Jan Dangerfield, Stuart Haring and, Julian Gilbey Solutions for Exercise 5: EXERCISE 5C

A box of mass $5 \mathrm{kg}$ sits in a lift. A second box of mass $3 \mathrm{kg}$ sits on the first box. The lift accelerates upwards with acceleration $0.7 \mathrm{m}{\mathrm{s}}^{-2}.$

Work out the contact force between the two boxes. The tension in the lift cable is unchanged but the boxes are swapped over, so the first box sits on the second box.

A box of mass $5 \mathrm{kg}$ sits in a lift. A second box of mass $3 \mathrm{kg}$ sits on the first box. The lift accelerates upwards with acceleration $0.7 \mathrm{m}{\mathrm{s}}^{-2}.$ The tension in the lift cable is unchanged but the boxes are swapped over, so the first box sits on the second box.

Show that this increases the contact force between the boxes.

A passenger lift has mass $500 \mathrm{kg}.$ The breaking tension of the cable is $12000 \mathrm{N}.$ The maximum acceleration of the lift is $0.75 \mathrm{m}{\mathrm{s}}^{-2}.$If the lift travels at its maximum acceleration, calculate the maximum mass of the passengers:
(i ) when the lift is accelerating upwards.
(ii ) when the lift is accelerating downwards.

A passenger lift has mass $500 \mathrm{kg}.$ The breaking tension of the cable is $12000 \mathrm{N}.$ The maximum acceleration of the lift is $0.75 \mathrm{m}{\mathrm{s}}^{-2}.$

Taking the average mass of a person to be $75 \mathrm{kg},$ what is the maximum number of passengers that should be allowed to travel in the lift?

The tension in a lift cable is $11070 \mathrm{N}.$ The lift is accelerating upwards at $a \mathrm{m}{\mathrm{s}}^{-2}.$ A man of weight $800 \mathrm{N}$ stands in the lift on a set of bathroom scales. The scales suggest that the weight of the man is $820 \mathrm{N}.$ Assuming that the scales have negligible weight, find the weight of the lift.

Two masses, $A$ of $2 \mathrm{kg}$ and $B$ of $3 \mathrm{kg},$ are connected by a light inextensible string that passes over a small, smooth, fixed pulley. Initially, the masses are held stationary and are then released.

Find the acceleration of each mass. 

Two masses, $A$ of $2 \mathrm{kg}$ and $B$ of $3 \mathrm{kg},$ are connected by a light inextensible string that passes over a small, smooth, fixed pulley. Initially, the masses are held stationary and are then released. The pulley is fixed to the wall of a lift. The lift is initially stationary. The lift has mass $400 \mathrm{kg}$ and a man of mass $75 \mathrm{kg}$ is travelling in the lift, along with the pulley system. There is nothing else in the lift. The lift starts to move upwards, from rest, by a tension in the lift cable of $4992 \mathrm{N}$.

Find the acceleration of the lift.

Two masses, $A$ of $2 \mathrm{kg}$ and $B$ of $3 \mathrm{kg},$ are connected by a light inextensible string that passes over a small, smooth, fixed pulley. Initially, the masses are held stationary and are then released.

Find the acceleration of each of $A$ and $B,$ as viewed by a person standing stationary outside the lift.