Questions: Conservation of Linear Momentum in Systems

Question 1

Two cars collide and exert enormous forces on each other for 0.1 seconds. A student claims 'momentum cannot be conserved because the collision forces are so large.' What is the student getting wrong?

• A. The student is correct — large internal forces always violate momentum conservation
• B. The collision forces are internal to the two-car system; Newton's third law guarantees they cancel in pairs and don't change the system's total momentum
• C. Momentum is only conserved when forces are small and act over long time periods
• D. The student should apply energy conservation instead, since momentum doesn't apply to contact forces

Answer: (B)

The size of internal forces is irrelevant to conservation. Newton's third law guarantees that every internal force has an equal and opposite reaction force within the system — they cancel in pairs when summed. Only external forces can change the total system momentum. The collision forces between the two cars are enormous but internal to the two-car system, so they cancel and total momentum is conserved (subject to external impulses like friction being negligible during the brief collision).

Question 2

A stationary grenade explodes into three fragments. What is the total momentum of all three fragments immediately after the explosion?

• A. Impossible to determine without knowing the explosion force magnitude and direction
• B. Greater than zero, since the explosion adds kinetic energy and thus momentum to the system
• C. Zero, because the grenade was at rest and external impulses during the brief explosion are negligible
• D. Equal to the impulse of the explosive force times the duration of the explosion

Answer: (C)

Before the explosion, the system (the grenade) has zero momentum. The explosion forces are entirely internal to the system — the explosive gases push the fragments, but those are all parts of the same system. External forces (gravity, air) act for such a short time that their impulse mg·Δt ≈ 0. Therefore total momentum after = total momentum before = 0. The three fragments' momenta must vector-sum to zero. This is the 'explosion run in reverse' principle.

Question 3

If you analyze only one object in a two-object collision — say, just Ball A — the contact force from Ball B is an internal force to your analysis and can be ignored.

• T. True
• F. False

Answer: False

The contact force is internal only if BOTH balls are included in the system. If your system boundary contains only Ball A, then the force from Ball B acts on your system from outside — it is external, it produces an impulse, and it changes Ball A's momentum. This is why analyzing the full two-ball system is powerful: the contact forces become internal and cancel, leaving only any external impulses. Shrinking the system boundary makes those forces external and must be included.

Question 4

Conservation of linear momentum can hold in one coordinate direction even when it fails in another direction due to an external force.

• T. True
• F. False

Answer: True

Conservation is directional and applies independently in x, y, and z. A hockey puck sliding across frictionless ice and struck by a glancing blow in the x-direction conserves momentum in the y-direction (no external y-impulse) even though y-direction momentum is not conserved in x. This independence is frequently the key to solving 2D collision problems: if the ball can only leave in one direction, that constraint gives you an equation for one component that's independent of the others.

Question 5

Explain why the choice of system boundary is critical when applying conservation of momentum, and how choosing the right boundary simplifies a seemingly complex problem.

Model answer: The system boundary determines which forces are internal (and therefore cancel by Newton's third law) and which are external (and must be tracked as impulses). Internal forces always cancel in pairs and cannot change total momentum. By choosing a boundary where all large interaction forces are internal and external impulses are negligible, you convert a problem involving unknown contact forces into a simple bookkeeping equation: total momentum before = total momentum after.

This is the strategic insight that makes conservation laws powerful. In a billiard ball collision, the contact forces peak at thousands of newtons and vary in complex ways during the millisecond impact. You never need to model them — just include both balls in your system, confirm that external impulses are negligible during the brief collision, and write one vector equation. The complexity of the internal mechanics is completely bypassed. The art of mechanics problems is often choosing the right system.