Gravitational potential energy and kinetic energy

A man is running along a straight path. What is the approximate value of his kinetic energy?

Feb/March 2016

A water pumping system has a pump that takes in $2.0\,\text{kW}$ of electrical power while lifting water. Each second, the system raises $16\,\text{kg}$ of water to a vertical height of $7.0\,\text{m}$. What is the efficiency of the pumping system?

Feb/March 2016

A car with a mass of $1400\,\text{kg}$ is moving along a straight, level road at a steady speed of $25\,\text{m s}^{-1}$. The engine’s output power is $30\,\text{kW}$. The car then moves uphill on a slope of $2^\circ$ to the horizontal, while still keeping the same steady speed. What is the output power of the car’s engine when it is travelling up the slope?

Feb/March 2017

A car with mass $1100\,$kg is moving at a steady speed of $15\,\text{m s}^{-1}$ uphill on a slope inclined at $10^{\circ}$ to the horizontal. The total frictional forces on the car act down the slope and have a magnitude of $\dfrac{W}{5}$, where $W$ represents the car’s weight. What is the useful output power of the car’s engine?

Feb/March 2018

A bead starts from rest at point $P$ and moves along a wire, as shown. The track bends round to form a vertical circle with diameter $40\,\text{cm}$. At point $Q$, the bead’s speed is $1.4\,\text{m s}^{-1}$. Air resistance and friction on the wire are negligible. What is the height $h$ from which the bead is released?

Feb/March 2018

Boxes $X$ and $Y$ each have the same mass. Box $X$ is raised straight up by a force of magnitude $F$ until it has moved through a height $h$. Box $Y$ is dragged up a slope by a force with the same magnitude so that it reaches the same height, as shown. Which statement is correct?

Feb/March 2018

Explain what the term work done means.

Feb/March 2018

Leonardo da Vinci suggested a flying machine that would operate in the manner of a screw, raising the pilot into the air. The pilot turns the ‘screw’. The combined mass of the machine and the pilot is $120\,\text{kg}$. What useful output power must the pilot supply to travel vertically upward at a steady speed of $2.5\,\text{m s}^{-1}$?

Feb/March 2019

A ball is launched straight up from the Earth’s surface. Which statement describes the ball’s energy as it moves higher through the air?

Feb/March 2020

An object is transported in a vertical plane from X to Y, and then from Y to Z, as shown in the diagram. The distances between the different points are marked on the diagram. The lines XY and VZ are vertical. The object has a weight of $20\,\text{N}$. How much gravitational potential energy does the object gain when it moves from X to Z?

Feb/March 2020

An egg with a mass of $25\,\text{g}$ drops straight downward from the top of a table that is $900\,\text{mm}$ above the ground. Air resistance is negligible. Determine the kinetic energy of the egg when it reaches the ground.

Feb/March 2021

An escalator has a length of $60\,\text{m}$ and raises passengers by a vertical distance of $30\,\text{m}$, as illustrated. When no passengers are on it, the power needed to operate the escalator against friction is $2.0\,\text{kW}$. Passengers of mean mass $60\,\text{kg}$ use the escalator, and the power needed to overcome friction stays unchanged. What power is needed to run the escalator while it is carrying $20$ passengers and moving at $0.75\,\text{m s}^{-1}$?

Feb/March 2022

A rock with a mass of $40\,\text{kg}$ is dropped from rest at a point $20\,\text{m}$ above the surface of a planet. When the rock reaches the planet’s surface, its kinetic energy is $32\,\text{kJ}$. The planet has no atmosphere. What is the weight of the rock on the surface of the planet?

Feb/March 2022

A ball is launched from level ground into the air and moves along the trajectory shown in the diagram. At points $Q$, $R$, $S$ and $T$, the ball has kinetic energies $E_Q$, $E_R$, $E_S$ and $E_T$ respectively. The diagram shows the height above the ground of each of these four points. Air resistance may be ignored. Which difference between the kinetic energies is the smallest?

Feb/March 2024

Inside a hydroelectric power station, a turbine lies at a vertical depth of $30\,\text{m}$ below the surface of a large lake. Water flows through the turbine at a rate of $340\,\text{m}^3\,\text{per minute}$. The combined efficiency of the turbine and generator system is $90\%$. The density of water is $1000\,\text{kg m}^{-3}$. Calculate the useful power output of the power station?

