Engineering
Physics
Conservation of Energy
Newtons Second Law of Motion
Constrained Relation
Question

Two masses A & B each of 5 kg are suspended by a light inextensible string passing over a smooth massless pulley such that mass A rest on smooth table & B is held at the position shown. Mass B is now gently lifted up to the pulley and allowed to fall from rest. Determine up to what height will A rise for the ensuing 

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Solution
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When mass B (5 kg) is lifted and released, it accelerates downward due to gravity, pulling mass A (5 kg) horizontally on the smooth table. Since the pulley is smooth and massless, the tension is equal on both sides. The acceleration a of the system is given by a=mgm+m=g2. Mass A moves horizontally with this acceleration. When B hits the ground, A has a velocity v. After that, A continues moving with constant velocity (no acceleration) until it rises to a height h on the curved path. Using energy conservation, the kinetic energy of A converts to potential energy: 12mv2=mgh. Solving, h=v22g. From kinematics, v2=2as, where s=1 m (initial height). Substituting a=g2, v2=g, so h=g2g=0.5 m.

Final answer: 0.5 m