Energy conservation

An accelerating aircraft is represented in the force diagram. In the instant shown, the aircraft moves at $40\,\text{m s}^{-1}$. At what rate does its kinetic energy increase?

Feb/March 2016

State what the term work done means.

Feb/March 2016

A process has a total energy input $E_{in}$, with part of it being converted into useful energy output $U$ and the rest being transferred to wasted energy $W$. What efficiency does the process have?

Feb/March 2017

A gas is trapped in a cylinder that has a frictionless piston fitted to it. At the start, the gas occupies a volume $V_1$ and is in equilibrium with the external pressure $p$. The gas is then heated gradually so that it expands while the pressure remains constant, forcing the piston to move back until the gas volume has risen to $V_2$. How much work is done by the gas in this expansion?

Feb/March 2017

An older-style $60\,$W lamp changes $95\%$ of its energy supply into heat. A modern $4.0\,$W lamp produces the same light power output as the older lamp. What is the efficiency of the modern lamp?

Feb/March 2018

A small diesel engine consumes a volume of $1.5 \times 10^{4}\,\text{cm}^3$ of fuel per hour and delivers a useful power output of $40\,\text{kW}$. It may be assumed that $34\,\text{kJ}$ of energy is transferred to the engine when it uses $1.0\,\text{cm}^3$ of fuel. Determine the rate at which energy is transferred from the engine as wasted energy.

Feb/March 2018

Which statement most accurately describes the principle of conservation of energy?

Feb/March 2019

The information below comes from a test carried out on a petrol engine in a motor car. power output: $150\,\text{kW}$ fuel consumption: $20$ litres per hour energy content of fuel: $40\,\text{MJ}$ per litre Determine the ratio $\dfrac{\text{power output}}{\text{power input}}$?

Feb/March 2019

A gas occupies a volume of $0.012\,\text{m}^3$ in a cylinder at a pressure of $1.0 \times 10^5\,\text{Pa}$. $400\,\text{J}$ of work is done on the gas, while the pressure stays constant throughout. What is the gas’s final volume?

Feb/March 2020

A sledge with a mass of $50\,\text{kg}$ is resting on snow. It is dragged horizontally for $10\,\text{m}$ while opposing a friction force of $200\,\text{N}$, and then it is pulled horizontally over ice for another $10\,\text{m}$. The ice exerts no friction on the sledge. Next, it is raised vertically by $1\,\text{m}$ and, finally, it is taken back to its starting point at constant speed. In which part of the journey is the greatest amount of work done on the sledge?

Feb/March 2020

A car moves up a slope at a steady speed of $25\,\text{m s}^{-1}$. The engine-driven wheels provide a forward force of $3000\,\text{N}$. Air resistance and friction together produce a total opposing force of $2100\,\text{N}$. The component of the car's weight acting down the slope is $900\,\text{N}$. Determine the rate at which thermal energy is dissipated.

Feb/March 2020

State the meaning of work done.

Feb/March 2020

A gas is enclosed in a cylinder fitted with a movable piston. The cylinder has a circular cross-section with diameter $20.0\,\text{cm}$. The gas pressure is $102\,\text{Pa}$, and at the start the piston is $30.0\,\text{cm}$ above the cylinder base. When the gas is heated, the piston rises until it is $35.0\,\text{cm}$ above the base. Throughout this change, the pressure stays constant. What amount of work is done by the gas in moving the piston?

Feb/March 2021

State the meaning of work done.

Feb/March 2021

In a process, the total energy input $E_{\text{in}}$ is divided so that some is passed on as useful energy output $U$, while the remainder is passed on as wasted energy $W$. What is the efficiency of the process?

Feb/March 2022

A child travels down a long slide, as illustrated in Fig. 4.1. The child begins from rest at the top X of the slide. While moving to the lower end Y, an average resistive force of $76\,\text{N}$ acts opposite to the child’s motion. At Y, the child’s kinetic energy is $300\,\text{J}$. The loss in gravitational potential energy of the child as it goes from X to Y is $3200\,\text{J}$.

Feb/March 2022

A boat travels with constant velocity $v$ in still water. A constant drag force $F$ acts on the boat. What power is required by the boat to move through the water?

Feb/March 2024

The battery in a small tablet computer starts out uncharged. It is linked to a constant $10\,\text{W}$ power supply for $2.0$ hours in order to charge the battery. The charging process has an efficiency of $80\%$. What amount of energy is stored in the battery?

