1. (Humphrey, p. 84, no. 2)

Two pulleys of weights 12 lb and 8 lb are connected by a fine string hanging over a smooth fixed pulley. Over the former is hung a fine string with weights 3 lb and 6 lb at its ends, and over the latter a fine string with weights 4 lb and x lb. Find x so that the string over the fixed pulley remains stationary, and find the tension in it.

2. (Part of Humphrey, p. 75, nos. 566)

A mass of 9 lb resting on a smooth horizontal table is connected by a light string, passing over a smooth pulley at the edge of the table to a mass of 7 lb hanging freely. Find the common acceleration, the tension in the string and the pressure on the pulley.

3. Two particles of mass B and C are connected by a light string passing over a smooth pulley. Find their common acceleration.

4. Particles of mass 3 and 6 lb are connected by a light string passing over a smooth weightless pulley; this pulley is suspended from a smooth weightless pulley and offset by a particle of mass 8 lb. Find the acceleration of each particle.

5. A man of 12 stone and a weight of 10 stone are connected by a light rope passing over a pulley. Find the acceleration of the man. If the man pulls himself up the rope so that his acceleration is one half its former value, what is the upward acceleration of the weight?

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