Elastic Collision of Carts · PhysicsBowl 2024 #13

Physics · mechanics

Problem

A small cart with a mass of 50 g is rolling on a frictionless track with a velocity of +10

\frac{m}{s}

. It then has a head-on, elastic collision with a stationary cart of mass 100 g. What is the speed of each cart immediately after the collision? The 50-g cart speed is listed first followed by the 100-g cart speed in all choices. a. -3.3

\frac{m}{s}

and +6.7

\frac{m}{s}

b. +3.3

\frac{m}{s}

and -6.7

\frac{m}{s}

c. -6.7

\frac{m}{s}

and +3.3

\frac{m}{s}

d. +6.7

\frac{m}{s}

and -3.3

\frac{m}{s}

e. +3.3

\frac{m}{s}

and +6.7

\frac{m}{s}

Intuitive explanation

In an elastic collision, both momentum and kinetic energy are conserved—you need both equations working together. Since the lighter cart hits a heavier stationary one head-on, expect the lighter cart to bounce backward and the heavier one to move forward, but not as fast as the incoming cart. Set up conservation of momentum and energy, then solve the resulting system to find both final velocities.

Intuitive explanation

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