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.

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 contact force between the platform and the crate.  $(\mathrm{g}=10 {\mathrm{ms}}^{-2})$

Particles $P$ and $Q,$ of masses $0.6 \mathrm{kg}$ and $0.4 \mathrm{kg},$ respectively, are joined by a light inextensible string that passes over a small, smooth, fixed pulley. The particles are held at rest with the string taut and its straight parts vertical. Initially, both particles are $1.45 \mathrm{m}$ above the ground and $0.25 \mathrm{m}$ below the pulley. The system is released from rest.

Find the speed of $P$ when $Q$ reaches the pulley. The string then breaks and $P$ falls to the ground.

Particles $P$ and $Q,$ of masses $0.6 \mathrm{kg}$ and $0.4 \mathrm{kg},$ respectively, are joined by a light inextensible string that passes over a small, smooth, fixed pulley. The particles are held at rest with the string taut and its straight parts vertical. Initially, both particles are $1.45 \mathrm{m}$ above the ground and $0.25 \mathrm{m}$ below the pulley. The system is released from rest.

Find the speed of$P$ and $Q$ reaches the pulley. The string then breaks and $\mathrm{P}$ falls to the ground.  Find the time from when the system is released to when $P$ hits the ground.

Particles $A$ and $B,$ each of mass $0.5 \mathrm{kg},$ are attached to the ends of a light inextensible string. Particle $A$ is held on a smooth slope inclined at $30°$ to the horizontal. The string passes over a small smooth pulley at the top of the slope and particle $B$ hangs vertically below the pulley. Particle $A$ is released and moves up the slope.Particle $B$hits the ground after $1.2 s$ It then stays on the ground and particle $A$ travels further up the slope. Particle A does not reach the pulley in the subsequent motion.

Find the acceleration of particle $A$ up the slope.