Elasticity

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What happens to objects after collision? Does one retract? stay at rest? or move along with the other? These questions can be answered through analyses of elasticity of objects. For example, there is a drastic contrast of elasticity between a small rubber ball and a handful of dough. One is highly elastic and the other is highly inelastic. So when describing collisions, one can qualitatively state that the collision is either elastic, or inelastic.

Now, to quantitatively explain elasticity, there is the coefficient of restitution for two objects in a head-on, direct collision:

e = -(v_1f - v_2f)/(v_1i - v_2i)

Using the equation, If e=1 (perfectly elastic collisions), the relative velocity before impact equals in magnitude the relative velocity after impact. And if e=0 (perfectly inelastic collisions) the two bodies adhere after impact. Steel against steel has a high value for e whereas fabric is almost inelastic. In real life, the values of e for all things fall somewhere in the interval of 0 < e < 1.

In this site, we will study one-dimensional, head-on collisions. The collisions involved on the pool table are two-dimensional however, with special case like equal mass for all balls. We will study the particular two-dimensional collision of pool balls of its geometry and more in the following sections.

Sample Problem
I roll a basketball (initially at rest) to the wall which is 10 meters away with an acceleration of 5 m/s². The ball bounces off with 9 m/s. What is the coefficient of restitution of my basketball? (Give in decimals)

Your Answer:

Solution