Feb/March 2024

In deriving the equation shown, which relationship is applied? $\text{power} = \text{force} \times \text{velocity}$

Feb/March 2025

A block is let go from rest at the top of a slope that is inclined at an angle to the horizontal. As shown in the diagram, the slope has length $L$. No resistive forces act on the block. What is the block’s speed at the bottom of the slope?

Feb/March 2025

A skateboarder and her skateboard have a combined mass of $70\,\text{kg}$. By pushing against the ground with her foot, she produces a forward force $F$ of $25\,\text{N}$ on herself and the skateboard, as shown in the diagram. Before the skateboarder raises her foot away from the ground, the skateboarder and skateboard move forwards by $0.50\,\text{m}$. What is the work done by $F$ on the skateboarder and skateboard?

Feb/March 2025

A projectile is projected at an angle of $45^\circ$ above the horizontal and has initial kinetic energy $E$. If air resistance is taken to be negligible, what is the projectile’s kinetic energy at its greatest height?

Feb/March 2025

An upward force of $1000\,\text{N}$ is required to raise the crane hook at constant speed. The crane is then employed to lift a load of mass $1000\,\text{kg}$ with a speed of $0.50\,\text{m s}^{-1}$. What proportion of the power produced by the crane’s motor is spent in raising the hook and the load? Take the acceleration of free fall $g$ as $10\,\text{m s}^{-2}$.

May/June 2010

An ion passes through a sequence of electrodes in a vacuum and is accelerated. A graph showing the power supplied to the ion is drawn against time. What does the area beneath the graph between two times represent?

May/June 2010

An ion is speeded up by a chain of electrodes in a vacuum. A graph showing the power supplied to the ion is drawn against time. What does the area beneath the graph between two times represent?

May/June 2010

The SI base units for the product of pressure and volume are the same as those for

May/June 2010

An ion moves through a vacuum and is accelerated by a sequence of electrodes. A graph shows the power delivered to the ion against time. What does the area under the graph between two times represent?

May/June 2010

A $2.0\,\text{kg}$ block is let go from rest on an incline. It moves $7.0\,\text{m}$ along the slope and loses a vertical height of $3.0\,\text{m}$. The block is acted on by a frictional force of $5.0\,\text{N}$ parallel to the slope. What speed does the block have after descending this distance?

May/June 2011

Which process does not need energy to be provided?

May/June 2011

A hammer that has $10\,\text{J}$ of kinetic energy strikes a nail and drives it $5.0\,\text{mm}$ into a plank. After the collision, both the hammer and the nail are brought to rest. What is the average force acting on the nail as it moves through the $5.0\,\text{mm}$?

May/June 2011

The table gives a summary of several descriptions of evaporation. Which row in the table is correct?

May/June 2011

A man of mass $80\,\text{kg}$ attaches himself to one end of a rope that goes over a single fixed pulley. He pulls the free end of the rope so that he rises with an average speed of $50\,\text{cm s}^{-1}$. What is the average useful power at which he is working?

May/June 2011

Which process does not need energy to be provided?

May/June 2011

Explain what the term work done means.

May/June 2011

The diagram represents a barrel hanging from a frictionless pulley fixed to a building. The rope that supports the barrel passes over the pulley and is tied to a stake at the foot of the building. A man is standing near the stake. The underside of the barrel is $18\,\text{m}$ above the top of the man’s head. The mass of the barrel is $120\,\text{kg}$ and the mass of the man is $80\,\text{kg}$. After untying it from the stake, the man continues to hold the rope and is pulled upwards as the barrel drops. What is the man’s upward speed when his head is level with the bottom of the barrel? (Use $g = 10\,\text{m s}^{-2}$.)

May/June 2012

The details below come from a test carried out on a petrol engine in a motor car. Power delivered: $150\,\text{kW}$ Fuel use: $20\,\text{litres per hour}$ Fuel energy content: $40\,\text{MJ per litre}$ Which expression can be used to find the efficiency of the engine?

May/June 2012

What is meant by the internal energy of an object?

May/June 2012

An engine in a car applies an average force of $500\ \text{N}$ as it moves the car $1.0\ \text{km}$ in $200\ \text{s}$. What is the average power produced by the engine?

May/June 2012

The force opposing the motion of a car is assumed to vary in proportion to the square of the car’s speed. At a speed of $20\,\text{m s}^{-1}$, the force has magnitude $800\,\text{N}$. What effective power must the car’s engine provide to keep the car moving at a constant speed of $40\,\text{m s}^{-1}$?

May/June 2012

What is meant by the internal energy of an object?

