Two ice skaters push off each other from rest. The internal push forces between them are enormous. What is the total linear momentum of the two-skater system immediately after they separate?
ALarge and positive, because large forces were applied during the push
BProportional to the impulse each skater received from the other
CZero, because internal forces cancel in Newton's third law pairs
DDepends on which skater pushed harder during the interaction
When two skaters push on each other, those are *internal* forces within the system. By Newton's third law, Skater A pushes B with force F while B pushes A with -F. These cancel exactly when summing across the system. Starting from rest (total P = 0) with no external horizontal forces, total momentum remains zero — the skaters move in opposite directions with equal and opposite momenta. No matter how hard they push, the total system momentum is conserved. The individual impulses are large; the *net* external impulse is zero.
Question 2 Multiple Choice
During a collision lasting 0.002 seconds, the contact forces are too brief and complex to measure. You can measure velocities before and after. Which method finds the impulse delivered to one object?
AWork-energy theorem: impulse equals the change in kinetic energy
CYou cannot find impulse without knowing the detailed force-time profile
DNewton's second law applied as J = F·a, where a is measured acceleration
The impulse-momentum theorem states J = ΔP = m·Δv. If you know the mass and initial and final velocities, you can compute the impulse without knowing the force-time history. This is the practical power of the approach: ∫F dt = ΔP relates impulse to measurable quantities even when the force profile is unknown. Option A confuses work (force over displacement) with impulse (force over time) — these are fundamentally different quantities connected to different conserved quantities (energy vs. momentum).
Question 3 True / False
For an isolated system with no external forces, total linear momentum is conserved regardless of how large the internal forces between particles are.
TTrue
FFalse
Answer: True
Internal forces always come in Newton's third law pairs: if particle A exerts F on particle B, then B exerts -F on A. When summing all forces across the system to compute dP/dt, every internal force is exactly canceled by its reaction partner. The net result is F_ext = dP/dt. If F_ext = 0, then dP/dt = 0 and total momentum P is constant. The magnitude of internal forces is completely irrelevant — even enormous internal forces (like those in an explosion) leave total system momentum unchanged.
Question 4 True / False
Impulse is defined as force multiplied by displacement.
TTrue
FFalse
Answer: False
Impulse is force multiplied by *time* — or more precisely, the integral of force over time: J = ∫F dt. Force multiplied by displacement is *work*, which relates to changes in kinetic energy via the work-energy theorem. Impulse and work are both integrals of force, but over different variables (time vs. displacement), and each connects to a different conserved quantity (momentum vs. energy). Confusing the two leads to applying the wrong framework when choosing between impulse-momentum and work-energy methods.
Question 5 Short Answer
In a system of particles, why do internal forces not contribute to changes in total linear momentum? State the physical principle and explain its consequence for collision analysis.
Think about your answer, then reveal below.
Model answer: Internal forces come in Newton's third law pairs: if particle A exerts force F on particle B, then B simultaneously exerts -F on A. When summing all forces across the entire system, every internal force is canceled by its equal and opposite reaction. Only external forces remain, giving F_ext = dP/dt. If external forces are zero (or negligible over a brief collision), total momentum is conserved. For collision analysis, this means you can equate total momentum before and after the collision without knowing anything about the contact forces during it.
This is Newton's third law applied at the system level. It's why an isolated system's momentum is conserved: every internal push is matched by an equal and opposite push. In collision problems, internal contact forces are typically far larger than any external forces over the brief contact duration — so external impulse is negligible and total momentum is conserved. The framework replaces 'what were the forces?' with 'what were the velocities before and after?' — a powerful simplification that works precisely because internal forces cancel.