Feb/March 2025

A constant force $F$ acts on a car of mass $m$ and moves the car up the slope by a distance $s$ at constant velocity $v$. The slope makes an angle $\alpha$ with the horizontal. Which expression gives the efficiency of the process?

May/June 2010

A constant force $F$, acting on a car of mass $m$, moves the car up the incline through a distance $s$ at constant velocity $v$. The angle between the incline and the horizontal is $\alpha$. Which expression represents the efficiency of this process?

May/June 2010

An upward force of $1000\ \text{N}$ is required to raise the crane hook at constant speed. The crane is then employed to raise a load with mass $1000\ \text{kg}$ at a speed of $0.50\ \text{m s}^{-1}$. What fraction of the power produced by the crane motor is devoted to lifting the hook and the load? Take the acceleration due to gravity $g$ to be $10\ \text{m s}^{-2}$.

May/June 2010

A car of mass $m$ is pulled uphill over a distance $s$ at constant speed $v$ by a constant force $F$. The incline makes an angle $\alpha$ with the horizontal. Which expression gives the efficiency of the process?

May/June 2010

A force of $1000\,\text{N}$ is required to raise the hook of a crane at constant speed. The crane is then used to lift a load of mass $1000\,\text{kg}$ at a speed of $0.50\,\text{m s}^{-1}$. What amount of the power developed by the motor of the crane is used in lifting the hook and the load? Assume the acceleration of free fall $g$ is equal to $10\,\text{m s}^{-2}$.

May/June 2010

A cyclist is travelling up a slope with a constant gradient. The cyclist takes $8.0\,\text{s}$ to climb the slope. Figure 3.1 shows how the cyclist’s speed $v$ varies with time $t$.

May/June 2010

A steel sphere is released so that it falls vertically onto a horizontal metal plate. It reaches the plate with speed $u$, then moves away with speed $v$, and rises vertically to half of its starting height. Which expression gives the value of $\frac{v}{u}$?

May/June 2011

A man has a mass of $80\,\text{kg}$. He fastens himself to one end of a rope that runs over a single fixed pulley. He then pulls the other 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

A body moving at a speed of $10\,\text{m s}^{-1}$ possesses kinetic energy of $1500\,\text{J}$. If the body’s speed is raised to $40\,\text{m s}^{-1}$, what kinetic energy does it now have?

May/June 2011

A steel sphere is released so that it falls vertically onto a horizontal metal plate. It strikes the plate with speed $u$, then departs from it with speed $v$, and rises vertically again to half of its starting height. Which expression represents $\frac{v}{u}$?

May/June 2011

A block of mass $2.0\,\text{kg}$ is set free from rest on a slope. It moves $7.0\,\text{m}$ along the slope and drops through a vertical height of $3.0\,\text{m}$. A frictional force of $5.0\,\text{N}$ acts parallel to the slope. Determine the speed of the block after it has fallen this distance?

May/June 2011

An object moving at a speed of $10\,\text{m s}^{-1}$ has a kinetic energy of $1500\,\text{J}$. When the speed of the object is raised to $40\,\text{m s}^{-1}$, what is its new kinetic energy?

May/June 2011

Explain what the term work done means.

May/June 2011

A cube made of concrete has side $0.60\,\text{m}$ and a uniform density of $2.0 \times 10^3\,\text{kg m}^{-3}$. It is raised $5.0\,\text{m}$ vertically by a crane. What change in potential energy does the cube have?

May/June 2012

What would be a sensible estimate for the athlete's average kinetic energy during a $100\ \text{m}$ race lasting $10\ \text{s}$?

May/June 2012

At first, four identical uniform blocks, each with mass $m$ and thickness $h$, lie separately on a table. What work is done on the blocks when they are stacked one on top of another?

May/June 2012

The diagram illustrates the layout of a water wheel that turns a generator to generate electrical energy. The water has a flow rate of $200\ \text{kg s}^{-1}$. The generator delivers a current of $32\ \text{A}$ at a voltage of $230\ \text{V}$. If any change in the water’s kinetic energy is ignored, what is the efficiency of the system?

May/June 2012

What would be a sensible estimate for the average kinetic energy of an athlete while running a $100\,\text{m}$ race lasting $10\,\text{s}$?

