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Laws of Conservation

Problem 1.172

Particle 1 moving with velocity v=10 m/sv=10 \mathrm{~m} / \mathrm{s} experienced a head-on collision with a stationary particle 2 of the same mass. As a result of the collision, the kinetic energy of the system decreased by η=1.0%\eta=1.0 \%. Find the magnitude and direction of the velocity of particle 1 after the collision.

Reveal Answer
1.172. Will continue moving in the same direction, although this time with the velocity v′=(1−1−2η)v/2v^{\prime}=(1-\sqrt{1-2 \eta}) v / 2. For η≪1\eta \ll 1 the velocity v′≈ηv/2=5 cm/sv^{\prime} \approx \eta v / 2=5 \mathrm{~cm} / \mathrm{s}
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