A particle strikes a smooth fixed wall with velocity making 60° with the normal. The coefficient of restitution is e = 1/2. If the fraction of initial kinetic energy lost is N/16, find N.

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G1 Physics · Accepted Answer

Only the normal component of velocity changes in a collision with a smooth wall. The tangential component remains unchanged. If the incident speed is u and the angle with the normal is 60°: u_n = ucos60°. Normal kinetic energy before collision is proportional to u_n². After collision, the normal speed magnitude becomes eu_n, so the loss in normal kinetic energy is proportional to (1−e²)u_n². Hence the fraction of total initial kinetic energy lost is ΔK/K = (1−e²)(u_n²/u²) = (1−e²)cos²60°. Subst…