May/June 2012

The diagram depicts a barrel hanging from a frictionless pulley fitted to a building. The rope that supports the barrel passes over the pulley and is fastened 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 man’s head. The mass of the barrel is $120\,\text{kg}$ and the mass of the man is $80\,\text{kg}$. After untying the rope from the stake, the man holds onto it and is pulled upwards as the barrel descends. 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

A cube made of concrete has side length $0.60\,\text{m}$ and a uniform density of $2.0 \times 10^3\,\text{kg m}^{-3}$. It is raised vertically by a crane through $5.0\,\text{m}$. What change occurs in the cube’s potential energy?

May/June 2012

A solid rubber ball with a diameter of $8.0\,\text{cm}$ is let go from rest with the top of the ball $80\,\text{cm}$ above a horizontal surface. It moves straight down and then rebounds so that the greatest height attained by the top of the ball is $45\,\text{cm}$, as shown. If the kinetic energy of the ball is $0.75\,\text{J}$ immediately before it hits the surface, what is its kinetic energy immediately after it has left the surface?

May/June 2013

A bow with a mass of $400\,\text{g}$ propels an arrow of mass $120\,\text{g}$ straight upwards. Immediately before release, the bow stores $80\,\text{J}$ of potential energy. The efficiency of the system is $28\%$. What height does the arrow reach if air resistance is ignored?

May/June 2013

An engine is pulling a train along a mountain railway track that is inclined at an angle of $30^\circ$ to the horizontal. The train is transporting $200$ passengers, each with an average mass of $70\,\text{kg}$, and it is moving at $6.0\,\text{m s}^{-1}$. The mass of the train itself is $80\,000\,\text{kg}$. Of the power supplied by the engine, $40\%$ is used to lift the train and its passengers. Calculate the power of the engine?

May/June 2013

A ball of mass $m$ is projected upwards through height $h$ in air with initial velocity $v$, as shown. The effect of air resistance is taken to be negligible. The acceleration of free fall is $g$. What is the total work done by the gravitational force on the ball as it travels from $P$ to $Q$?

May/June 2013

The diagram illustrates a setup that is used to determine the output power of an electric motor. The wheel fixed to the motor’s axle has a circumference of $0.5\,\text{m}$, and the belt passing over it is at rest when the weights have the values shown. If the wheel is turning at $20$ revolutions per second, what is the output power of the motor?

May/June 2013

A body falls vertically from rest through air. State and explain the energy changes that occur as it falls.

May/June 2013

A weight $W$ is suspended from a trolley travelling along a rail. While the trolley moves horizontally by a distance $p$, it at the same time lifts the weight through a height $q$. Hence, the weight is displaced a distance $r$ from X to Y. It begins and ends at rest. What amount of work is done on the weight in this process?

May/June 2014

The equation $P = k \rho A v^n$ gives the maximum theoretical power $P$ of a wind turbine, where $\rho$ represents the density of air, $A$ denotes the area swept out by the turbine blades, $v$ is the speed of the air and $k$ is a constant with no units. What is the value of $n$?

May/June 2014

A mass at point X within a uniform gravitational field is acted on by a gravitational force of $0.200\,\text{N}$. Its gravitational potential energy is $1.00\,\text{J}$. The mass is then relocated to point Y. What is the gravitational potential energy now?

May/June 2014

A small mass is set down at point P on the inner surface of a smooth hemisphere, and it is then released from rest. When it arrives at the lowest point T, its speed is $4.0\,\text{m s}^{-1}$. The diagram, which is not to scale, shows the mass’s speed at other points Q, R and S while it slides down. Air resistance is negligible. From P to T, the mass loses potential energy $E$. At which point has the mass lost potential energy $\frac{E}{4}$?

May/June 2014

An escalator measures $60\,\text{m}$ in length and raises passengers by a vertical distance of $30\,\text{m}$, as illustrated. When there are no passengers on it, the power needed to drive the escalator against friction is $2.0\,\text{kW}$. The escalator carries passengers with an average mass of $60\,\text{kg}$, while the power needed to overcome friction stays constant. What power is needed to drive the escalator when it is carrying $20$ passengers and moving upwards at $0.75\,\text{m s}^{-1}$?

May/June 2014

A uniform solid cuboid made of concrete, with dimensions $0.50\,\text{m} \times 1.20\,\text{m} \times 0.40\,\text{m}$ and weight $4000\,\text{N}$, is at rest on a level surface with the $1.20\,\text{m}$ edge upright, as illustrated in diagram 1. Calculate the least energy needed to rotate the cuboid through $90^{\circ}$ into the arrangement shown in diagram 2, where the $0.50\,\text{m}$ edge is upright.

