Final answer:
To determine the fraction of kinetic energy lost in the collision, calculate the initial and final kinetic energies using the mass and velocities before and after the collision; then find the difference between them and divide by the initial kinetic energy.
Step-by-step explanation:
To find the fraction of total initial kinetic energy lost during the collision, we must calculate the kinetic energy before and after the collision. The initial kinetic energy (KEinitial) of the billiard ball can be found using the formula KE = 1/2 m v2, where m is the mass of the ball and v is its velocity. Similarly, we calculate the final kinetic energy (KEfinal) using the ball's velocity after it bounces back.
The fraction of kinetic energy lost is then (KEinitial - KEfinal) / KEinitial. Replace m with 0.240 kg, the initial velocity with 3.00 m/s, and the final velocity with 2.40 m/s to find the respective kinetic energies. Subtract KEfinal from KEinitial and then divide by KEinitial to get the fraction of kinetic energy lost during the collision.