Answer:
Step-by-step explanation:
A. To find the speed of the 6.0 kg ball after the collision, we can use the principle of conservation of momentum. The total momentum of the system before the collision is equal to the total momentum after the collision.
Momentum before collision = Momentum after collision
m1v1 + m2v2 = (m1 + m2)vf
where:
m1 = 2.0 kg (mass of first ball)
m2 = 6.0 kg (mass of second ball)
v1 = 12 m/s (velocity of first ball)
v2 = 4.0 m/s (velocity of second ball)
vf = final velocity of the combined balls after collision
Since the 2.0 kg ball moves in the opposite direction with a speed of 8.0 m/s after the collision, and the total mass of the two balls is 8.0 kg, we can write:
vf = (m1v1 + m2v2) / (m1 + m2) = (2.0 kg x (-8.0 m/s) + 6.0 kg x 4.0 m/s) / 8.0 kg = 2.33 m/s
So the speed of the 6.0 kg ball after the collision is 2.33 m/s.
B. To find the KE for each ball before and after the collision, we can use the formula:
KE = 0.5mv^2
where:
m = mass of the ball
v = velocity of the ball
For the 2.0 kg ball, the KE before and after the collision is:
KE before = 0.5 x 2.0 kg x (12 m/s)^2 = 72 J
KE after = 0.5 x 2.0 kg x (8.0 m/s)^2 = 32 J
For the 6.0 kg ball, the KE before and after the collision is:
KE before = 0.5 x 6.0 kg x (4.0 m/s)^2 = 48 J
KE after = 0.5 x 6.0 kg x (2.33 m/s)^2 = 20.44 J
C. To find the amount of KE that is lost during the collision, we can subtract the total KE after the collision from the total KE before the collision:
KE lost = KE before - KE after = (72 J + 48 J) - (32 J + 20.44 J) = 40.56 J
So the amount of KE that is lost during the collision is 40.56 J.