May/June 2014

Define power in terms of work done and elapsed time.

May/June 2014

Explain the meaning of gravitational potential energy and kinetic energy.

May/June 2014

The diagram illustrates a pump known as a hydraulic ram. For one pump of this type, the long approach pipe contains $500\,\text{kg}$ of water. When the speed of this water reaches $2.0\,\text{m s}^{-1}$, a valve closes, and the kinetic energy of the water is then used to raise a small amount of water through a height of $15\,\text{m}$. The pump has an efficiency of $10\%$. What mass of water can be raised $15\,\text{m}$?

May/June 2015

A uniform solid block has weight $500\,\text{N}$, width $0.4\,\text{m}$ and height $0.6\,\text{m}$. It is positioned on the edge of a step with depth $0.8\,\text{m}$, as illustrated. The block is pushed over the step edge and turns through $90^{\circ}$ before settling so that the $0.6\,\text{m}$ edge is horizontal. What is the change in gravitational potential energy of the block?

May/June 2015

The diagram illustrates a hydroelectric power station. The reservoir is connected to the turbines by a pipe with a uniform cross-sectional area. Water moves from X to Y at a constant speed. Which statement about the change in the energy of the water as it travels from X to Y is correct?

May/June 2015

A fisherman raises a fish with mass $250\,\text{g}$ from rest by a vertical distance of $1.8\,\text{m}$. The fish reaches a speed of $1.1\,\text{m s}^{-1}$. What energy is gained by the fish?

May/June 2015

Water from a reservoir is delivered to the turbine of a hydroelectric system at a mass flow rate of $500\,\text{kg s}^{-1}$. The reservoir is located $300\,\text{m}$ above the turbine level. The generator driven by the turbine produces an electrical output of $200\,\text{A}$ at a potential difference of $6000\,\text{V}$. Calculate the efficiency of the system.

May/June 2015

An aeroplane, when fully loaded, has a total mass of $1.2 \times 10^5\,\text{kg}$ as it rises after take-off. It is ascending at an angle of $23^\circ$ above the horizontal and moving at a speed of $50\,\text{m s}^{-1}$. What is the rate at which its potential energy is increasing at this moment?

May/June 2015

In an underground station, an escalator is carrying $250$ people while moving at a velocity of $4.3\,\text{m s}^{-1}$. The mean mass of one person is $78\,\text{kg}$, and the escalator is inclined at an angle of $40^\circ$ to the horizontal. What minimum power is needed to raise these people?

May/June 2016

An electric motor that drives a lift delivers an output power of $20\,\text{kW}$. The lift together with its passengers has a total mass of $1500\,\text{kg}$. The motor lifts the lift by a vertical distance of $20\,\text{m}$. How long is required?

May/June 2016

The diagram illustrates the design of a water wheel that turns a generator to generate electrical power. The flow rate of the water is $200\,\text{kg s}^{-1}$. The generator provides a current of $32\,\text{A}$ at a voltage of $230\,\text{V}$. If any change in the kinetic energy of the water is ignored, what is the efficiency of the system?

May/June 2016

Explain the meanings of gravitational potential energy and kinetic energy.

May/June 2016

A man ascends a ladder at a constant, slow pace. What is the principal energy transfer occurring for the man while he climbs?

May/June 2017

A railway engine increases the speed of a train with a total mass of 800 tonnes (1 tonne = 1000 kg) from rest until it reaches $50\,\text{m s}^{-1}$. What amount of useful work has to be carried out on the train for it to attain this speed?

May/June 2017

Water passes from a lake to a turbine positioned a vertical distance of $90\,\text{m}$ beneath the lake surface, as illustrated. The water’s mass flow rate is $2400\,\text{kg min}^{-1}$. The turbine operates with an efficiency of $75\%$. Calculate the output power of the turbine.

May/June 2017

A railway engine speeds up a train with a total mass of $1200$ tonnes ($1\,\text{tonne} = 1000\,\text{kg}$), taking it from rest to $75\,\text{m s}^{-1}$. How much useful work has to be done on the train for it to reach this speed?

May/June 2017

What is the most suitable estimate for the kinetic energy of a family car moving at $50\,\text{km h}^{-1}$?

