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Making Sense of Data.

Extracts from this document...

Introduction

AS Making Sense of Data

By Osman Khan

Lee 12

Aim

        The aim of this investigation is to extract as much information as possible from the results given to us from an experiment.

Diagram

        Below is a diagram showing how I expect the apparatus was set up for the experiment. I have also written a list of some of the apparatus I expected was used.

Palm Top                Ramp

Trolley                        Block

Light Gate                G-Clamp

Trolley

image00.png

Light Gate

image02.pngimage18.pngimage01.png

122cmimage02.png

image20.pngimage02.pngimage19.png

image21.pngimage22.png

image03.pngimage04.pngimage02.pngimage05.png

2.5cmimage06.png

image07.png

image08.png

1.9cm        Block

Ramp

Method

        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 time taken for the card, of length 3cm, to pass through it.

The trolley, of mass 623g, was released 122cm up the slope from front of the card. This was done accurately by using a set square to line up the front of the card with the 122cm mark on the ramp. Once this had been achieved the set square was moved away and the trolley went down the ramp. The set square ensured the trolley was not pushed forwards but only moves down the slope due to its own accord. 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.

...read more.

Middle

        Firstly I will calculate the velocity of the card through the light gate using the formula:

(First Light Gate)

Speed        = Distance / Time

= 0.03 / 0.15544                (the card is 3cm long = 0.03m)

                = 0.193

I will now do this for all the light gate positions.

Next I shall work out the time for the card 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 first light gate the trolley takes:

        T        = 0.2 / 0.193

                = 1.03s

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 first light gate

        A        = 0.193 / 1.03

                = 0.186ms-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 as a particle 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.

Modelling the Trolley

The Trolley can be modelled as a right angle triangle and thus further information can be found out such as the angle of the slope and then consequently the friction can be found out.

image09.png

122cm

2.5cm

image10.png

        Angle θ

Working out the angle

If                Sin θ = 2.5/122

Therefore              θ = sin-1 (2.5/122)

                         = 1.17*

Therefore the angle of the slope is 1.17 degrees.

Using this I can now work out what the acceleration of the model is.

...read more.

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 KE = 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 can not posses as much kinetic. Lower down the slope it has less GPE so it can posses more KE.

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 goes 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 GPE = mgh, the more height it has the more GPE it shall have. As it moves down the slope it is not as high up, so it has less GPE.

Graph 5:        Comparing GPE with KE

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

...read more.

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