A plank of wood \(A B\), of mass 8 kg and length 6 m , rests on a support at \(P\), where \(A P = 4 \mathrm {~m}\). When particles of mass 1 kg and \(k \mathrm {~kg}\) are suspended from \(A\) and \(B\) respectively, the plank rests horizontally in equilibrium.
Modelling the plank as a uniform rod, find
the value of \(k\),
the magnitude of the force exerted by the support on the plank at \(P\).
Forces of magnitude 4 N and 6 N act in directions which make an angle of \(40 ^ { \circ }\) with each other, as shown. Calculate
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the magnitude of the resultant of the two forces,
the angle, in degrees, between the resultant and the 4 N force.
A stone is dropped from rest at a height of 7 m above horizontal ground. It falls vertically, hits the ground and rebounds vertically upwards with half the speed with which it hit the ground. Calculate
the time taken for the stone to fall to the ground,
the speed with which the stone hits the ground,
the height to which the stone rises before it comes to instantaneous rest.
State two modelling assumptions that you have made.