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Investigating the acceleration of Connected Particles

Extracts from this document...

Introduction

Mohammed Abdullah                                                                     AS Level Mechanics

Investigating the acceleration of

Connected Particles

Aim

The aim of this experiment is to investigate the motion of a trolley on a plane and compare the results with a mathematical model.

Model’s Assumptions

  • No Friction – When creating the mathematical model I am going to assume that there is no friction acting upon the trolley. This is due to the fact that the trolley will be running upon a smooth plane, which offers no resistance. The trolley is also constructed upon wheels, which minimises the affects of friction between wheel and surface if any. Furthermore the track used for the trolley is specifically designed for the trolley, therefore reducing friction even more.
  • Smooth Pulley – The pulley over which the weights pulling the trolley will be passing through, will be smooth. This is for the reasons that the most costly and smoothest pulley available to me will be used. Therefore this should not also provide any resistance, which may impede the flow of motion.
  • Inextensible String – The string, which will be attached to the trolley to accelerate it, will be inextensible, i.e. the string used will not be elastic.
  • Flat Surface – The plane over which the trolley is going to be run must be flat, i.e. it must not be slanted up or down or to a side, or else gravity will also be playing a major part in the acceleration or deceleration of the trolley. To ensure the track is flat I placed a ping-pong ball on the track. If the ball rolled up, down or to a side then I would know that the track is not flat and would adjust it in accordance with the motion of the ping-pong ball.
  • String not at an angle – The string running off the trolley should be parallel to the track. This is due to the fact that a non-parallel string would be pulling the trolley down as well as forwards.

image00.pngimage01.png

image02.pngimage03.png

        Pulling Forwards = χ Cos θ

        Pulling Down      = χ Cos α

  • No Swaying – In the mathematical model I am going to assume that the falling mass does not sway. This uses the same concept as the rope not being parallel to the trolley. If the mass sways, the falling mass is not using its full potential.

image04.pngimage05.png

image06.pngimage07.png

Pulling Down = m

Pulling Sideways = m Cos θ

  • Negligible Air-Resistance – This is due to the unique construction of the trolley; low frame, compact design and no extended parts or objects disrupting the aero-dynamics.
...read more.

Middle

1498

60

1

0.38

1498

70

1

0.44

1498

80

1

0.50

Experimental Results

To work out the acceleration for the actual experiment I am going to use the equations of motion, namely                            s = ut + ½ at2.

Transpose s = ut + ½ at2 for ‘a’.

u = 0                        Therefore ‘ut’ can be taken out of the equation.

s = ½ at2        (*2)

2s = at2

a = 2s/t2

To work out the acceleration of the actual experiment using the above formula.

Mass of trolley (M) = 498g

Mass of weight (m) =   20g

Distance                 =     1m

Time                       = 2.06s

a = 2s/t2

a = 2*1/2.062

a = 2/4.2436

a = 0.47 ms-2

All the accelerations have been worked using the above technique and have been presented in the table of results below.

...read more.

Conclusion

2) hence doubling the error in timing.

The other two graphs of M = 998g & 1498g, there are no anomalous results. I think the reason for this is, because of the increased weight of the trolley; the trolley will clearly be travelling slower, hence giving more accurate and reliable timing.

The gradient of the line in all the graphs should be in theory 9.81, but this clearly is not the case. Thus I am going to work out the gradient of the lines and compare it with the math model and observe how well the two compare with each other.

Gradient of line for M = 498g

    1.25 – 0.9/0.1 – 0.072

= 0.35/0.028

=12.5

Gradient of line for M = 998g

0.65 – 0.4/0.045-0.032

        = 0.25/0.013

        = 19.23

Gradient of line for M = 1498g

0.46 – 0.3/0.04 – 0.026

        = 0.16/0.014

        = 11.43

As can be seen from the above results the math model did fairly well to model the real life situation of two connected particles.

Evaluation

The model I designed does not match the results I obtained in the experiment. This is because either I overlooked some variable quantities or the initial assumptions were flawed. On the other hand it may have been the procedure, which was at fault. In any case all these must be investigated into further. Each assumption ought to be scrutinized independently to deduce whether it is viable with regards to the experiment, in that, some assumptions were unnecessary and others were not made.

I think that if the experiment had been conducted in a vacuum and I used air–tracks the experiment would have been a lot more successful.

...read more.

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