The mass of a lift is $200 \mathrm{kg}$ and the maximum tension in the lift cable is $2500 \mathrm{N}.$The lift carries a load of $40 \mathrm{kg}$. Work out the contact force between the lift floor and the load.

A crate of mass $m \mathrm{kg}$ is put into a lift. The lift accelerates upwards at $a \mathrm{m}{\mathrm{s}}^{-2}.$ The mass of the lift is $M \mathrm{kg}.$

Find the tension in the lift cable.

A crate of mass $m \mathrm{kg}$ is put into a lift. The lift accelerates upwards at $a \mathrm{m}{\mathrm{s}}^{-2}.$ The mass of the lift is $M \mathrm{kg}.$

Find the contact force between the lift floor and the crate.

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?

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.