Model the Particle, in order to find out friction etc.

Newton’s second law states, ‘The Force, F, applied to a particle is proportional to the mass, m, of the particle and the acceleration produced.’

This can then be represented by the equation F = ma.

In order to model the trolley I must know the acceleration. I will therefore use the SUVAT equations first.

Firstly, I shall work out is the time that the trolley took to reach the light gate by rearranging the equation:

                s = ½ (v + u)t

Therefore         2s = (v + u)t

                t = 2s / v                        (as initial velocity is always zero)

Therefore for the 0.1m light gate the trolley takes:

                t = 0.2 / 0.189

                t = 1.06s

I can now do this for all the other light gate positions also.

I can now work out the acceleration of the trolley through the light gate by using the formula:

                a = (v – u) / t

For the 0.1m light gate:

                a = 0.189 / 1.06 (because u = 0)

                a = 0.179ms-2

I will now apply this equation for all the other light gate positions.

Now that I have acceleration for the trolley I can model it going down a slope and find out the model acceleration. This value can then be subtracted from the actual value to give resistance to the path of the trolley.

This is the simplified right-angle triangle from the diagram on the page before. This will make it easier to see what is happening.

image01.png

The angle theta (θ)

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Conclusion

Graph 3:        Graph showing how the Kinetic Energy of the trolley changes as it goes down the slope.

The graph shows as that as the trolley goes further down the slope, its kinetic energy increases. This is very easy to explain in that as it moves down the slope it picks up more speed. The equation for kinetic energy is k.e. = ½mv2. The mass of the particle does not change and so the rise in kinetic energy is solely due to the trolley increasing in speed. When it is higher up the slope, it has more gravitational potential energy so it cannot posses as much kinetic. Lower down the slope it has less G.p.e. so it can posses more k.e.

Graph 4:        Graph to show how the Gravitational Potential Energy of the trolley changes as it goes down the slope.

The graph shows that as the trolley travels further down the slope it has less gravitational potential energy. This is also easy to explain in that when it is at the top of the ramp it has more height. Since G.p.e. = mgh, the more height it has the more G.p.e. it shall have. As it moves down the slope it is not as high up, so it has less G.p.e.

Graph 5:        Comparing G.p.e. with k.e.

This graph basically illustrates the connection between G.p.e. and k.e. It shows that when one increases the other must decrease. Using this graph and plotting interpolation lines and then using the G.p.e. against distance graph one can work out the position of the trolley at a given location. image04.pngimage04.png

...read more.

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