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 total initial kinetic energy of the ball.
The initial kinetic energy (KE) of an object can be calculated using the formula:
KE = (1/2) * mass * velocity^2
Given that the mass of the ball is 0.60 kg and its velocity is 100 m/s, we can substitute these values into the formula:
KE_initial = (1/2) * 0.60 kg * (100 m/s)^2
= 0.5 * 0.60 kg * 10000 m^2/s^2
= 3000 J (joules)
Now, to find the fraction of the ball's initial kinetic energy stored in the spring, we need to determine the final potential energy (PE) stored in the spring. Since the ball sticks in the barrel at the point of maximum compression of the spring, we assume that all the ball's kinetic energy is converted into potential energy stored in the spring.
The formula for potential energy stored in a spring is given by:
PE_spring = (1/2) * k * x^2
Where k is the spring constant and x is the displacement from the equilibrium position.
Since there is no information given about the spring constant or the displacement, we cannot calculate the exact value of potential energy stored in the spring. However, we can still find the fraction of initial kinetic energy stored in the spring by dividing the final potential energy by the initial kinetic energy.
Therefore, the fraction of the ball's initial kinetic energy stored in the spring = PE_spring / KE_initial.
Note that in this case, we do not have enough information to determine the numerical value of the fraction, but we can conclude that all the ball's initial kinetic energy is stored in the spring.