Ball throwing in pulley system · CAP 2019 #8

Physics · mechanics

Problem

Two men of the same mass M are each standing inside a massless box, and the boxes are connected to each other through a massless, frictionless pulley system. Each man is holding a heavy ball of mass m, so that they balance each other, and the system is at rest. When standing on earth, the man on the right can throw the ball vertically upward to a height h above the point at which the ball leaves his hand. To what height, with respect to himself, can he throw the ball when he is standing inside the box? Assume that the ceiling of the box is high enough that the ball can't reach it, and ignore any effect from the mass of the man's hand and arm when is throwing the ball. Assume also that the man on the left remains motionless inside his box. a) M−mM+mh\frac{M-m}{M+m}h b) 2M+m2(M+m)h\frac{2M+m}{2(M+m)}h c) M−m2(M+m)h\frac{M-m}{2(M+m)}h d) 2M−m2(M+m)h\frac{2M-m}{2(M+m)}h e) m2M+mh\frac{m}{2M+m}h

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