Two balls with masses of 2.0kg and 6.0kg travel toward each other at speeds of 12 m/s and 4.0 m/s respectivly. If the balls have a head on inelastic collision and the 2.0 kg ball recoils with a speed of 8.0 m/s how much kinetic energy is lost in the collision?

What do you think? Momentum is conserved. What is the difference between intitial and final KE?

i don't need your sass, i need the answer

To find the kinetic energy lost in the collision, we need to calculate the total initial kinetic energy of the system (before the collision) and compare it with the total final kinetic energy (after the collision).

1. Calculate the initial kinetic energy:
- The kinetic energy for the 2.0 kg ball (ball 1) is given by:
KE1 = (1/2) * mass1 * velocity1^2
KE1 = (1/2) * 2.0 kg * (12 m/s)^2

- The kinetic energy for the 6.0 kg ball (ball 2) is given by:
KE2 = (1/2) * mass2 * velocity2^2
KE2 = (1/2) * 6.0 kg * (4.0 m/s)^2

- Calculate the total initial kinetic energy:
Total KE_initial = KE1 + KE2

2. Calculate the final kinetic energy:
- The kinetic energy for the 2.0 kg ball (ball 1) after collision is given by:
KE1' = (1/2) * mass1 * velocity1'^2
KE1' = (1/2) * 2.0 kg * (8.0 m/s)^2

- The kinetic energy for the 6.0 kg ball (ball 2) after collision is given by:
KE2' = 0 (since the 6.0 kg ball comes to rest)

- Calculate the total final kinetic energy:
Total KE_final = KE1' + 0

3. Calculate the kinetic energy lost:
Kinetic Energy Lost = Total KE_initial - Total KE_final

Now, let's substitute the values and calculate the kinetic energy lost in the collision.

KE1 = (1/2) * 2.0 kg * (12 m/s)^2
KE2 = (1/2) * 6.0 kg * (4.0 m/s)^2
KE1' = (1/2) * 2.0 kg * (8.0 m/s)^2

Total KE_initial = KE1 + KE2
Total KE_final = KE1' + 0

Kinetic Energy Lost = Total KE_initial - Total KE_final

Substitute the values and perform the calculations to find the answer.