Work based on the experimental cycle testing Newtons Essay Example for Free

Work based on the experimental cycle testing Newtons Essay 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 models 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: Newtons 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: (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 using this model I will take a value for the coefficient restitution as 0. 8. This value was acquired from a web site called www. gamasutra. com/features/20000516/lander_pfv. htm, which was about making a computer model of the pool game. The site was demonstrating the effect spin would have on the ball in the computer game. Below are the results from using the model. From inspection all the values for ?are less than ? by an average of 4. 5 degrees. This shows the effect the coefficient of friction and the elasticity of the cushions on the table. Method: The first part to the method was to collect the correct apparatus. This included finding a ramp to launch the ball each time. This is more suitable that a cue because I could keep the velocity constant with the ramp. No ramp existed for launching snooker balls so I made one using a mudguard mounted on a wood frame. The ramp was made so that the ball rolled down the rims of the guard so that it did not hit the screw fixing along the centre of the mudguard seen in the picture. The ramp was modified so that just before the end of the ramp the rims were made wider so that the ball was released on to the surface without bouncing. The ramp was tested before the experiment so see if it was accurate enough to hit the same point consistently, which it achieved. The ramp also considered the height the ball was released every launch by a notch at the top of the ramp. (see picture) The ball was held at the top of the ramp by a single figure holding the centre of the ball, this reduced spin on the ball when travelling down the slope. The same ball was used every launch to eliminate variables. The ramp was positioned on the surface so that it was always the same distance for a marked point on the cushion. The ramp was moved along this perimeter to change the angle of approach. To position the ramp I used trigonometry using the lengths of two cushions. Below is an example of the calculations required to put the ramp in the exact place. This value was then measured up the black line on the diagram above and traced onto the perimeter of the cushion points semi circle. This method was accurate but as the angle increased the ramp was moved closer to the cushion opposite the marker point. This meant the table was too narrow to continue readings, so I had to change the adjacent length to allow the readings to continue. When the ramp was correctly lined up, which was done by trial and improvement of rolling balls down the ramp, I ran the test three times to get an average. Each run of the experiment measured the distance from the cushion to the perpendicular cushion where the ball had hit. This was then processed in the same way but the opposite way round. This was then repeated for all the angles between 10? and 90?. All the readings taken were measured to the nearest 0. 5 of a cm. This has been taken into consideration in the table of results. The pictures show the markings in chalk on the table. The picture to the left has the 50? , 70? and 90? markings on it. Results: This table continues to show the coefficient of restitution as a result from comparing the two angles. These values for the coefficient of restitution varied from 0. 5495 to 0. 7535, which showed that the collisions were not constant. This is down to either inconstancies in launching the ball or different frictional values along the balls path that could cause spin. Before I analyse the results more carefully I will point out the values in the table that I think are the most reliable. The values include 0. 7062, 0. 7277 and 0. 7535; these are taken from the angles ranging between 50? , 60? and 70?. At these angles the collision between the ball and the cushion is more consistent and there is less component force parallel to the cushion to make the ball slide through the mark on the cushion. The graph shows the upper and lower bound for the coefficient of restitution, it was necessary to include the upper and lower bounds due to the inaccuracies of the measured angles. The lengths were measured to the nearest millimetre. The prediction stated that the coefficient of restitution should be constant at 0. 8. The results show that the coefficient never reaches this level so there is clearly a factor that needs explaining. The difference is probably because of the frictional effect on the ball and a variation of spin on the ball as it rolled down the ramp. Also there would have been slight inconsistencies in my method due to human inaccuracy. Corrections On review of the method I have found that the I have translated the model into my method with a small mistake. The angles that I initially measured were measuring from the wrong point on the ball. The trig method I used meant the balls centre had to hit the cushion; instead it was the surface of the ball. To correct this mistake I had to look at the diameter of the ball and decrease the according lengths. The balls diameter was 52 mm so this meant I had to decrease the two measurements perpendicular to the cushion. These were D1 and D2, the table below shows the corrections made followed by the corrected graph. These corrections changed the angles of ? so that the smaller angles got smaller and larger angles stayed the same. This had the effect of deducing the coefficient of restitution for the smaller angles but not for the larger angles. This is why the corrected graph starts lower and then maps onto the original graph. As well as the variation due to human inaccuracy in measuring shown above there are other forms of variation that affected my results, these were spin and sliding. The effect of these is too complicated so I have explained them and drawn diagrams to give an idea. Both of these could have changed the results by an unknown amount. Due to personal experience of the game it is usually for the ball to slide more along the cushion at smaller angles, this could be because of friction and would explain the difference between my results and the predictions. On the diagram is shown the ball sliding through the mark. The ball is supposed to hit the black mark, but instead hits at the red mark and rolls along the cushion to leave at the light green mark. Concise points for improving the players games * With small angles of attack the player must realize that the ball will be at a higher chance of experiencing sliding so will depart the collision at a smaller angle. * For high angles of attack the angle of departure will be slightly under the angle of approach. Evaluation To improve this experiment to get the best possible results from it think the introduction of a video camera could help position the ball on the cushion. This would work by having a measure attached to the side of the table and then video taping the balls cushion with the cushions. This would give more accurate marks. To reduce spin on the ball I would add a rubber surface to the ramp to ensure the ball had to roll down the slope and not spin or slide. This would set the ball rolling and so the points where the ball collided would be more accurate. The predictions came from a source off the Internet and they might not be the correct for the pool table I used. The predicted coefficient was an average for most pool tables, but really in order to evaluate this method I need the accurate coefficient for my table. This could be found by using light gates to measure the speed of the ball off the ramp and after the collision with the cushion. The speed of departure over the speed of approach would have given me the correct coefficient to compare to my results. Overall the correlation between the predicted results and my results is very bad, this means that my model is very basic and does not look at the effects on the table, such as spin and sliding. The model comparison has show me the effect of the certain variables and hopefully will improve my future games. Mechanics 2 Coursework James Ashley-Smith.