(I) You drop a basketball from a height of 5.0 m, which rebounds to a new height of 3.0 m. How much energy is lost to nonconservative forces? Give your answer as percentage of the initial energy.

Verified step by step guidance

1. Calculate the initial gravitational potential energy (PE) at the height of 5.0 m using the formula PE = mgh, where m is the mass of the basketball, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the initial height.
2. Calculate the gravitational potential energy at the rebound height of 3.0 m using the same formula PE = mgh, where h is now the rebound height.
3. Determine the energy lost to nonconservative forces by subtracting the potential energy at the rebound height from the initial potential energy.
4. To find the percentage of the initial energy that was lost, divide the energy lost by the initial potential energy and then multiply by 100%.
5. Express your final answer as a percentage, which represents the proportion of the initial energy that was lost to nonconservative forces such as air resistance and internal friction within the basketball.

Key Concepts

Gravitational Potential Energy

Gravitational potential energy (PE) is the energy an object possesses due to its position in a gravitational field. It is calculated using the formula PE = mgh, where m is mass, g is the acceleration due to gravity, and h is the height above a reference point. In this scenario, the initial potential energy of the basketball when dropped from 5.0 m can be compared to its potential energy at the rebound height of 3.0 m.

Energy Conservation and Nonconservative Forces

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In this case, some energy is lost to nonconservative forces, such as air resistance and internal friction, which dissipate mechanical energy as heat or sound. The difference in potential energy before and after the bounce indicates the energy lost to these nonconservative forces.

Percentage Energy Loss

To determine the percentage of energy lost, one must calculate the initial and final potential energies and find the difference. The energy lost can then be expressed as a percentage of the initial energy using the formula: (Energy Lost / Initial Energy) × 100%. This calculation provides insight into the efficiency of the energy transfer during the bounce of the basketball.