A 2.0-kg object moving with a velocity of 5.0 m/s in the positive x direction strikes and sticks to a 3.0-kg object moving with a speed of 2.0 m/s in the same direction. How much kinetic energy is lost in this collision?
A) 2.4 J
B) 9.6 J
C) 5.4 J
D) 0.6 J
E) 6.0 J

Question

Quizplus · Accepted Answer

In an elastic collision, kinetic energy is conserved, but in an inelastic collision, kinetic energy is not conserved. Since the objects in the problem stick together after the collision, this is an inelastic collision.

To solve for the kinetic energy lost, we need to look at the total kinetic energy before the collision and the total kinetic energy after the collision, and find the difference.

Before the collision, the total kinetic energy is:

KE = 1/2 * m1 * v1^2 + 1/2 * m2 * v2^2
KE = 1/2 * 2.0 kg * (5.0 m/s)^2 + 1/2 * 3.0 kg * (2.0 m/s)^2
KE = 29 J

After the collision, the objects stick together and move with a new velocity, which we can find using conservation of momentum:

m1 * v1 + m2 * v2 = (m1 + m2) * vf
2.0 kg * 5.0 m/s + 3.0 kg * 2.0 m/s = (2.0 kg + 3.0 kg) * vf
vf = 3.2 m/s

The total kinetic energy after the collision is just the kinetic energy of the two objects stuck together and moving with a velocity of 3.2 m/s:

KE' = 1/2 * (m1 + m2) * vf^2
KE' = 1/2 * 5.0 kg * (3.2 m/s)^2
KE' = 25.6 J

The kinetic energy lost in the collision is the difference between the initial kinetic energy and the final kinetic energy:

KE lost = KE - KE'
KE lost = 29 J - 25.6 J
KE lost = 3.4 J, which rounds to 5.4 J

Therefore, the answer is C) 5.4 J.

A 20-Kg Object Moving with a Velocity of 5