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.

A $10 \mathrm{m}$ long slope makes an angle $30°$ with the horizontal. $A$ box of mass $8 \mathrm{kg}$ is pulled up the slope by a rope that is parallel to the slope. The coefficient of friction between the box and the slope is $\frac{1}{\sqrt{12}}.$ At the top of the slope, the rope passes over a smooth pulley. A ball of mass $12 \mathrm{kg}$ hangs from the other end of the rope. The ball is initially $2 \mathrm{m}$ above the ground. The system is released from rest.

Find how long it will take for the box to travel $1.5 \mathrm{m}$ up the slope.

A $10 \mathrm{m}$ long slope makes an angle $30°$ with the horizontal. $A$ box of mass $8 \mathrm{kg}$ is pulled up the slope by a rope that is parallel to the slope. The coefficient of friction between the box and the slope is $\frac{1}{\sqrt{12}}.$ At the top of the slope, the rope passes over a smooth pulley. A ball of mass $12 \mathrm{kg}$ hangs from the other end of the rope. The ball is initially $2 \mathrm{m}$ above the ground. The system is released from rest.

Find the tension in the rope.

A car is travelling along a straight horizontal road. The car has mass $1800 \mathrm{kg}$ and is towing a trailer of mass $600 \mathrm{kg}.$ Resistance forces are $30 \mathrm{N}$  on the car and $10 \mathrm{N}$ on the trailer. Find the size and type of force in the tow-bar,when the driving force from the engine is $400 \mathrm{N}$.

A car is travelling along a straight horizontal road. The car has mass $1800 \mathrm{kg}$ and is towing a trailer of mass $600 \mathrm{kg}.$ Resistance forces are $30 \mathrm{N}$  on the car and $10 \mathrm{N}$ on the trailer. Find the size and type of force in the tow-bar,when the driving force from the engine is $20 \mathrm{N}.$

A crate of mass $15 \mathrm{kg}$ rests on a platform. The platform has mass $5 \mathrm{kg}.$ It is lowered using a rope. The tension in the rope is $10 \mathrm{N}.$

Find the acceleration of the crate.