Cambridge O Level Physics · Syllabus 5054 · Motion, Forces and Energy

Efficiency

What is Efficiency?

Efficiency is the useful energy output divided by the total energy input, or equivalently the useful power output divided by the total power input, and may be given as a percentage by multiplying by 100. It has no unit and can never exceed 100 per cent.

This definition is part of the Motion, Forces and Energy chapter in Cambridge O Level Physics.

Efficiency in context

Energy is stored as kinetic, gravitational potential, chemical, elastic (strain), nuclear, electrostatic or internal (thermal), and it moves between those stores along four pathways: mechanical work done by forces, electrical work done by currents, heating, and electromagnetic, sound and other waves. Energy is never created or destroyed — the total is always conserved — but not all of it ends up where you wanted it, and efficiency measures the fraction that does. Power measures how quickly the transfer happens.

Common mistakes with Efficiency

Error Correction Common-Mistake Clinic Twenty-five statements that sound reasonable and are wrong. Each entry gives the correction, a sentence you can safely write in an answer, and a one-line check. Work through them with the answers covered: if you can produce the correction and the check unprompted, that misconception is fixed. The twenty-five Topic 1 misconceptions #The claim — and why it is wrongThe corrected modelExam-safe sentenceQuick check 1 “Distance and displacement are interchangeable.” They agree only for motion in a straight line without reversing. Distance is the total path length, a scalar. Displacement is the straight-line change in position, a vector with a direction. “The distance travelled is \(14\ \mathrm{km}\), but the displacement is \(10\ \mathrm{km}\) on a bearing of \(037^\circ\).” A runner completes one lap of a \(400\ \mathrm{m}\) track. Distance? Displacement? (\(400\ \mathrm{m}\); zero.) 2 “Speed and velocity mean the same thing.” Everyday speech treats them as synonyms; physics does not. Speed is distance per unit time, a scalar. Velocity is change in displacement per unit time, a vector. “The car travels at a constant speed of \(15\ \mathrm{m/s}\), but its velocity changes because it goes round a bend.” Can an object move at constant speed and still be accelerating? (Yes — if it changes direction.) 3 “Negative acceleration always means slowing down.” The sign refers to a chosen axis, not to speeding up or slowing down. An object slows down when acceleration and velocity have opposite signs. If both are negative, it speeds up in the negative direction. “The acceleration is \(-9.8\ \mathrm{m/s^2}\) throughout, so the ball slows on the way up and speeds up on the way down.” A ball falls with \(a = -9.8\ \mathrm{m/s^2}\) and \(v\) negative. Speeding up or slowing down? (Speeding up.) 4 “A flat distance–time graph means constant speed.” The two motion graphs use the same shape for different meanings. Flat on a distance–time graph means the distance is not changing, so the object is at rest. Flat on a speed–time graph means constant speed. “Between \(10\ \mathrm{s}\) and \(18\ \mathrm{s}\) the distance does not change, so the object is stationary.” What does a horizontal line mean on each of the two graphs? (At rest; constant speed.) 5 “Area under a distance–time graph gives distance.” That area has units of metre-seconds and no physical meaning here. Distance is read directly off the vertical axis of a distance–time graph. Area gives distance only under a speed–time graph. “The distance at \(t = 20\ \mathrm{s}\) is read from the graph as \(40\ \mathrm{m}\).” Multiply the axis units of a distance–time graph together. Is the result a quantity you use? (m s — no.) 6 “Zero resultant force means no forces act.” Balanced is not the same as absent. A zero resultant means the forces present cancel. A book on a table has two forces of equal size acting on it. “The forces are balanced, so the resultant force is zero and the velocity does not change.” How many forces act on a book resting on a table? (Two: weight and contact force.) 