May/June 2017

A man of mass $80\,\text{kg}$ attaches himself to one end of a rope that passes 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 2017

A train with a mass of $3.3 \times 10^{6}\ \text{kg}$ is travelling at constant speed up a slope that makes an angle of $0.64^{\circ}$ to the horizontal. The train’s engine has a useful output power of $14\ \text{MW}$. Assume that no frictional forces oppose the train’s motion. Calculate the speed of the train.

May/June 2018

A cannon-ball with mass $3.50\ \text{kg}$ is launched at a speed of $22.0\ \text{m s}^{-1}$ from a gun on a ship, positioned at a height of $6.00\ \text{m}$ above sea level. Its total energy is made up of the gravitational potential energy relative to the sea surface and the kinetic energy. Determine the total energy of the cannon-ball as it exits the gun?

May/June 2018

A steel sphere is let go so that it falls straight down onto a level metal plate. It strikes the plate with speed $u$, rebounds from it with speed $v$, and rises vertically to half its initial height. Air resistance is to be ignored. Which expression gives the value of $\frac{v}{u}$?

May/June 2018

A car with mass $500\,\text{kg}$ is stationary at point $X$ on a slope, as illustrated. The car’s brakes are then released, and with the engine turned off the car rolls down the slope. By point $Y$, the car has descended through a vertical height of $30\,\text{m}$ and is travelling at a speed of $11\,\text{m s}^{-1}$. What is the energy dissipated by frictional forces as the car moves from $X$ to $Y$?

May/June 2018

Water from a reservoir is supplied to the turbine in a hydroelectric system at a rate of $510\,\text{kg s}^{-1}$. The reservoir lies $280\,\text{m}$ above the turbine level. The generator, which is driven by the turbine, produces an electrical output of current $205\,\text{A}$ at a potential difference of $5800\,\text{V}$. What is the efficiency of the system?

May/June 2018

A ball is projected straight up into the air. It reaches the highest point of its motion and then starts to move straight downwards. Assume that the ball’s gravitational potential energy is zero at the point where it starts. Which statement about the ball is not correct?

May/June 2018

An upward force of $1000\,\text{N}$ is required to raise the hook of a crane at constant velocity. The crane is then employed to lift a load with mass $1000\,\text{kg}$ at a constant velocity of $0.50\,\text{m s}^{-1}$. What power is required to lift the hook and the load?

May/June 2018

A train on a mountain railway is transporting $200$ people with an average mass of $70\,\text{kg}$ up a slope inclined at $30^\circ$ to the horizontal and moving at a speed of $6.0\,\text{m s}^{-1}$. The train itself has a mass of $80\,000\,\text{kg}$. The fraction of the engine’s power that is used to lift the passengers and the train is $40\%$. What is the power of the engine?

May/June 2019

A student may either run or walk up the stairs to her classroom. Which statement explains how the power needed, and the gravitational potential energy gained, when she runs up the stairs compare with when she walks up them?

May/June 2019

At the surface of a planet, lifting a $1.0\,\text{kg}$ mass through a vertical distance of $10\,\text{m}$ against gravity requires $30\,\text{J}$ of work. What amount of work is required on this planet to lift a $4.0\,\text{kg}$ mass through $5.0\,\text{m}$?

May/June 2019

What is the approximate kinetic energy of an Olympic athlete while sprinting at top speed in a $100\,\text{m}$ race?

May/June 2019

A resultant force $F$ causes an object of mass $m$ to travel a straight-line distance $s$. This force produces acceleration $a$, changing the speed from initial speed $u$ to final speed $v$.

May/June 2019

What would be a sensible estimate for the kinetic energy of a car moving at $30\,\text{m s}^{-1}$?

May/June 2020

A block with weight $80\,\text{N}$ is moved a distance of $60\,\text{cm}$ along a slope that makes an angle of $30^\circ$ with the horizontal. The frictional force between the block and the slope surface is $25\,\text{N}$.\n\nWhat is the work $W_g$ done against the gravitational force and the work $W_f$ done against the frictional force?

May/June 2020

An escalator in an underground station is carrying $25$ people and is travelling at a speed of $4.3\,\text{m s}^{-1}$. The mean mass of a person is $78\,\text{kg}$, and the escalator is at an angle of $40^\circ$ to the horizontal. What is the minimum power needed to lift these people?

May/June 2020

A man is taking part in a race along a straight path. What is an approximate value of his kinetic energy?

