Lift with occupant problems

6 A crate, which has a mass of 220 kg , is being lowered on the end of a cable onto the back of a lorry.

1. Draw a diagram to show the forces acting on the crate. The crate is lowered in three stages.
   Stage 1 It starts from rest and accelerates at \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) until it reaches a speed of \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
   Stage 2 It descends at a constant speed of \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
   Stage 3 It decelerates at \(0.75 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) and eventually comes to rest.
2. Find the tension in the cable in each of the three stages.
3. Sketch the velocity-time graph for the complete downward motion of the crate.
4. The crate is lowered 15 m altogether. By considering your velocity-time graph, find the total time taken.

A woman travels in a lift. The mass of the woman is 50 kg and the mass of the lift is 950 kg. The lift is being raised vertically by a vertical cable which is attached to the top of the lift. The lift is moving upwards and has constant deceleration of \(2 \text{ m s}^{-2}\). By modelling the cable as being light and inextensible, find

1. the tension in the cable; [3]
2. the magnitude of the force exerted on the woman by the floor of the lift. [3]

In this question use \(g = 10\) m s⁻². A man of mass 80 kg is travelling in a lift. The lift is rising vertically. \includegraphics{figure_14} The lift decelerates at a rate of 1.5 m s⁻² Find the magnitude of the force exerted on the man by the lift. [3 marks]

A person, of mass 68 kg, stands in a lift which is moving upwards with constant acceleration. The lift is of mass 770 kg and the tension in the lift cable is 8000 N.

1. Determine the acceleration of the lift, giving your answer correct to two decimal places. [3]
2. State whether the lift is getting faster, staying at the same speed or slowing down. [1]
3. Calculate the magnitude of the reaction of the floor of the lift on the person. [3]

The diagram below shows a forklift truck being used to raise two boxes, \(P\) and \(Q\), vertically. Box \(Q\) rests on horizontal forks and box \(P\) rests on top of box \(Q\). Box \(P\) has mass 25 kg and box \(Q\) has mass 55 kg. \includegraphics{figure_7}

1. When the boxes are moving upwards with uniform acceleration, the reaction of the horizontal forks on box \(Q\) is 820 N. Calculate the magnitude of the acceleration. [3]
2. Calculate the reaction of box \(Q\) on box \(P\) when they are moving vertically upwards with constant speed. [1]