Questions: Conservation of Linear Momentum

Question 1

Two identical hockey pucks on frictionless ice collide head-on. Puck A moves right at 4 m/s; Puck B moves left at 2 m/s. Which quantity is definitely conserved in this collision?

• A. Kinetic energy only.
• B. Both kinetic energy and momentum.
• C. Total linear momentum only.
• D. Neither kinetic energy nor momentum, because the pucks exert forces on each other.

Answer: (C)

On frictionless ice, no external horizontal forces act on the two-puck system, so total linear momentum is conserved. Kinetic energy is conserved only in a perfectly elastic collision — it may or may not be conserved here depending on the type of collision. Momentum conservation applies regardless of whether the collision is elastic or inelastic.

Question 2

In an inelastic collision between two objects, momentum is not conserved because kinetic energy is lost to heat and deformation.

• T. True
• F. False

Answer: False

Momentum conservation and energy conservation are independent principles. Momentum conservation follows from Newton's third law applied to internal forces — the internal forces between the two objects are equal and opposite, so they contribute zero net impulse to the system. This holds whether or not kinetic energy is conserved. Kinetic energy can be converted to heat, sound, or deformation without violating momentum conservation.

Question 3

Explain how Newton's third law guarantees that total momentum is conserved in a two-object isolated system during a collision.

Model answer: During the collision, object A exerts force F_AB on object B, and by Newton's third law, object B exerts an equal and opposite force F_BA = -F_AB on object A. The impulses over the same time interval are equal and opposite: J_AB = -J_BA. The change in momentum of A is -ΔpB, so the total change in momentum of the system is zero: the total momentum is constant.

This derivation makes clear that momentum conservation is not an independent law but a consequence of Newton's third law. It also explains why the system must be isolated: if external forces act (e.g., friction on one puck), those forces are not paired with equal-and-opposite reactions within the system, so they produce a net impulse that changes total momentum.