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Difficulty: HardNewton's Laws of Motion and Linear Momentum

In an isolated system where two colliding bodies of unequal mass undergo a perfectly elastic head-on collision, the body with the larger mass imparts a greater magnitude of impulse on the lighter body than the lighter body imparts on the heavier body.

Answer: Answer

Answer

The statement is false. By Newton's Third Law, interaction forces are equal in magnitude and opposite in direction at all times, making the impulse imparted by each body on the other equal in magnitude.
The statement is false because Newton's Third Law dictates that the force exerted by object 1 on object 2 is equal in magnitude to the force exerted by object 2 on object 1 at every instant during contact. Integrating force over time yields equal magnitudes of impulse (∣J1∣=∣J2∣|J_1| = |J_2|), independent of mass differences.

Step-by-Step Solution

1
Apply Newton's Third Law to interaction forces.
F12=−F21F_{12} = -F_{21}, where F12F_{12} is the force exerted on body 2 by body 1, and F21F_{21} is the force exerted on body 1 by body 2.
Forces between interacting objects always occur in equal and opposite action-reaction pairs regardless of mass.
2
Integrate both forces over the duration of collision Δt\Delta t.
J12=∫F12 dt=−∫F21 dt=−J21J_{12} = \int F_{12} \, dt = -\int F_{21} \, dt = -J_{21}.
Impulse is defined as the time-integral of force.
3
Compare impulse magnitudes.
∣J12∣=∣J21∣|J_{12}| = |J_{21}|.
Taking the magnitude of both sides shows that both bodies experience equal magnitudes of impulse regardless of mass ratio or collision elasticity.

Key Concept

Newton's Third Law and Equality of Mutual Impulse
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Topics

Newton's Laws of Motion and Linear Momentum

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