A ball of mass 0.60 kg is fired with velocity 100 m/s into the barrel of a spring gun of mass 2.4 kg initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. No energy is lost to friction. What fraction of the ball's initial kinetic energy is stored in the spring?

Question

A ball of mass 0.60 kg is fired with velocity 100 m/s into the barrel of a spring gun of mass 2.4 kg initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. No energy is lost to friction. What fraction of the ball's initial kinetic energy is stored in the spring?

Answer 1

To determine the fraction of the ball's initial kinetic energy stored in the spring, we need to calculate the total kinetic energy of the ball before it sticks into the barrel, and then compare it to the spring's potential energy when it is at maximum compression.

First, let's calculate the initial kinetic energy of the ball:

Initial kinetic energy (KE_initial) = 1/2 * mass * velocity^2

Given:
Mass of the ball (m_ball) = 0.60 kg
Velocity of the ball (v_ball) = 100 m/s

KE_initial = 1/2 * 0.60 kg * (100 m/s)^2
KE_initial = 1/2 * 0.60 kg * 10000 m^2/s^2
KE_initial = 3000 J

The initial kinetic energy of the ball is 3000 Joules.

Next, let's calculate the potential energy stored in the compressed spring:

Potential energy in a spring (PE_spring) = 1/2 * spring constant * displacement^2

Since no energy is lost to friction and the surface is frictionless, all the initial kinetic energy of the ball is converted into potential energy stored in the compressed spring.

PE_spring = KE_initial = 3000 J

Finally, let's calculate the fraction of the ball's initial kinetic energy stored in the spring:

Fraction = PE_spring / KE_initial

Fraction = 3000 J / 3000 J
Fraction = 1

Therefore, the fraction of the ball's initial kinetic energy stored in the spring is 1, which means all of the initial kinetic energy is stored in the spring.