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• Level: GCSE
• Subject: Maths
• Word count: 1606

Mechanics 2 Coursework - Assumptions related to both the model and the experiment.

Extracts from this document...

Introduction

Assumptions related to both the model and the experiment

Assumptions that are made for both the model and the experiment:

• The gravity, g, is taken to be 9.8ms-1
• The ball is taken to be a particle
• The accuracy of the timing is subjective – the start and end times are based upon the testers’ judgement.
• Readings are taken from the bottom of the ball and not the centre.
• The downward direction is taken to be positive, therefore any rebounds are negative.
• Air resistance is not taken into account.
• Values are taken to 2 d.p.

Manipulating the model

Firstly, a theoretical equation needs to be obtained linking e (the elasticity of the ball), h1 (the downward height) and h2 (the rebound height).  This can be obtained using the equations of linear motion.

When dropping the ball:

s = h1                a = g                u = 0                v = ?

Using         v2 = u2 + 2as

v2 = 0 + (2gh1)

v =  2h1g

When rebounding the ball:

s = -h2                a = -g                u = ?                v = 0

Using         v2 = u2 + 2as

u2 = v2 – 2as

u2 = -2 x –h2 x –g

u = -  2h2g

Using v = -eu, we can find an equation in terms of e.

2h1g = -e(-  2h2g)

2h1g = e  2h2g

e =

e =

From the above model, it can be seen that the gradient will give us a value of e2.

Middle

2hog = 0 + gt

t =

From this, the final equation for the sum time can be established:

=

Where h is the initial drop height, g is the gravitational pull (at 9.8ms-1 and e is the elasticity (which is found using the first equation obtained in terms of h1 and h2)

Conducting the Experiment

Method:

Other methods used to reduce the experimenter errors were to have two people checking the rebound height – this lowers the chance of experimenter judgement affecting the results adversely.  The whole method process was used for both the rebound heights and time taken to stop bouncing.  The results are shown on the following page.

Results:

Experiment One – rebound height (in cms)

 Drop Height / Drop no. 1 2 3 4 5 Mean 100cm 50 52.5 53 50 51 51.3 80cm 27 29 28 27 28 27.8 60cm 21 22 19 20 21 20.6 40cm 12 11 11.5 12 12.5 11.8 20cm 9 5 6 7 7 6.8

Experiment Two – Time Taken to stop bouncing (in seconds)

 Drop Height / Drop no. 1 2 3 4 5 Mean 100cm 4 3.8 3.9 3.9 3.9 3.9 80cm 3.3 3.2 3.1 3.1 3.2 3.18 60cm 2.9 2.8 3 2.8 2.5 2.8 40cm 2.5 2.6 2.5 2.6 2.4 2.52 20cm 1.9 1.9 2 1.8 2 1.92

Applying the model to the results

For values of e:

Using the first equation,

e =

Using the graph, values for the maximum, minimum and mean gradients can be obtained, thus giving maximum, minimum and mean values of e.

Mean value of e =

e = 0.75 to 2 d.p

Maximum value of e =

e = 0.77 to 2 d.p

Minimum

Conclusion

Initial results indicated that taking the means, and rounding them to 2.d.p may have caused the difference between the model and the actual results.  However, workings have taken place using the maximum and minimum times and values of e, which also show a similar difference between the model and the actual results.

Revision of the process

In order to improve the model:

• Fewer assumptions would be used
• Air resistance would be taken into account
• Also the fact that the ball is not a fixed particle needs to be taken into account – this is a major contributing factor to the difference between the model and the results.

In order to improve the experiment:

• Take more measurements for the times and rebound heights.
• Use a technological method to measure the times and rebound heights to increase the validity of the results.
• Increase the accuracy of the value of gravity.

The effects that these amendments would have are that the accuracy of the results would be increased.  This, in turn, would mean the value of e would be more exact, thus giving a model that gives times closer to the experimental times.

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