Question

The kinetic energy of a rolling billiard ball is given by KE=1/2mv². Suppose a 0.17-kg billiard ball is rolling down a pool table with an initial speed of 4.5m/s . As it travels, it loses some of its energy as heat. The ball slows down to 3.6m/sand then collides straight-on with a second billiard ball of equal mass. The first billiard ball completely stops and the second one rolls away with a velocity of 3.6m/s . Assume the first billiard ball is the system.

Answer 1

In the given scenario, a 0.17-kg billiard ball rolling down a pool table collides with a second billiard ball. The collision is inelastic and the first ball comes to a stop while the second ball rolls away with a velocity of 3.6 m/s. The amount of kinetic energy lost during the collision is 0.3213 J, and approximately 53.4% of the original energy remains.

Step-by-step explanation:

In the given scenario, a 0.17-kg billiard ball is rolling down a pool table with an initial speed of 4.5 m/s and collides with a second billiard ball of equal mass. The first ball comes to a stop and the second ball rolls away with a velocity of 3.6 m/s. The collision can be described as an inelastic collision since the first ball did not bounce back.

To calculate the amount of kinetic energy lost during the collision, we can use the formula KE = 1/2mv². The initial kinetic energy of the first ball can be calculated as KE = 1/2 * 0.17 kg * (4.5 m/s)², which equals 0.6885 J. The final kinetic energy of the second ball can be calculated as KE = 1/2 * 0.17 kg * (3.6 m/s)², which equals 0.3672 J. Therefore, the kinetic energy lost during the collision is 0.6885 J - 0.3672 J = 0.3213 J.

The percent of the original energy that is left can be calculated as (final kinetic energy / initial kinetic energy) * 100%. In this case, the percent of the original energy left is (0.3672 J / 0.6885 J) * 100% ≈ 53.4%.

Answer 2

To calculate the average force exerted on the ball by the bumper, we can use the formula for impulse, which is equal to the change in momentum. To calculate the kinetic energy lost during the collision, we can use the formula for kinetic energy. To calculate the percent of the original energy that is left, we can divide the final kinetic energy by the initial kinetic energy and multiply by 100.

Step-by-step explanation:

To calculate the average force exerted on the ball by the bumper, we can use the formula for impulse, which is equal to the change in momentum.

The initial momentum of the ball can be calculated by multiplying its mass (0.240 kg) by its initial velocity (3.00 m/s).

The final momentum can be calculated by multiplying its mass by its final velocity (2.40 m/s).

The change in momentum is equal to the final momentum minus the initial momentum.

The collision lasts for 0.0150 s, so we can calculate the average force by dividing the change in momentum by the duration of the collision.

To calculate the kinetic energy lost during the collision, we can use the formula for kinetic energy, which is equal to one-half times the mass times the velocity squared.

The initial kinetic energy can be calculated by substituting the initial mass (0.240 kg) and velocity (3.00 m/s) into the formula.

The final kinetic energy can be calculated by substituting the final mass (0.240 kg) and velocity (2.40 m/s) into the formula.

The kinetic energy lost is equal to the initial kinetic energy minus the final kinetic energy.

To calculate the percent of the original energy that is left, we can divide the final kinetic energy by the initial kinetic energy and multiply by 100.