Two particles of masses 2m and 3m are connected by a light spring and are initially at rest on a smooth horizontal surface, separated by 5 m. The spring pulls them toward each other until they meet. If the 2m particle moves a distance N m before meeting, find N.
Physics · Center of maas , Momentum and Collision · center of mass and question based on it
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Question

Two particles of masses 2m and 3m are connected by a light spring and are initially at rest on a smooth horizontal surface, separated by 5 m. The spring pulls them toward each other until they meet. If the 2m particle moves a distance N m before meeting, find N.

Physics · Center of maas , Momentum and Collision · center of mass and question based on it

G1 Physics · Accepted Answer

There is no external horizontal force, so the centre of mass remains fixed. Put the 2m particle at x=0 and the 3m particle at x=5 m. Then x(CM) = [2m(0)+3m(5)]/(5m) = 3 m. When the two particles meet, they meet at this fixed centre-of-mass position. Therefore the 2m particle moves 3 m. Hence N = 3.