How to Calculate Coefficient of Restitution and Bounce Height of a Ball
What is the coefficient of restitution between the ball and the plates?
A `70 g` ball B dropped from a height `h_(0) = 9m` reaches a height `h_(2) = 0.25 m` after bouncing twice from identical `210 g` plates. Plate A rests directly on hard ground, while plate C rests on a foam-rubber mat. Determine: (i) The coefficient of restitution between the ball and the plates, (ii) The height `h_(1)` of the ball's first bounce.
The coefficient of restitution between the ball and the plates is...
To calculate the coefficient of restitution, we apply the law of conservation of energy and properties of elastic collisions. The coefficient of restitution (e) can be determined using the formula: e = sqrt(h2/h1), where h2 is the final bounce height and h1 is the initial bounce height.
The bouncing of the ball off the plates involves the loss of energy during collisions, leading to a decrease in velocity. By calculating the ratio of the final bounce height to the initial bounce height, we can determine the coefficient of restitution between the ball and the plates.
In this case, the calculated coefficient of restitution will provide insights into the energy dissipation and bounce efficiency of the system. Understanding the coefficient of restitution is essential in predicting the behavior of the ball during collisions and bounces.