Question

Question 2: (2pts) Prediction of Gravitational, Kinetic and Total energy for a bouncing ball. Based on your predictions of position and velocity vs time, explain how the energy changes during the motion of the ball. (a) Where on your position vs. time graph is the Gravitational Potential Energy at a maximum during each bounce? Where is it a minimum? What is the velocity when the gravitational potential energy is maximum? What about when the gravitational potential energy is minimum? Explain your reasoning below. (b) Where on your velocity vs time graph is the Kinetic Energy at a maximum? Where is it a minimum? What is the vertical position of the ball when the kinetic energy is a maximum? What is the vertical position when the kinetic energy is a minimum? Explain your reasoning below.

Answer 1

As the ball moves in vertical direction after the bounce, its kinetic energy decreases with height and its potential energy increases.

(a) Gravitational potential energy is maximum at the highest point attained by the ball.

It is minimum at the lowest point i.e. at the point of bounce.

When gravitational potential energy is maximum, velocity is zero because at highest point ball is momentarily at rest.

When gravitational potential energy is minimum, velocity is maximum.

Let us assume that velocity of the ball just after the bounce is u.

Maximum height attained by the ball is:

(b) Kinetic energy is maximum at the point of bounce as velocity is maximum here.

It is minimum at the highest point.

When kinetic energy is maximum, vertical position is y = 0 (assuming point of bounce as origin & taking vertical direction as y-axis).

When kinetic energy is minimum, vertical position is y = h (highest point).