7 “A moving object needs a forward resultant force.” This is the pre-Newtonian intuition that motion needs a cause. A resultant force is needed to change motion, not to maintain it. At constant velocity the resultant is zero. “The driving force equals the resistive forces, so the resultant force is zero and the car travels at constant speed.” What is the resultant force on a parachutist at terminal velocity? (Zero.) 8 “Mass and weight use the same unit.” Everyday language says “a kilogram in weight”. Mass is in kilograms; weight is a force in newtons. They are linked by \(W = mg\) but are different quantities. “The mass is \(2.5\ \mathrm{kg}\) and the weight is \(24.5\ \mathrm{N}\).” Give the unit of each. (kg; N.) 9 “Mass changes on the Moon.” It confuses the pull of gravity with the matter present. Mass measures the quantity of matter and is unchanged. Only the weight changes, because \(g\) is smaller. “The mass is unchanged at \(2.5\ \mathrm{kg}\); the weight falls from \(24.5\ \mathrm{N}\) to \(4.0\ \mathrm{N}\) because \(g\) is smaller.” An astronaut floats in orbit. Has their mass changed? (No — they are in continuous free fall.) 10 “Heavy objects always fall faster.” True for a feather and a hammer in air, and false for both in a vacuum. With air resistance negligible, \(a = W/m = mg/m = g\): the mass cancels, so all objects accelerate equally. Differences in air come from drag, not from weight. “Both balls have the same acceleration \(g\), because the mass cancels in \(a = mg/m\).” Why do a coin and a feather land together in an evacuated tube? (No air resistance, so only weight acts and \(a = g\) for both.) 11 “Heavy objects always sink.” A steel ship weighs thousands of tonnes and floats. Whether an object floats depends on its average density compared with that of the liquid, not on its weight. “The stone sank, so its density must be greater than \(1000\ \mathrm{kg/m^3}\).” Why does a steel ship float? (Its average density, including the enclosed air, is less than that of water.) 12 “Friction is always unwanted.” Without it you could not walk, drive, brake or tie a knot. Friction is useful in brakes, tyres, shoes, knots and screws, and unwanted in bearings and engines where it wastes energy by heating. “Friction between the tyres and the road is what provides the force that accelerates and steers the car.” Name one useful and one unwanted effect of friction. (Brakes work; engine parts wear and heat.) 13 “Friction always opposes an object's overall motion.” It opposes the relative sliding of the surfaces. A walker's sole tries to slide backwards, so friction on the shoe acts forwards. The same is true of a car's driving wheels. “The tyre pushes backwards on the road, so friction from the road on the tyre acts forwards and drives the car.” Which way does friction act on a walker's shoe? (Forwards.) 14 “The elastic limit and the limit of proportionality are automatically identical.” They are different ideas, and this syllabus requires only one of them. The limit of proportionality is where the load–extension graph stops being a straight line. This syllabus states that an understanding of the elastic limit is not required, so do not use the two terms as synonyms. “Point P is the limit of proportionality, because beyond it the graph is no longer a straight line.” Which point does the syllabus ask you to identify on a load–extension graph? (The limit of proportionality.) 15 “The extension is the length of the stretched spring.” A frequent slip that makes every spring constant wrong. Extension \(=\) stretched length \(-\) original unloaded length. “\(x = 23.0 - 15.0 = 8.0\ \mathrm{cm}\), so \(k = 4.0/0.080 = 50\ \mathrm{N/m}\).” Which reading must you take before adding any load? (The unloaded length.) 16 “An outward force keeps an object moving in a circle.” The sensation of being thrown outwards is real; the outward force is not. The resultant force acts towards the centre, perpendicular to the velocity. Remove it and the object continues along the tangent. “The tension provides a resultant force towards the centre, which changes the direction of the velocity but not its magnitude.” The string breaks. Which way does the ball go? (Straight on, along the tangent.) 17 “Moment uses the distance to the force arrow.” It uses the perpendicular distance to the line of action. Extend the force's line of action and measure the perpendicular distance from the pivot to that line. If the line passes through the pivot, the moment is zero. “Moment \(=\) force \(\times\) perpendicular distance from the pivot to the line of action of the force.” Why does pushing a door at the hinge not open it? (The perpendicular distance is zero.) 18 “A low centre of gravity alone guarantees stability.” A coin on its edge has a low centre of gravity and falls over instantly. Stability depends on both the height of the centre of gravity and the width of the base: together they decide how far the object must tilt before the weight line leaves the base. “The wider base and lower centre of gravity together mean the bus must tilt much further before it topples.” Name the two design changes that make a vehicle more stable. (Lower centre of gravity; wider wheelbase.) 