A 6.9 kg bowling ball travelling at 6.4 m/s strikes a stationary 1.4 kg bowling pin. After the collision, the pin flies forward at 6.4 m/s.
How much kinetic energy was lost in the collision?
There is something wrong with the assumptions of this problem. Collisions of bowling balls with pins are highly elastic. The kinetic energy of rotation of the bowling ball also should be considered. It changes very little.
A pin hit head-on by a bowling ball will end up with a velocity a lot faster than that of the ball. If you don't believe it, go to a bowling alley.
They probably want you to assume conservation of momentum for the collision. This is OK, but the assumed velocity of the pin after collision is not.
6.9*6.4 = 6.9V' + 6.4*1.4
V2 (the final velocity of the ball) = 5.1 m/s
Use that velocity and what you already know to compute the KE loss they want to to compute. Warning: it will not be close to what would really happen.
Your teacher may be unaware of the importance of rotational KE, so assume it stays the same.
To calculate the kinetic energy lost in the collision, we need to determine the initial kinetic energy of the system before the collision and the final kinetic energy of the system after the collision.
The initial kinetic energy can be calculated using the formula:
Initial Kinetic Energy = (1/2) * Mass of the Bowling Ball * (Velocity of the Bowling Ball)^2
Given:
Mass of the Bowling Ball (m1) = 6.9 kg
Velocity of the Bowling Ball (v1) = 6.4 m/s
Plugging in the values:
Initial Kinetic Energy = (1/2) * 6.9 kg * (6.4 m/s)^2
Initial Kinetic Energy = 139.3664 Joules
Now, the final kinetic energy can be calculated using the formula:
Final Kinetic Energy = (1/2) * Mass of the Bowling Pin * (Velocity of the Bowling Pin)^2
Given:
Mass of the Bowling Pin (m2) = 1.4 kg
Velocity of the Bowling Pin (v2) = 6.4 m/s
Plugging in the values:
Final Kinetic Energy = (1/2) * 1.4 kg * (6.4 m/s)^2
Final Kinetic Energy = 57.344 Joules
To find the kinetic energy lost in the collision, we subtract the final kinetic energy from the initial kinetic energy:
Kinetic Energy Lost = Initial Kinetic Energy - Final Kinetic Energy
Kinetic Energy Lost = 139.3664 Joules - 57.344 Joules
Kinetic Energy Lost = 82.0224 Joules
Therefore, the kinetic energy lost in the collision is 82.0224 Joules.