A basketball of mass 0.60 kg is dropped from rest from a...

A basketball of mass 0.60 kg is dropped from rest from a height of 1.05 m. It rebounds to a height of 0.57 m. (a) How much mechanical energy was lost during the collision with the floor? (b) A basketball player dribbles the ball from a height of 1.05 m by exerting a constant downward force on it for a distance of 0.080 m. In dribbling, the player compensates for the mechanical energy lost during each bounce. If the ball now returns to a height of 1.05 m, what is the magnitude of the force?

Key Concepts

Gravitational Potential Energy

This is the energy an object has due to its position in a gravitational field, calculated by the formula mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. It represents the energy that can be converted to kinetic energy when the object falls, and it’s a key concept in analyzing energy changes during free fall and rebounds.

Mechanical Energy

Mechanical energy is the sum of an object’s kinetic energy and gravitational potential energy. In an ideal scenario without non-conservative forces, mechanical energy is conserved. In real situations, some energy is lost due to factors like inelastic collisions or friction, and this loss can be quantified by comparing initial and rebound energies.

Energy Loss

Energy loss in physical systems often occurs during non-elastic collisions or interactions where some mechanical energy is transformed into other forms such as thermal energy, sound, or internal energy. Quantifying energy loss helps understand the efficiency of energy transfer processes and is crucial for evaluating real-world systems such as the rebound of a basketball.

Work-Energy Principle

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In situations where energy is lost and subsequently replenished (as in dribbling a ball to compensate for energy loss in a bounce), the force applied over a distance is responsible for doing this work. This principle is essential for calculating the magnitude of the force needed to restore the lost energy.

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