19 “Momentum is conserved for each object separately.” Each object's momentum usually changes a great deal. The total momentum of the isolated system is conserved. What one object loses, the other gains. “Total momentum before \(=\) total momentum after, because no external resultant force acts on the system.” Trolley A loses \(0.72\ \mathrm{kg\,m/s}\). What does B gain? (\(0.72\ \mathrm{kg\,m/s}\).) 20 “Momentum conservation means kinetic energy is conserved.” Two different quantities obeying two different rules. Momentum is conserved in every isolated-system collision. Kinetic energy is conserved only in a perfectly elastic one, and never when objects stick together or deform. “Momentum is conserved; kinetic energy is not, because some is transferred to internal energy and sound as the trolleys deform.” Two trolleys stick together. Is kinetic energy conserved? (No.) 21 “Airbags reduce the momentum change.” The passenger stops either way, so \(\Delta p\) is fixed by the crash. The airbag increases the time over which the momentum change happens, and \(F = \Delta p/\Delta t\) then gives a smaller average force. “The airbag increases the time taken to stop, so for the same change of momentum the average force on the passenger is smaller.” \(\Delta p = 1500\ \mathrm{kg\,m/s}\) in \(0.020\ \mathrm{s}\), then in \(0.20\ \mathrm{s}\). Compare the forces. (\(75\,000\ \mathrm{N}\); \(7500\ \mathrm{N}\).) 22 “Energy is used up.” Conservation of energy says the total never changes. Energy is transferred and dissipated, never destroyed. “Wasted” energy has moved to a less useful store, usually the internal energy of the surroundings. “The energy has been transferred to the internal energy of the brakes and the surrounding air, and to sound.” Where is the energy after a bouncing ball stops? (Internal energy of ball, floor and air, plus sound.) 23 “Power and energy are the same.” One says how much, the other how fast. Energy is measured in joules; power is the rate of transfer, measured in watts, where \(1\ \mathrm{W} = 1\ \mathrm{J/s}\). “Both motors do \(1200\ \mathrm{J}\) of work, but the one that takes \(3.0\ \mathrm{s}\) has four times the power of the one that takes \(12\ \mathrm{s}\).” Give the unit of each. (J; W.) 24 “Efficiency can exceed 100%.” That would mean creating energy. The useful output is only part of the total input, and by conservation the outputs sum to the input, so the ratio cannot exceed \(1\). “Efficiency \(= 9/60 = 0.15\), which is \(15\%\).” A calculation gives \(667\%\). What has gone wrong? (The fraction is upside down.) 25 “Renewable energy has no environmental impact.” Renewable describes the supply, not the impact. Every resource has some impact: dams flood valleys, turbines occupy land and affect birds, barrages alter estuaries, and panels must be manufactured and disposed of. “Wind is renewable and releases no combustion products in use, but the turbines have a visual and noise impact and the output cannot be scheduled.” Name one environmental drawback of hydroelectric power. (A valley is flooded, destroying habitats.) Two more, on pressure — the pair that most often appear together The claim — and why it is wrongThe corrected modelExam-safe sentenceQuick check “A larger area produces a larger pressure for the same force.” The relationship is inverted: \(p = F/A\). With the force fixed, a larger area gives a smaller pressure. That is exactly why snowshoes, skis and wide tyres work, and why a drawing pin has a point. “The weight is unchanged but the contact area is larger, so the pressure on the snow is smaller and the wearer does not sink in.” Flat shoes or stilettos: which gives the greater pressure on a floor? (Stilettos — far smaller area.) “Liquid pressure depends on the shape of the container.” \(\Delta p = \rho g \Delta h\) contains no width, area or volume. Only the vertical depth and the density matter. A wide tank has a greater total force on its base than a narrow tube, but only because the base has a larger area — the pressure at a given depth is identical. “The pressure depends only on the depth and the density of the liquid, so it is the same at that level in all three vessels.” Two connected vessels of different width hold water. At what levels does it settle? (The same level in both.) How to use this clinic: cover the right-hand three columns and read only the claim. If you can produce the correction, the exam-safe sentence and the check from memory, move on. If you cannot, go back to the section that teaches it — re-reading the correction alone does not fix a misconception, retrieving it does.