May/June 2012

The information shown below comes from a test carried out on a petrol engine in a motor car. power delivered: $150\,\text{kW}$ fuel used per hour: $20\,\text{litres per hour}$ fuel energy content: $40\,\text{MJ per litre}$ Which expression should be used to determine the efficiency of the engine?

May/June 2012

The blades of a wind turbine sweep out an area of $2000\,\text{m}^2$. It changes the power in the wind into electrical power with an efficiency of $50\%$. How much electrical power is produced when the wind speed is $10\,\text{m s}^{-1}$? (The density of air is $1.3\,\text{kg m}^{-3}$.)

May/June 2013

The diagram depicts a wheel with a circumference of $0.30\,\text{m}$. One end of a rope is attached to a force meter. The rope runs over the wheel and carries a load of $100\,\text{N}$ hanging freely. The wheel is powered by an electric motor and rotates steadily at $50\,\text{revs s}^{-1}$. At this rotational speed, the force meter gives a reading of $20\,\text{N}$. What is the motor's output power?

May/June 2013

Which row gives the correct characteristics of the process of evaporation?

May/June 2013

A gas is trapped in a cylinder that has a frictionless piston fitted to it. At the start, the gas occupies a volume $V_1$ and is in equilibrium with an outside pressure $p$. The gas is then heated gradually so that it expands, driving the piston backwards until the gas volume becomes $V_2$. How much work is done by the gas in this expansion?

May/June 2013

A car's engine applies a force of $600\,\text{N}$ while the car is moved $1.0\,\text{km}$ in $150\,\text{s}$. What is the average output power of the engine?

May/June 2014

Which of the following statements about boiling and evaporation is correct?

May/June 2014

A crystalline solid is heated at a steady rate, and the graph below shows how the temperature changes with time. Which statement about the particles in the material is correct?

May/June 2014

Which physical quantity may be expressed in electronvolts (eV)?

May/June 2014

An electric motor has an input power $P_{in}$, useful output power $P_{out}$ and efficiency $\eta$. What is the power lost in the motor?

May/June 2014

When water in a pond freezes, it changes state from liquid to solid. As this happens, its volume changes and energy is transferred to or from the surroundings. Which row is correct?

May/June 2014

Which process does not need energy to be provided?

May/June 2014

A metal ball with mass $40\,\text{g}$ drops vertically onto a spring, as shown in Fig. 4.1. The spring is mounted so that it stands upright. When the ball touches the spring, its speed is $2.8\,\text{m s}^{-1}$. As the spring is compressed, the ball is brought to rest.

May/June 2014

Explain what the term work done means.

May/June 2014

A group of nine dogs can drag a sledge with a total force of $800\,\text{N}$ at a speed of $1.5\,\text{m s}^{-1}$ for $360$ minutes. What is the mean work done by each dog over this period?

May/June 2015

A horizontal force $F$ is exerted on a frictionless trolley as it moves through a distance $s$, and the trolley’s kinetic energy changes from $4.0\,\text{J}$ to $8.0\,\text{J}$. If the trolley is then acted on by a force of $2F$ across a distance of $2s$, what would the initial kinetic energy of $4.0\,\text{J}$ change to?

May/June 2015

A gas inside a cylinder receives thermal energy $q$. As it expands at constant pressure $p$, the gas performs useful work as its volume changes from $V_0$ to $V_F$, as illustrated. Which expression gives the efficiency of this change?

May/June 2016

The power $P$ needed to move an object through a medium at constant speed is determined by the speed $v$ and the resistive force $F$ acting on the object. The resistive force $F$ is also determined by the speed $v$. Which row gives a possible relationship between speed $v$, resistive force $F$ and power $P$?

May/June 2016

A hammer carrying $10\,\text{J}$ of kinetic energy strikes a nail and drives it $5.0\,\text{mm}$ into a plank. After the impact, both the hammer and the nail are at rest. What is the approximate average force acting on the nail during the $5.0\,\text{mm}$ penetration?

May/June 2016

A boy riding a bicycle begins from rest and moves down a hill that is inclined at $30^\circ$ to the horizontal. The boy together with the bicycle has a total mass of $25\,\text{kg}$. A frictional force of $30\,\text{N}$ acts, and this force does not depend on the bicycle’s velocity. What is the kinetic energy of the boy and the bicycle after they have travelled $20\,\text{m}$ down the slope?

May/June 2016

A bungee jumper leaps from a platform and is slowed down by an elastic bungee cord, as illustrated. As the jumper begins the jump, his initial gravitational potential energy is changed into kinetic energy and elastic potential energy in the cord. During which part of the jump are all three forms of energy non-zero?

