Analysis Of The Tennis Ball

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Introduction
Suppose a ball is released from a distance and rolls down an inclined plane, as shown in figure 1. At the bottom of the inclined plane, the ball strikes a level tabletop and bounces away. The inclined plane may be rotated to give a steeper angle, which will affect the time of travel across the tabletop.
The ball’s horizontal component of velocity is (Walding, Rapkins and Rossiter, 2004, pg. 62): v_x = v cos θ Figure 1: Experiment set up. Red indicates acting forces, green indicates velocity.
As the ball bounces across the tabletop, the horizontal component of velocity (vx) will remain unchanged, assuming no kinetic energy is lost. The vertical component of the velocity (vy), force normal of the tabletop and the force of gravity …show more content…

However, it is obvious that the tennis ball was most affected by friction, as it has the greatest difference between the theory and data. This was also visually apparent during the experiment. It was observed that the tennis ball slowed down considerably more that the other two balls. This is because the outer surface of a tennis ball is made from a furry cloth material, which generates more friction that a smooth surface, like the other two balls. (Bowden, 1951, pg. 302; Tremaine and Weinberg, 1984)
Secondly, published coefficient of restitution values varied considerably depending on the source. It is easier to calculate coefficient of restitution values experimentally rather than theoretically, therefore coefficient of restitution values can vary from source to source (Elert, 2006). Thus, the accuracy of these values is poor, and the calculated velocity is equally poor. As a result, predictions made are inconclusive.
Thirdly, the experiment design was prone to human error. Human reaction times make it impossible to record accurate results with a stopwatch. Similarly, the calculated velocity values were an average velocity. Realistically, the instantaneous velocity at the start of the tabletop should have been measured so that the velocity is unaffected by friction, drag and other external …show more content…

As stated above, stopwatches introduced a large degree of random error, and a number of uncontrolled variables. Using time gates to record the instantaneous velocity at the start of the tabletop would eliminate most of these variables, including friction. Therefore it would be beneficial to use time gates rather than stopwatches.
The distances on the inclined plane (s1 = 1.5m) and tabletop (s2 = 4.0m) were chosen to make the error margin smaller. By making these distances longer, the affect of friction was larger; however this effect is relatively small. Shorter distances would have resulted in large error margins; therefore it was beneficial to have longer inclined plane and tabletop distances.
As a result of this study, the relationship between a ball 's horizontal velocity and the angle of the inclined plane it travels down is known. Therefore maximizing horizontal velocity on a ramp is as straightforward as the theory. This has lots of practical applications, such as bowling ramps and bike jumps, where largest the possible horizontal velocity is required.

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