Last reviewed 2 Sept 2026Syllabus 2026-2028

What is Efficiency?

Efficiency in context

Common mistakes with Efficiency

Error Correction Common-Mistake Clinic Twenty-five statements that sound reasonable and are wrong. Each entry gives the correction, a sentence you can safely write in an answer, and a one-line check. Work through them with the answers covered: if you can produce the correction and the check unprompted, that misconception is fixed. The twenty-five Topic 1 misconceptions #The claim — and why it is wrongThe corrected modelExam-safe sentenceQuick check 1 “Distance and displacement are interchangeable.” They agree only for motion in a straight line without reversing. Distance is the total path length, a scalar. Displacement is the straight-line change in position, a vector with a direction. “The distance travelled is \(14\ \mathrm{km}\), but the displacement is \(10\ \mathrm{km}\) on a bearing of \(037^\circ\).” A runner completes one lap of a \(400\ \mathrm{m}\) track. Distance? Displacement? (\(400\ \mathrm{m}\); zero.) 2 “Speed and velocity mean the same thing.” Everyday speech treats them as synonyms; physics does not. Speed is distance per unit time, a scalar. Velocity is change in displacement per unit time, a vector. “The car travels at a constant speed of \(15\ \mathrm{m/s}\), but its velocity changes because it goes round a bend.” Can an object move at constant speed and still be accelerating? (Yes — if it changes direction.) 3 “Negative acceleration always means slowing down.” The sign refers to a chosen axis, not to speeding up or slowing down. An object slows down when acceleration and velocity have opposite signs. If both are negative, it speeds up in the negative direction. “The acceleration is \(-9.8\ \mathrm{m/s^2}\) throughout, so the ball slows on the way up and speeds up on the way down.” A ball falls with \(a = -9.8\ \mathrm{m/s^2}\) and \(v\) negative. Speeding up or slowing down? (Speeding up.) 4 “A flat distance–time graph means constant speed.” The two motion graphs use the same shape for different meanings. Flat on a distance–time graph means the distance is not changing, so the object is at rest. Flat on a speed–time graph means constant speed. “Between \(10\ \mathrm{s}\) and \(18\ \mathrm{s}\) the distance does not change, so the object is stationary.” What does a horizontal line mean on each of the two graphs? (At rest; constant speed.) 5 “Area under a distance–time graph gives distance.” That area has units of metre-seconds and no physical meaning here. Distance is read directly off the vertical axis of a distance–time graph. Area gives distance only under a speed–time graph. “The distance at \(t = 20\ \mathrm{s}\) is read from the graph as \(40\ \mathrm{m}\).” Multiply the axis units of a distance–time graph together. Is the result a quantity you use? (m s — no.) 6 “Zero resultant force means no forces act.” Balanced is not the same as absent. A zero resultant means the forces present cancel. A book on a table has two forces of equal size acting on it. “The forces are balanced, so the resultant force is zero and the velocity does not change.” How many forces act on a book resting on a table? (Two: weight and contact force.) 7 “A moving object needs a forward resultant force.” This is the pre-Newtonian intuition that motion needs a cause. A resultant force is needed to change motion, not to maintain it. At constant velocity the resultant is zero. “The driving force equals the resistive forces, so the resultant force is zero and the car travels at constant speed.” What is the resultant force on a parachutist at terminal velocity? (Zero.) 8 “Mass and weight use the same unit.” Everyday language says “a kilogram in weight”. Mass is in kilograms; weight is a force in newtons. They are linked by \(W = mg\) but are different quantities. “The mass is \(2.5\ \mathrm{kg}\) and the weight is \(24.5\ \mathrm{N}\).” Give the unit of each. (kg; N.) 9 “Mass changes on the Moon.” It confuses the pull of gravity with the matter present. Mass measures the quantity of matter and is unchanged. Only the weight changes, because \(g\) is smaller. “The mass is unchanged at \(2.5\ \mathrm{kg}\); the weight falls from \(24.5\ \mathrm{N}\) to \(4.0\ \mathrm{N}\) because \(g\) is smaller.” An astronaut floats in orbit. Has their mass changed? (No — they are in continuous free fall.) 10 “Heavy objects always fall faster.” True for a