A 0.240-kg billiard ball that is moving at 3.00 m/s strikes the bumper of a pool table and bounces straight back at 2.40 m/s (80% of its original speed). The collision lasts 0.0150 s. (a) Calculate the average force exerted on the ball by the bumper. (b) How much kinetic energy in joules is lost during the collision? (c) What percent of the original energy is left?
Step-by-step solution In this problem a billiard ball strikes the bumper of a pool table so, calculate the force exerted on the ball by the bumper ,also find the loss in the kinetic energy during the collision and also show the percent of energy left after the collision. Step 1 of 10 (a) The expression of exerted force is: …… (1) Here, is the mass of the ball, is the change in velocity and is the time duration exerted to the ball. Step 2 of 10 Use the formula to get the change in velocity , …… (2) Here, is the initial velocity of the billiard ball and is the final velocity. Substitute the values for and for in equation (2) and get, Hence, the change in velocity is 5.40 m/s. Step 3 of 10 Substitute for , for and for in equation (1), Therefore, the exerted force is . Step 4 of 10 (b) The expression of initial kinetic energy is, …… (3) Here m is the mass, is the initial velocity. Step 5 of 10 Substituting in the equation (3) and get: Hence, the initial kinetic energy is 1.08 J