Question

15) A tennis ball launcher works by using a spring to propel the ball forward. One model of tennis ball launcher has advertised that it is capable of imparting 18000 J of kinetic energy to a 4 kg ball initially at rest. A student carefully measures the compression of the spring to be 0.7 m. What is the elastic energy stored in the compressed spring?

Answer 1

The elastic energy stored in the compressed spring is 17640 J.

Step-by-step explanation:

The elastic energy stored in the compressed spring can be calculated using the formula:

Elastic Energy = (1/2) k x^2

where k is the spring constant and x is the compression of the spring.

In this case, the spring constant is not given, but we can calculate it using the given information. The kinetic energy imparted to the ball is equal to the elastic energy stored in the compressed spring.

Given: Kinetic energy = 18000 J

Mass of the ball = 4 kg

Using the formula for kinetic energy:

Kinetic energy = (1/2) mass x velocity^2

Since the ball is initially at rest, the velocity is 0.

Therefore, 18000 J = (1/2) x 4 kg x 0^2

So, the spring constant can be calculated as 18000 J = (1/2) x k x 0.7^2

Simplifying the equation gives k = 72000 N/m

Now, we can calculate the elastic energy stored in the compressed spring:

Elastic Energy = (1/2) x 72000 N/m x 0.7^2 = 17640 J

Therefore, the elastic energy stored in the compressed spring is 17640 J.