A block of mass m slides on a smooth wedge of mass 3m. The wedge rests on a smooth horizontal floor. At an instant, the block has speed 8 m/s relative to the wedge along an incline that makes 60° with the horizontal, with the relative horizontal component directed to the right. If the speed of the wedge is N m/s, find N.
Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum
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Question

A block of mass m slides on a smooth wedge of mass 3m. The wedge rests on a smooth horizontal floor. At an instant, the block has speed 8 m/s relative to the wedge along an incline that makes 60° with the horizontal, with the relative horizontal component directed to the right. If the speed of the wedge is N m/s, find N.

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

G1 Physics · Accepted Answer

There is no external horizontal force on the block-wedge system, so horizontal momentum is conserved. Let the wedge move left with speed V. Relative to the wedge, the block's horizontal velocity component is 8cos60° = 4 m/s to the right. Therefore the block's horizontal ground velocity is 4−V. Horizontal momentum conservation gives m(4−V) + 3m(−V) = 0. Thus 4−4V = 0, giving V = 1 m/s. Hence N = 1.