May/June 2016

A body of mass $0.30\,\text{kg}$ is projected vertically upwards from the ground with an initial speed of $8.0\,\text{m s}^{-1}$. It attains a greatest height of $1.9\,\text{m}$. Determine how much work is done against air resistance while the body rises to this maximum height?

May/June 2016

A racing car develops an output power of $300\,\text{kW}$ while moving at a constant speed of $60\,\text{m s}^{-1}$. Determine the total resistive force on the car.

May/June 2016

Over a period of time, fuel provides energy $X$ to a car. As the car speeds up, part of this energy is changed into kinetic energy. The remaining energy $Y$ is transferred away as thermal energy. Find the efficiency of the car.

May/June 2017

A mass is lifted vertically upward. Over time $t$, its gravitational potential energy increases by $E_p$ and its kinetic energy increases by $E_k$. What is the average power supplied to the mass?

May/June 2017

The graph shows how the compression of a spring changes as the force on it increases. A block is moving along a level surface with no friction towards the spring, as illustrated. The spring stops the block. Once the spring has been compressed by $4.0\,\text{cm}$, the block’s entire kinetic energy has been converted into elastic potential energy in the spring. What is the kinetic energy of the block at the moment it first touches the spring?

May/June 2017

A cyclist moves up a hill at a steady speed. The frictional force opposing the cyclist’s motion is $8.0\,\text{N}$. The cyclist uses $450\,\text{J}$ of energy to cover a distance of $20\,\text{m}$. What is the increase in the cyclist’s gravitational potential energy?

May/June 2017

A stone with mass $m$ drops from rest from the top of a cliff of height $h$ into the sea beneath. Immediately before reaching the sea, the stone has speed $v$. What is the average force of air resistance acting on the stone while it falls?

May/June 2017

Which derivation of the equation connecting power, force and velocity is correct?

May/June 2017

A puck used in ice hockey, with a mass of $150\,\text{g}$, is travelling at an initial speed of $2.0\,\text{m s}^{-1}$ over the ice-rink surface. It then glides $30\,\text{m}$ in a straight path before coming to rest. What average frictional force acts on the puck?

May/June 2017

The table’s first column shows four examples of work in progress. The second column provides extra detail about the action. Which row is incorrect?

May/June 2017

A steam turbine is used to turn a generator. The power entering the turbine is $P_I$, and the power leaving it is $P_O$. The power lost in the turbine is $P_L$, as shown. What is the efficiency of the turbine?

May/June 2017

A boy pulls a sledge across a horizontal surface by means of a rope attached to it, and the sledge moves with constant velocity. The rope has a tension of $100\ \text{N}$ and is kept at $30^{\circ}$ above the horizontal. What amount of work does the boy do on the sledge as it is pulled a distance of $5.0\ \text{m}$ along the surface?

May/June 2019

A grasshopper with mass $0.12\ \text{g}$ leaps upwards. Over a period of $0.020\ \text{s}$, it pushes off using its back legs and then leaves the ground at a speed of $3.0\ \text{m s}^{-1}$. What is the average power developed by the grasshopper's legs?

May/June 2019

A combined heat and power (CHP) station produces electrical power and useful heat. The diagram illustrates the input power and the output powers of a CHP station. What is the efficiency of the CHP station in producing useful power?

May/June 2019

A bungee jumper steps off a high bridge while connected to it by a long elastic rope that obeys Hooke’s law. The jumper’s gravitational potential energy is taken relative to the lowest point reached by the jumper. Which graph shows how the jumper’s gravitational potential energy, and the elastic potential energy in the rope, vary with the vertical distance fallen from the top of the bridge?

May/June 2019

Which statement about the principle of conservation of energy is correct?

May/June 2019

The graph in Fig. 3.1 shows how the force $F$ changes with extension $x$ for a spring. One end of a spring with an unstretched length of $0.40\ \text{m}$ is fixed to a stationary point. A block of weight $2.5\ \text{N}$ is hung from the spring and then released, so it moves downward. At a certain moment, the spring’s length is $0.72\ \text{m}$. Take air resistance and the mass of the spring to be negligible.

May/June 2019

A mass fixed to the bottom end of a spring moves up and down. At which positions along the mass’s motion are the gravitational potential energy of the mass (GPE), the elastic potential energy in the spring (EPE) and the kinetic energy of the mass (KE) at their maximum values?

May/June 2020

Power is passed through a machine, as shown. What is the machine’s efficiency?

May/June 2020

Over a period of time, fuel provides a car with energy $X$. Part of this energy becomes kinetic energy while the car speeds up. The remaining energy $Y$ is transferred away as thermal energy. What is the efficiency of the car?

