Graphically Represented Collision

Classical Mechanics Level 2

Two objects moving on a frictionless, horizontal surface are involved in a head-on elastic collision. Their velocities as a function of time are shown in the graph below. Object 1 is in blue and object 2 is in red.

Which statement accurately describes the relative masses of the objects undergoing the collision?

Note that Δ v \Delta v refers to the change in velocity and Δ p \Delta p refers to the change in momentum .

Object 2 is more massive than object 1 because its Δ v \Delta v during the collision is larger Object 1 is more massive than object 2 because its Δ v \Delta v during the collision is smaller Object 2 is more massive than object 1 because its Δ p \Delta p during the collision is larger Object 1 is more massive than object 2 because its Δ p \Delta p during the collision is smaller

Jim Ciccarelli by Jim Ciccarelli , 53, USA

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1 solution

Jim Ciccarelli
Jun 4, 2018

The change in momentum (Δp) for objects in any collision will be equal in magnitude and opposite in direction, as a direct consequence of Newton's 3rd Law. Since the impulse is equal to mΔv, and the impulses must be equal and opposite, whichever object has the smaller change in velocity during the collision must have the larger mass.

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