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. Determine the maximum possible loss in kinetic energy due to the collision.

Step-by-step solution

The maximum loss in kinetic energy occurs when the collision is perfectly inelastic, meaning the two blocks stick together and move with a common velocity after the collision. Let m₁ = 2.0 kg , u₁ = 2.0 m/s , m₂ = 2.0 kg , and u₂ = 0 . By conservation of linear momentum: m₁ u₁ + m₂ u₂ = (m₁ + m₂) v 2.0 2.0 + 0 = (2.0 + 2.0) v 4.0 = 4.0 v v = 1.0 m/s Initial kinetic energy of the system is: K_i = 1 2 m₁ u₁^2 = 1 2 2.0 (2.0)^2 = 4.0 J Final kinetic energy of the system is: K_f = 1 2 (m₁ + m₂) v^2 = 1 2 4.0 (1.0)^2 =