Two blocks of masses m and 3m move together with centre-of-mass speed 5 m/s on a smooth horizontal surface. A compressed spring between them is released. After release, their relative speed is 8 m/s, and the lighter block moves faster in the original direction. If the speed of the lighter block is N m/s, find N.
Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum
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Question

Two blocks of masses m and 3m move together with centre-of-mass speed 5 m/s on a smooth horizontal surface. A compressed spring between them is released. After release, their relative speed is 8 m/s, and the lighter block moves faster in the original direction. If the speed of the lighter block is N m/s, find N.

Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum

G1 Physics · Accepted Answer

Before the spring is released, total momentum is (m+3m)×5 = 20m. Let the final velocities be v₁ for the lighter block and v₂ for the heavier block. Momentum conservation gives m v₁ + 3m v₂ = 20m, so v₁+3v₂ = 20. Their relative speed is v₁−v₂ = 8. Hence v₁ = v₂+8. Substituting gives v₂+8+3v₂ = 20, so 4v₂ = 12 and v₂ = 3 m/s. Therefore v₁ = 11 m/s and N = 11.