A ball of mass 0.30 kg is fired with velocity 100 m/s into the barrel of a spring gun of mass 2.2 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 determine the fraction of the ball's initial kinetic energy that is stored in the spring, we need to calculate the total energy of the system before and after the ball is fired into the spring gun.
Let's start by finding the initial kinetic energy (KEi) of the ball. The formula for kinetic energy is:
KE = (1/2) * m * v^2
where m is the mass of the object and v is its velocity.
Given:
- Mass of the ball (m) = 0.30 kg
- Velocity of the ball (v) = 100 m/s
Plugging in the values into the formula, we can calculate the initial kinetic energy (KEi):
KEi = (1/2) * 0.30 kg * (100 m/s)^2
Next, let's find the final kinetic energy (KEf) of the ball and the spring gun system. Since the ball sticks in the barrel and comes to rest at the point of maximum compression of the spring, all of its kinetic energy is transferred to the spring gun. So, the final kinetic energy is zero.
Now, we know that the total mechanical energy before and after the ball is fired into the spring gun is conserved since no energy is lost to friction. Therefore, the fraction of the ball's initial kinetic energy stored in the spring can be calculated as:
Fraction of KE stored in spring = (KEf / KEi)
Since KEf is zero, the fraction of the ball's initial kinetic energy stored in the spring is 0.
Therefore, none of the ball's initial kinetic energy is stored in the spring.