A stone of mass 0.6 kg falls vertically 1.5 m from A to B against resistance. Its downward speeds at A and \(B\) are \(5.5 \mathrm {~ms} ^ { - 1 }\) and \(7.5 \mathrm {~ms} ^ { - 1 }\) respectively.
Calculate the change in kinetic energy and the change in gravitational potential energy of the stone as it falls from A to B .
Calculate the work done against resistance to the motion of the stone as it falls from A to B .
Assuming the resistive force is constant, calculate the power with which the resistive force is retarding the stone when it is at A .
A uniform plank is inclined at \(40 ^ { \circ }\) to the horizontal. A box of mass 0.8 kg is on the point of sliding down it. The coefficient of friction between the box and the plank is \(\mu\).
Show that \(\mu = \tan 40 ^ { \circ }\).
The plank is now inclined at \(20 ^ { \circ }\) to the horizontal.
Calculate the work done when the box is pushed 3 m up the plank, starting and finishing at rest.