A boy in a lift

Consider the motion of the boy and take upward direction as positive.

By Newton's 2nd Law of motion,

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Consider the motion of the lift.

By Newton's 2nd Law of motion,

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Consider the motion of the mass m.

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From (1) + (2) + (3), we have

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We could have the same equation by considering different bodies as a whole

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The pulley system

m3g

Assume pulleys are light in weight and no friction exists.

Consider m1, m2 and m3 respectively,
By Newton's 2nd Law of motion