Introduction
When an object collides with another, momentum is conserved, but kinetic energy is not.
This experiment was designed to find if the coefficient of restitution, e, changes for high-velocity collisions. At low velocities colliding objects will tend to maintain their shape, size and elasticity, so e is likely to be constant over a range. However, at high velocities colliding objects may change their physical properties and therefore a change (probably a reduction) in e may be observed.
A small reduction in e was observed, but this was probably accounted for by air resistance and not a change in the material.

Theory
When a collision occurs, total momentum is conserved, but kinetic energy is not. When a ball, for example, bounces off the floor, it loses a little momentum to the Earth so the total momentum of the system is unchanged. Its KE, given by the formula [pic], assuming it was dropped from rest, will reduce and it will bounce to a height lower than its original height, as shown in diagram 1:
Diagram 1:

‘H’ is drop height and ‘h’ is bounce height.
The coefficient of restitution is the ratio of the difference in the initial speed and the final speed: (i) is the general formula for e, (ii) is when distances are measured on a drop (one object is stationary), and (iii) is when velocities are measured and one of the objects is stationary. Equation (ii) will be used here.

Method

Apparatus:

Rubber ball, camera, floor, 2 metre rulers.

Diagram 2:

The apparatus was set up as shown in diagram 2.

A 2-metre-ruler was formed by attaching 2 metre rulers together. The ball was dropped from 10 heights between 0 metres and 3 metres. The maximum height (bounce height) of the ball was measured using the camera for each drop height. The height of the camera was adjusted so that the height could be measured accurately (horizontal).

Errors:
The drop height (initial height) was set and so was accurate; however the bounce height was measured with a camera and so could be[pic]1 cm. It was necessary to release the ball identically every time, but, as the ball was released manually, it is unlikely it was released exactly from rest each time. It is estimated that the release error was also equivalent to[pic]1cm. The ball did not exactly hit the same area of floor each time; therefore if the floor was not entirely uniform there could be another error here, but it was probably insignificant.

Results

Table 1:
Drop height (m) |0.2 |0.6 |1 |1.3 |1.7 |2 |2.3 |2.5 |2.8 |3 | |Bounce height (m) |* |* |* |* |* |* |* |* |* |* | |e |* |* |* |* |* |* |* |* |* |* | |
Graph 1:
[pic]

The graph shows that the coefficient of restitution changes by approximately 2% when the drop height is increased from 0.2m to 3 m.
Errors:
[pic] and the error on h is approximately [pic]2cm.

The average value of h was 2 m. Therefore this error corresponds to 1% and therefore the error on e is approximately 0.5%.
The effect was larger than the error, so we may be confident that e decreased for taller drops. However, another error derived from the theory is air resistance. The ball slowed down more for taller drops so the apparent e was lower than the actual e. It is likely that the measured decrease in e was due to the theory neglecting to include air resistance.

Conclusion

The experiment attempted to find deviation in e due to the height from which the ball was dropped (this varied velocity). The observed change in e was too small to positively state that it was due to increased collision velocity (through deformation of the ball). It is more likely that air resistance accounts for the observation.

The experiment could be improved by increasing the drop height past 3 metres (this may increase the effect that was sought), having multiple cameras (to save time in adjusting height) and including air resistance in the theory.

----------------------- building tube

putty

building

tube

putty

building

tube

putty

H

h

[pic]

[pic]

Ball

Camera

Rulers