feather and a hammer in air, and false for both in a vacuum. With air resistance negligible, \(a = W/m = mg/m = g\): the mass cancels, so all objects accelerate equally. Differences in air come from drag, not from weight. “Both balls have the same acceleration \(g\), because the mass cancels in \(a = mg/m\).” Why do a coin and a feather land together in an evacuated tube? (No air resistance, so only weight acts and \(a = g\) for both.) 11 “Heavy objects always sink.” A steel ship weighs thousands of tonnes and floats. Whether an object floats depends on its average density compared with that of the liquid, not on its weight. “The stone sank, so its density must be greater than \(1000\ \mathrm{kg/m^3}\).” Why does a steel ship float? (Its average density, including the enclosed air, is less than that of water.) 12 “Friction is always unwanted.” Without it you could not walk, drive, brake or tie a knot. Friction is useful in brakes, tyres, shoes, knots and screws, and unwanted in bearings and engines where it wastes energy by heating. “Friction between the tyres and the road is what provides the force that accelerates and steers the car.” Name one useful and one unwanted effect of friction. (Brakes work; engine parts wear and heat.) 13 “Friction always opposes an object's overall motion.” It opposes the relative sliding of the surfaces. A walker's sole tries to slide backwards, so friction on the shoe acts forwards. The same is true of a car's driving wheels. “The tyre pushes backwards on the road, so friction from the road on the tyre acts forwards and drives the car.” Which way does friction act on a walker's shoe? (Forwards.) 14 “The elastic limit and the limit of proportionality are automatically identical.” They are different ideas, and this syllabus requires only one of them. The limit of proportionality is where the load–extension graph stops being a straight line. This syllabus states that an understanding of the elastic limit is not required, so do not use the two terms as synonyms. “Point P is the limit of proportionality, because beyond it the graph is no longer a straight line.” Which point does the syllabus ask you to identify on a load–extension graph? (The limit of proportionality.) 15 “The extension is the length of the stretched spring.” A frequent slip that makes every spring constant wrong. Extension \(=\) stretched length \(-\) original unloaded length. “\(x = 23.0 - 15.0 = 8.0\ \mathrm{cm}\), so \(k = 4.0/0.080 = 50\ \mathrm{N/m}\).” Which reading must you take before adding any load? (The unloaded length.) 16 “An outward force keeps an object moving in a circle.” The sensation of being thrown outwards is real; the outward force is not. The resultant force acts towards the centre, perpendicular to the velocity. Remove it and the object continues along the tangent. “The tension provides a resultant force towards the centre, which changes the direction of the velocity but not its magnitude.” The string breaks. Which way does the ball go? (Straight on, along the tangent.) 17 “Moment uses the distance to the force arrow.” It uses the perpendicular distance to the line of action. Extend the force's line of action and measure the perpendicular distance from the pivot to that line. If the line passes through the pivot, the moment is zero. “Moment \(=\) force \(\times\) perpendicular distance from the pivot to the line of action of the force.” Why does pushing a door at the hinge not open it? (The perpendicular distance is zero.) 18 “A low centre of gravity alone guarantees stability.” A coin on its edge has a low centre of gravity and falls over instantly. Stability depends on both the height of the centre of gravity and the width of the base: together they decide how far the object must tilt before the weight line leaves the base. “The wider base and lower centre of gravity together mean the bus must tilt much further before it topples.” Name the two design changes that make a vehicle more stable. (Lower centre of gravity; wider wheelbase.) 19 “Momentum is conserved for each object separately.” Each object's momentum usually changes a great deal. The total momentum of the isolated system is conserved. What one object loses, the other gains. “Total momentum before \(=\) total momentum after, because no external resultant force acts on the system.” Trolley A loses \(0.72\ \mathrm{kg\,m/s}\). What does B gain? (\(0.72\ \mathrm{kg\,m/s}\).) 