May/June 2020

A trolley is initially at rest at X. It moves down to Y and finally stops at Z. Which row could summarise the energy changes during this process?

May/June 2020

Explain what is meant by the term work done.

May/June 2020

A rocket is launched vertically. As it increases speed upward after leaving the launch pad, which energy stores are changing?

May/June 2021

A constant force $F$ is applied to a car of mass $m$, causing it to travel up a slope over a distance $s$ at constant velocity $v$. The angle of the slope to the horizontal is $\alpha$. The acceleration of free fall is $g$. Find the ratio $\frac{\text{gravitational potential energy gained by car}}{\text{work done by force }F}$?

May/June 2021

What would be a sensible estimate of the kinetic energy of an Olympic athlete sprinting in a $100\,\text{m}$ race?

May/June 2021

A car with mass $500\,\text{kg}$ is initially stationary at point X on a slope, as shown. Its brakes are then released and, with the engine switched off, the car rolls downhill. By point Y the car has descended a vertical distance of $30\,\text{m}$ and is travelling at $11\,\text{m s}^{-1}$. Calculate the energy dissipated by frictional forces as the car moves from X to Y?

May/June 2021

A pendulum is made of a solid sphere hanging from a fixed point P by a string, as illustrated in Fig. 3.1. The sphere moves to and fro. At one moment it is at the lowest point X, and its kinetic energy is 0.86\,\text{J} while its momentum is 0.72\,\text{N s} horizontally. After a short interval, it reaches position Y, where it is briefly at rest at the greatest vertical height h above X. The string remains the same length and has negligible mass. Air resistance can be ignored.

May/June 2021

Several objects of unequal mass are positioned on the flat surface of a table. They are then lifted to different heights above the table. Each object has the same increase in gravitational potential energy. Which graph most accurately represents how the height $h$ of the objects above the table changes with their mass $m$?

May/June 2022

A student tries to derive the expression for kinetic energy $E_K$. She starts with an object of mass $m$ that is initially stationary. A constant force $F$ acting on the object makes it accelerate to a final velocity $v$ over a displacement $s$. The kinetic energy gained by the object is equal to the work done on the object by the force $F$. Which equation would the student not need in order to derive the formula for $E_K$?

May/June 2022

The diagram illustrates how a quantity $y$ changes with a quantity $x$ for objects in a uniform gravitational field. What might $x$ and $y$ represent?

May/June 2022

State the definition of power.

May/June 2022

A mass $m$ travels a vertical distance $\Delta h$ in a uniform gravitational field and gains gravitational potential energy $\Delta E_P$. The acceleration of free fall is $g$. Use the idea of work done to show that $\Delta E_P = mg\,\Delta h$.

May/June 2022

A ball is launched straight upwards from the Earth’s surface. Which statement describes the ball’s energy while it moves upward through the air?

May/June 2023

At an airport, luggage is transported by a mechanical arrangement. This arrangement consists of a horizontal conveyor belt, a sloping conveyor belt, a lift and a frictionless slide. A suitcase is carried around the airport by this arrangement. The resistive forces that oppose the motion of the suitcase are negligible. For which movement of the suitcase is the net work done on the suitcase greatest?

May/June 2023

A box with weight $40\,\text{N}$ is moved across level ground through a distance of $2.4\,\text{m}$ by a horizontal force of $20\,\text{N}$. It is then raised vertically at constant velocity by a height of $1.6\,\text{m}$ using a vertical force. What is the total work done on the box by these two forces?

May/June 2024

A steel ball is descending through oil at a constant speed. Which graph shows how the gravitational potential energy $E_p$ and the kinetic energy $E_k$ of the ball change with time?

May/June 2024

A box with weight $W$ is drawn up a slope by a force $P$. The slope has length $d$, and the box gains a vertical height of $h$. The frictional force acting between the box and the slope is $F$. The diagram indicates the directions of the forces. The slope is used to lift the box vertically. Which expression represents the efficiency of the slope?

May/June 2024

A mass of $28\ \text{g}$ is lifted vertically by a distance of $4.6\ \text{m}$. What change occurs in the gravitational potential energy of the mass?

May/June 2024

An object is situated in a uniform gravitational field. The graph indicates how the change in gravitational potential energy $\Delta E_p$ of the object depends on the vertical distance $x$ through which the object is moved from a fixed point. Which graph shows how the gravitational force $F$ acting on the object varies with distance $x$?

May/June 2024