An 8.0-kg object moving 4.0 m/s in the positive x direction has a one-dimensional collision with a 2.0-kg object moving 3.0 m/s in the opposite direction. The final velocity of the 8.0-kg object is 2.0 m/s in the positive x direction. What is the total kinetic energy of the two-mass system after the collision?
A) 32 J
B) 52 J
C) 41 J
D) 25 J
E) 29 J

Question

Quizplus · Accepted Answer

The total momentum is conserved in a collision:

(8.0 kg)(4.0 m/s) + (2.0 kg)(-3.0 m/s) = (8.0 kg + 2.0 kg)(2.0 m/s)

Solving for the final velocity of the 2.0-kg object:

-12 kg m/s = 10 kg m/s - 16 kg m/s

-12 kg m/s + 16 kg m/s = 4 kg m/s

vf = 2 m/s in the positive x direction

The kinetic energy of each object before the collision is:

KE1 = (1/2)(8.0 kg)(4.0 m/s)^2 = 64 J
KE2 = (1/2)(2.0 kg)(3.0 m/s)^2 = 9 J

The total kinetic energy before the collision is:

KEtotal = KE1 + KE2 = 73 J

After the collision, the kinetic energy of each object is:

KE1' = (1/2)(8.0 kg)(2.0 m/s)^2 = 16 J
KE2' = (1/2)(2.0 kg)(2.0 m/s)^2 = 4 J

The total kinetic energy after the collision is:

KEtotal' = KE1' + KE2' = 20 J

Therefore, the total kinetic energy of the two-mass system after the collision is a decrease of 73 J - 20 J = 53 J. The only answer choice that is closest to this value is (C) 41 J.

An 80-Kg Object Moving 4