Two masses m1 = 1.0 kg and m2 = 2.0 kg collide inelastically and stick together. If m1 initially moves at 4.0 m/s and m2 is at rest, what is their common final velocity?

Two masses m1 = 1.0 kg and m2 = 2.0 kg collide inelastically and stick together. If m1 initially moves at 4.0 m/s and m2 is at rest, what is their common final velocity?

• A. 0.89 m/s to the left
• B. 1.33 m/s to the right
• C. 2.00 m/s to the right
• D. 0.50 m/s to the left

Answer: (B)

Momentum is conserved in collisions when no external forces act on the system. In an inelastic collision where the masses stick together, treat the momenta before and after as one system. Take right as positive. The first mass is moving at 4 m/s to the right, the second is at rest, so the initial momentum is (1 kg)(4 m/s) + (2 kg)(0) = 4 kg·m/s. After sticking, the total mass is 3 kg and moves with velocity v, giving final momentum (3 kg)(v). Setting initial and final momenta equal: 4 = 3v, so v = 4/3 ≈ 1.33 m/s to the right. So the common final velocity is 1.33 m/s to the right. In this inelastic collision, kinetic energy is not conserved—the extra energy goes into deformation, heat, and other forms—while momentum is conserved.

Momentum is conserved in collisions when no external forces act on the system. In an inelastic collision where the masses stick together, treat the momenta before and after as one system.

Take right as positive. The first mass is moving at 4 m/s to the right, the second is at rest, so the initial momentum is (1 kg)(4 m/s) + (2 kg)(0) = 4 kg·m/s. After sticking, the total mass is 3 kg and moves with velocity v, giving final momentum (3 kg)(v). Setting initial and final momenta equal: 4 = 3v, so v = 4/3 ≈ 1.33 m/s to the right.

So the common final velocity is 1.33 m/s to the right. In this inelastic collision, kinetic energy is not conserved—the extra energy goes into deformation, heat, and other forms—while momentum is conserved.