An electric motor has an input power of $240\ \text{W}$. The useful mechanical output power of the motor is $156\ \text{W}$.

A spring obeys Hooke's law. The graph shows the force applied to the spring against its extension.

A small object moves at constant speed in a horizontal circular path. The tension in the string provides the centripetal force.

A student pulls a dynamics cart along a straight track. The graph shows the component of the resultant force on the cart in the direction of displacement.

The Sankey diagram represents energy transfers in an electric kettle used to heat water.

A small generator can use either liquid fuel A or compressed gas fuel B. The table gives data for the two fuels and the generator efficiencies.

A skier of mass $62\ \text{kg}$ starts from rest and descends a slope. The vertical drop is $18\ \text{m}$ and the distance travelled along the slope is $75\ \text{m}$. At the bottom of the slope the skier has a speed of $16\ \text{m s}^{-1}$. Take $g = 9.8\ \text{m s}^{-2}$.

A small fuel-powered pump delivers useful output power of $900\ \text{W}$ for $30\ \text{min}$. The overall efficiency of the pump is $0.30$. The fuel has an energy density of $34\ \text{GJ m}^{-3}$.

A car of mass $1200\ \text{kg}$ travels along a level road at $20\ \text{m s}^{-1}$. At this instant the useful output power of the engine is $48\ \text{kW}$ and the resistive force on the car is $1500\ \text{N}$.

An object of mass $0.80\ \text{kg}$ moves in a straight line. Its momentum increases from $2.4\ \text{kg m s}^{-1}$ to $4.0\ \text{kg m s}^{-1}$ while it moves through $1.6\ \text{m}$.

A cart of mass $0.50\ \text{kg}$ is released from rest at the top of a track. The top of the track is $0.80\ \text{m}$ above the bottom. The length of the track is $2.5\ \text{m}$. At the bottom, the speed of the cart is $3.2\ \text{m s}^{-1}$. Take $g = 9.8\ \text{m s}^{-2}$.

A vertical spring launcher fires a small ball of mass $0.065\ \text{kg}$. The spring constant is $95\ \text{N m}^{-1}$ and the spring is compressed by $0.12\ \text{m}$ before release. Take $g = 9.8\ \text{m s}^{-2}$.

A falling mass pulls a cart along a horizontal track. The table shows measurements taken when the falling mass has descended through a fixed height. The string and pulley are assumed to be light.

A vertical spring launcher is used to project a small mass upward. The graph shows the maximum height reached above the release point for different values of the square of the spring compression.

A cyclist rides along a level road. The graph shows the useful driving force supplied at the wheel and the resistive force on the cyclist as functions of speed.

A ball is dropped from a height of $1.20\pm 0.02\ \text{m}$ and rebounds to a height of $0.86\pm 0.03\ \text{m}$. The efficiency of the bounce is defined as the ratio of rebound gravitational potential energy to initial gravitational potential energy.

A rider of mass $70\ \text{kg}$ moves down a roller-coaster track. The graph shows the height of the rider and the total mechanical energy of the rider--Earth system at different positions along the track.

A sled is pulled across snow using a rope. During the motion the tension and the angle of the rope to the horizontal change. The table gives the data for three equal displacement intervals.

A ball is dropped and allowed to bounce repeatedly on a hard surface. The graph shows the maximum height reached after each bounce. The mass of the ball is $0.145\ \text{kg}$.

A prototype drone may use one of two energy stores. The table gives the volume carried, the energy density of the store and the efficiency of converting stored energy into useful mechanical energy at the propellers.

A small electric winch is used to lift bricks vertically at a construction site. The winch receives electrical power from a generator. During one lift, a load of mass $85\ \text{kg}$ is raised through a vertical height of $12\ \text{m}$ in $18\ \text{s}$. The electrical energy supplied to the winch during the lift is $1.35\times 10^4\ \text{J}$.

A crate of mass $32\ \text{kg}$ is pulled up a rough ramp of length $5.0\ \text{m}$ at constant speed. The ramp makes an angle of $25^\circ$ to the horizontal. The pulling force has constant magnitude $210\ \text{N}$ and acts parallel to the ramp.

A lift carries passengers upward. The table gives the speed of the lift during one upward journey. The speed–time graph is formed by joining the data points with straight lines. The electrical input power to the motor is constant at $15\ \text{kW}$ over the same time interval. The total mass of the lift and passengers is $600\ \text{kg}$.

A test vehicle of mass $850\ \text{kg}$ collides with a crash barrier at $12.0\ \text{m s}^{-1}$. The graph shows the horizontal force exerted by the barrier on the vehicle as the barrier is compressed.

A small ball slides from rest at point A along a smooth curved track to point B. Point B is $1.8\ \text{m}$ lower than A. After B, the ball moves through a circular arc of radius $0.75\ \text{m}$. Friction and air resistance are negligible.

A student uses a spring launcher to project a small trolley of mass $0.42\ \text{kg}$ along a horizontal track. The spring obeys Hooke's law with spring constant $180\ \text{N m}^{-1}$. The spring is compressed by $0.120\ \text{m}$ before release. The trolley leaves the launcher and then moves along a rough section of track of length $1.5\ \text{m}$.

An electric bicycle and rider have a total mass of $92\ \text{kg}$. The bicycle travels at a constant speed of $6.5\ \text{m s}^{-1}$ up a road inclined at $4.0^\circ$ to the horizontal. The useful mechanical power delivered to the wheels is $520\ \text{W}$.

A test vehicle of mass $1200\ \text{kg}$ is accelerated along a straight horizontal track. The driving force decreases with displacement as shown in the graph. A constant resistive force of $550\ \text{N}$ acts on the vehicle throughout the motion. The vehicle starts from rest.

A pumped-storage power station pumps water from a lower reservoir to an upper reservoir during the night. During one interval, $4.8\times10^5\ \text{kg}$ of water is raised through a vertical height of $310\ \text{m}$ in $12\ \text{min}$. The overall efficiency of the pumping process is $78\%$.

A remote research station requires a useful electrical energy output of $2.4\times10^9\ \text{J}$ each day. A generator using liquid fuel has an efficiency of $32\%$. The energy density of the fuel is $3.6\times10^{10}\ \text{J m}^{-3}$.

A pendulum bob is released from rest at point A and swings along a circular arc to the lowest point B. The length of the pendulum is $0.90\ \text{m}$ and the string makes an angle of $38^\circ$ with the vertical at A. The mass of the bob is $0.16\ \text{kg}$.

A student investigates conservation of energy using a cart of mass $0.65\ \text{kg}$ connected by a light string over a pulley to a hanging mass of $0.120\ \text{kg}$. The cart starts from rest on a horizontal track. The hanging mass falls through $0.84\ \text{m}$ and the speed of both masses is then measured to be $1.50\ \text{m s}^{-1}$.

A climber of mass $68\ \text{kg}$ falls from rest before a safety rope starts to stretch. The rope behaves approximately as a spring of spring constant $1.9\times10^3\ \text{N m}^{-1}$ during the stretch. From the release point to the lowest point, the climber's centre of mass moves down a total distance of $5.6\ \text{m}$. The natural slack distance before the rope starts stretching is $3.2\ \text{m}$.

A car of mass $1400\ \text{kg}$ moves along a horizontal road. At a speed of $24\ \text{m s}^{-1}$ the total resistive force is $820\ \text{N}$. The engine delivers a constant useful power of $30\ \text{kW}$ to the wheels.