A block of mass 2.0 kg travelling at 2.0 m/s undergoes a head-on collision with another block of equal mass kept at rest. If the actual loss in kinetic energy is half of the maximum possible loss, determine the coefficient of restitution.

Step-by-step solution

The loss in kinetic energy during a head-on collision is given by the formula: K = 1 2 m₁ m₂ m₁ + m₂ (u₁ - u₂)^2 (1 - e^2) Given m₁ = m₂ = m and the second block is at rest ( u₂ = 0 ), the loss in kinetic energy becomes: K = 1 2 m m m + m u₁^2 (1 - e^2) = 1 4 m u₁^2 (1 - e^2) The maximum possible loss in kinetic energy occurs when the collision is perfectly inelastic, i.e., e = 0 : K_ max = 1 4 m u₁^2 It is given that the actual loss in kinetic energy is half of the maximum possible loss: K = 1 2 K_ max Substitutin