A rubber ball with mass 0.20 kg is dropped vertically from a height of 1.5 m above the floor. The ball bounces off of the floor, and during the bounce 0.60 J of energy is dissipated. What is the maximum height of the ball after the bounce?

To determine the maximum height of the ball after the bounce, we can use the principles of conservation of energy while taking into account the energy dissipated during the bounce.

1. First, calculate the initial potential energy (PE_initial) of the ball before it is dropped. The potential energy is given by the formula: PE = m * g * h where m is the mass, g is the acceleration due to gravity (9.81 m/s² on Earth), and h is the height.

2. Plug the given values into the formula: PE_initial = 0.20 kg * 9.81 m/s² * 1.5 m PE_initial = 2.943 J

This initial potential energy is entirely converted to kinetic energy (KE) just before the ball hits the floor, since the height at that point is essentially 0.

3. Now consider the energy dissipated during the bounce, which is 0.60 J. Subtract this from the initial potential energy to find the remaining energy: Energy_after_bounce = PE_initial - energy_dissipated Energy_after_bounce = 2.943 J - 0.60 J Energy_after_bounce = 2.343 J

4. This remaining energy is converted into potential energy again as the ball rises to its maximum height after the bounce. The potential energy at the maximum height (PE_max) will be equal to the remaining energy: PE_max = Energy_after_bounce

5. We now solve for the new height (h_max) using the PE_max: PE_max = m * g * h_max h_max = PE_max / (m * g) h_max = 2.343 J / (0.20 kg * 9.81 m/s²) h_max = 2.343 J / (1.962 kg*m/s²) h_max = 1.194 m

So the maximum height of the ball after the bounce is approximately 1.19 meters.