5 Fig. 5.1 shows a particle P, of mass 5 kg , and a particle Q, of mass 11 kg , which are attached to the ends of a light, inextensible string. The string is taut and passes over a small smooth pulley fixed to the ceiling.
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\caption{Fig. 5.1}
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When a force of magnitude \(H \mathrm {~N}\), acting at an angle \(\theta\) to the upward vertical, is applied to Q the particles hang in equilibrium, with the part of the string connecting the pulley to Q making an angle of \(40 ^ { \circ }\) with the upward vertical. It is given that the force acts in the same vertical plane in which the string lies.
- Determine the values of \(H\) and \(\theta\).
Particle Q is now removed. The string is instead attached to one end of a uniform beam B of length 3 m and mass 7 kg . The other end of B is in contact with a rough horizontal floor. The situation is shown in Fig. 5.2.
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\caption{Fig. 5.2}
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With B in equilibrium, at an angle \(\phi\) to the horizontal, the part of the string connecting the pulley to B makes an angle of \(30 ^ { \circ }\) with the upward vertical.
It is given that the string and B lie in the same vertical plane. - Determine the smallest possible value for the coefficient of friction between B and the floor.
- Determine the value of \(\phi\).