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?
To calculate the fraction of the ball's initial kinetic energy stored in the spring, we need to first determine the initial kinetic energy of the ball and then find the final potential energy of the compressed spring.
Let's break down the problem step by step:
Step 1: Calculate the initial kinetic energy of the ball.
The formula for kinetic energy is K.E. = 0.5 * mass * velocity^2.
Plugging in the values, we have:
K.E. = 0.5 * 0.60 kg * (100 m/s)^2 = 3000 J.
Step 2: Calculate the final potential energy of the compressed spring.
Since the ball is at the point of maximum compression, all of its energy must be stored in the spring. Therefore, the potential energy of the compressed spring at this point is equal to the ball's initial kinetic energy.
Potential Energy = 3000 J.
Step 3: Calculate the fraction of the ball's initial kinetic energy stored in the spring.
The fraction can be found by dividing the potential energy of the spring by the initial kinetic energy of the ball.
Fraction = (Potential Energy / Initial Kinetic Energy).
Plugging in the values, we have:
Fraction = (3000 J / 3000 J) = 1.
Therefore, the fraction of the ball's initial kinetic energy stored in the spring is 1, meaning all of the ball's initial kinetic energy is stored in the compressed spring.