Two particles of masses 2 kg and 3 kg move along the same straight line with velocities 10 m/s and 2 m/s respectively in the same direction. They collide with coefficient of restitution e = 1/2. If the loss of kinetic energy is ΔK = N/5 J, find N.
Physics · Center of maas , Momentum and Collision · collision and types of collision
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Question

Two particles of masses 2 kg and 3 kg move along the same straight line with velocities 10 m/s and 2 m/s respectively in the same direction. They collide with coefficient of restitution e = 1/2. If the loss of kinetic energy is ΔK = N/5 J, find N.

Physics · Center of maas , Momentum and Collision · collision and types of collision

G1 Physics · Accepted Answer

For a direct collision, the kinetic-energy loss can be written as ΔK = (1/2) μ(1 − e²)(u1 − u2)², where μ = m1m2/(m1 + m2) is the reduced mass. Here, μ = (2×3)/(2+3) = 6/5 kg, u1 − u2 = 10 − 2 = 8 m/s, e = 1/2. Therefore, ΔK = (1/2)(6/5)[1 − (1/2)²](8²) = (3/5)(3/4)(64) = 144/5 J. Given ΔK = N/5 J, N = 144.