2 Fig. 2 shows a wedge of angle \(30 ^ { \circ }\) fixed to a horizontal floor. Small objects P , of mass 8 kg , and Q , of mass 10 kg , are connected by a light inextensible string that passes over a smooth pulley at the top of the wedge. The part of the string between P and the pulley is parallel to a line of greatest slope of the wedge. Q hangs freely and at no time does either P or Q reach the pulley or P reach the floor.
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\caption{Fig. 2}
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- Assuming the string remains taut, find the change in the gravitational potential energy of the system when Q descends \(h \mathrm {~m}\), stating whether it is a loss or a gain.
Object P makes smooth contact with the wedge. The system is set in motion with the string taut.
- Find the speed at which Q hits the floor if
(A) the system is released from rest with Q a distance of 1.2 m above the floor,
(B) instead, the system is set in motion with Q a distance of 0.3 m above the floor and P travelling down the slope at \(1.05 \mathrm {~ms} ^ { - 1 }\).
The sloping face is roughened so that the coefficient of friction between object P and the wedge is 0.9 . The system is set in motion with the string taut and P travelling down the slope at \(2 \mathrm {~ms} ^ { - 1 }\). - How far does P move before it reaches its lowest point?
- Determine what happens to the system after P reaches its lowest point.
- Calculate the power of the frictional force acting on P in part (iii) at the moment the system is set in motion.
\section*{Question 3 begins on page 4.}