20 “Momentum conservation means kinetic energy is conserved.” Two different quantities obeying two different rules. Momentum is conserved in every isolated-system collision. Kinetic energy is conserved only in a perfectly elastic one, and never when objects stick together or deform. “Momentum is conserved; kinetic energy is not, because some is transferred to internal energy and sound as the trolleys deform.” Two trolleys stick together. Is kinetic energy conserved? (No.) 21 “Airbags reduce the momentum change.” The passenger stops either way, so \(\Delta p\) is fixed by the crash. The airbag increases the time over which the momentum change happens, and \(F = \Delta p/\Delta t\) then gives a smaller average force. “The airbag increases the time taken to stop, so for the same change of momentum the average force on the passenger is smaller.” \(\Delta p = 1500\ \mathrm{kg\,m/s}\) in \(0.020\ \mathrm{s}\), then in \(0.20\ \mathrm{s}\). Compare the forces. (\(75\,000\ \mathrm{N}\); \(7500\ \mathrm{N}\).) 22 “Energy is used up.” Conservation of energy says the total never changes. Energy is transferred and dissipated, never destroyed. “Wasted” energy has moved to a less useful store, usually the internal energy of the surroundings. “The energy has been transferred to the internal energy of the brakes and the surrounding air, and to sound.” Where is the energy after a bouncing ball stops? (Internal energy of ball, floor and air, plus sound.) 23 “Power and energy are the same.” One says how much, the other how fast. Energy is measured in joules; power is the rate of transfer, measured in watts, where \(1\ \mathrm{W} = 1\ \mathrm{J/s}\). “Both motors do \(1200\ \mathrm{J}\) of work, but the one that takes \(3.0\ \mathrm{s}\) has four times the power of the one that takes \(12\ \mathrm{s}\).” Give the unit of each. (J; W.) 24 “Efficiency can exceed 100%.” That would mean creating energy. The useful output is only part of the total input, and by conservation the outputs sum to the input, so the ratio cannot exceed \(1\). “Efficiency \(= 9/60 = 0.15\), which is \(15\%\).” A calculation gives \(667\%\). What has gone wrong? (The fraction is upside down.) 25 “Renewable energy has no environmental impact.” Renewable describes the supply, not the impact. Every resource has some impact: dams flood valleys, turbines occupy land and affect birds, barrages alter estuaries, and panels must be manufactured and disposed of. “Wind is renewable and releases no combustion products in use, but the turbines have a visual and noise impact and the output cannot be scheduled.” Name one environmental drawback of hydroelectric power. (A valley is flooded, destroying habitats.) Two more, on pressure — the pair that most often appear together The claim — and why it is wrongThe corrected modelExam-safe sentenceQuick check “A larger area produces a larger pressure for the same force.” The relationship is inverted: \(p = F/A\). With the force fixed, a larger area gives a smaller pressure. That is exactly why snowshoes, skis and wide tyres work, and why a drawing pin has a point. “The weight is unchanged but the contact area is larger, so the pressure on the snow is smaller and the wearer does not sink in.” Flat shoes or stilettos: which gives the greater pressure on a floor? (Stilettos — far smaller area.) “Liquid pressure depends on the shape of the container.” \(\Delta p = \rho g \Delta h\) contains no width, area or volume. Only the vertical depth and the density matter. A wide tank has a greater total force on its base than a narrow tube, but only because the base has a larger area — the pressure at a given depth is identical. “The pressure depends only on the depth and the density of the liquid, so it is the same at that level in all three vessels.” Two connected vessels of different width hold water. At what levels does it settle? (The same level in both.) How to use this clinic: cover the right-hand three columns and read only the claim. If you can produce the correction, the exam-safe sentence and the check from memory, move on. If you cannot, go back to the section that teaches it — re-reading the correction alone does not fix a misconception, retrieving it does.

What is Efficiency?

Efficiency in context

Concepts related to Efficiency

Common mistakes with Efficiency

What is Efficiency?

Efficiency in context

Concepts related to Efficiency

Common mistakes with Efficiency