Work based on the experimental cycle testing Newton's law of impact

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Mechanics 2 Coursework                James Ashley-Smith

                Grecians

Work based on the experimental cycle testing Newton’s law of impact

Introduction: 

For this piece of coursework I have chosen to look at the laws of impact on a pool table. This will involve making initial assumption that will be made from inspection of the model and experience in playing the game. With these assumptions in mind I will carry out an experiment on the table to justify or correct my assumptions. After a clear understanding of the reality of the model I will attempt to compile a few practical points that will improve the performance of the player when they are playing in the specific environment that is being modelled.

The model’s environment:

        There are many shots that can be played on the pool table that require different aspects of skill. The specific environment that I will be testing is the snookered shot. This means there is a ball between the cue ball and my colour (red). One of the options I have is to rebound the shot off the cushion and hit the ball. This would normally require experience in order to be accurate enough to hit the cushion in the right place. The model I will be testing will help the play know where to hit the cushion in order to hit the red ball. The elasticity of the cushion and the velocity of the ball are variables when determining the impulse from the cushion on the ball, this will affect the angle on the cushion.

Assumptions:

        Due to my experience with playing pool I have formulated a few important factors for the experiement. I will start by looking at the constants these include velocity, which will remain the same through out the experiment. The next is the momentum, which will be treated as having been conserved and not lost in the collision with the cushion. These two points will allow me to use a basic model that uses only the knowledge I have acquired. In addition to this I will exclude the effect of sliding or spin on the ball, the motion of this is too difficult for me to model.

The model:

        Newton’s laws of impacts state that the initial speeds U1 and U2 collide so that final speeds V1 and V2 are produced under the effect of the coefficient of restitution. This can be written as:                                    

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    (e is the coefficient of restitution)

This is the same as writing:

This can be changed into component form to show the following:

Parallel the cushion component

  • Momentum is conserved.

Perpendicular to the cushion component

  • By showing the perpendicular component in comparison to the parallel component a final model is produced.

With this model I can use the pool table to find the both angles with out using velocities or momentums.

Predictions:

        By ...

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