May/June 2020

Under which situation is work done on an object?

May/June 2020

A ball moves down a curved track, as illustrated. Point X is $0.40\,\text{m}$ higher than point Y. At point X, the ball’s speed is $2.5\,\text{m s}^{-1}$. Frictional forces may be ignored. What is the speed of the ball at point Y?

May/June 2020

The force diagram represents an aircraft that is speeding up. At the moment shown, the aircraft’s velocity is $40\,\text{m s}^{-1}$. At what rate is its kinetic energy increasing?

May/June 2020

State the meaning of velocity.

May/June 2020

To unwrap a tape roll with a length of $50\,\text{m}$, a steady force of $20\,\text{N}$ is needed. How much work is done in unwrapping the entire roll?

May/June 2021

A trolley with mass $600\,\text{kg}$ starts at point P on a slope, with its position $80\,\text{m}$ above ground level, as shown. It is let go from rest and travels down the slope, finally stopping at point Q, which is at height $h$ above ground level. The distance travelled by the trolley along the slope from P to Q is $1.5\,\text{km}$. A steady resistive force of $300\,\text{N}$ acts against the trolley’s motion on the slope. Find $h$.

May/June 2021

A body with a weight of $15.0\,\text{N}$ is dragged across a horizontal surface at a steady speed of $2.00\,\text{m s}^{-1}$. The pulling force on the body is $12.0\,\text{N}$ at an angle of $30.0^\circ$ to the horizontal, as illustrated. What is the power used to move the body?

May/June 2021

A stone is descending vertically through the air at a steady (terminal) velocity. Which change in energy is taking place?

May/June 2021

An object with weight $12\,\text{N}$ is at rest on a platform at the top of a container fitted with two pistons, as illustrated. The container holds a fixed mass of gas, and the pistons can move freely. The plunger is then pressed slowly $4.0\,\text{cm}$ to the right. Consequently, the object rises slowly by $0.50\,\text{cm}$. What is the amount of work done on the object?

May/June 2021

A child whose weight is $330\,\text{N}$ begins at point X, which is at the top of a slide beside a swimming pool, as shown in Fig. 3.1. Starting from rest, the child travels to the lowest part of the slide, which is vertically $4.0\,\text{m}$ below X. The child then carries on to point Y at the end of the slide, which is vertically $1.1\,\text{m}$ above the lowest point. The child’s kinetic energy at Y is $540\,\text{J}$.

May/June 2021

A box travels down a rough ramp. The box’s gravitational potential energy changes by $16\ \text{J}$ as it moves from position X to position Y. At X, the box has kinetic energy of $24\ \text{J}$, and at Y it has kinetic energy of $35\ \text{J}$. How much work is done against the frictional force?

May/June 2022

An electric motor is given a total energy of $E$. A quantity of energy, $Q$, is wasted, while the rest is used for useful work. What is the efficiency of the motor?

May/June 2022

A new kind of filament lamp has been created by researchers and it has an efficiency of $40\%$. The efficiency of older filament lamps is $5.0\%$. Both lamp types give the same useful output power. What is the ratio $\dfrac{\text{input power to new type of lamp}}{\text{input power to old type of lamp}}$?

May/June 2022

What does the term efficiency of a system mean?

May/June 2022

A car weighing $15\,000\,\text{N}$ is travelling on a horizontal road. At a particular moment, the thrust force from the engine on the car is $12\,000\,\text{N}$ and the resistive force on the car is $3000\,\text{N}$. The car's velocity at this instant is $24\,\text{m s}^{-1}$. Calculate the power output from the engine.

May/June 2022

A man is riding in a buggy that is being pulled by a wire connected to a kite. The wire makes an angle of $40^\circ$ to the horizontal and maintains a steady tension of $200\,\text{N}$. The man and buggy move $20\,\text{m}$ in a straight horizontal line. The wire and the buggy’s route lie in the same vertical plane. What is the work done by the tension force on the man and buggy?

May/June 2023

A steam turbine is employed to turn a generator. The input power to the turbine is $P_I$ and the output power is $P_O$. The power loss in the turbine is $P_L$, as illustrated. What is the efficiency of the turbine?

May/June 2023

A changing force is applied so that the train is supplied with constant power. Which graph best represents how the force $F$ varies with the train’s velocity $v$?

May/June 2023

A car is travelling on a horizontal road at a constant velocity $v$ while a resistive force $F$ acts on it. The engine of the car has an efficiency of $25\%$. What is the input power to the engine?

May/June 2023