Work and conservation of energy — OCR A-Level Physics
Test yourself on Work and conservation of energy with OCR A-Level practice questions.
7 days Premium · Then free forever · No card, no charge
Work and conservation of energy explained
Work is done when a force moves its point of application through a displacement, and for a constant force in the direction of motion W = Fs, where W is work in joules, F is the force in newtons and s is the displacement in metres.
Read the full explanation
One joule is the work done when a force of one newton moves an object one metre in the direction of the force, so 1 J = 1 N m. If the force acts at an angle θ to the displacement, only the component along the displacement does work, W = Fs cos θ. For example, a 20 N force pushing a box 3.0 m along its direction does W = 20 × 3.0 = 60 J. Work done on an object transfers energy to it, and work done by it transfers energy away.
(b) W = Fx cos i for work done by a force
Work done by a force is the energy transferred when the force moves its point of application. The equation W = Fx cos θ gives the work done when a constant force F acts at an angle θ to the displacement x. The cos θ factor selects the component of force along the displacement. If θ = 0°, cos 0° = 1, so W = Fx. If θ = 90°, cos 90° = 0, so no work is done by that force. If θ = 180°, cos 180° = −1, so W = −Fx, meaning energy is transferred away from the object. Work is a scalar quantity measured in joules (J); 1 J = 1 N m. For example, pulling a box with a 50 N force at 30° to a 4.0 m horizontal displacement gives W = 50 × 4.0 × cos 30° ≈ 173 J. Always resolve the force along the displacement before multiplying.
(c) the principle of conservation of energy
The principle of conservation of energy states that energy cannot be created or destroyed; it can only be transferred from one form to another or from one place to another. The total energy of a closed system remains constant. In mechanics, this means that when energy is transferred between stores, the total before and after is the same, provided no energy is transferred to or from outside the system. For example, a falling ball transfers gravitational potential energy to kinetic energy; if air resistance is negligible, the decrease in potential energy equals the increase in kinetic energy. If friction or air resistance acts, some energy is transferred to thermal energy, but the total energy is still conserved. This principle allows you to set up energy balance equations and solve for unknown speeds, heights or energy transfers.
(d) energy in different forms; transfer and conservation
Energy exists in different forms or stores, including kinetic, gravitational potential, elastic potential, thermal, chemical, nuclear, electrostatic and magnetic. Energy can be transferred between these stores by mechanical work, electrical work, heating or radiation. For example, a stretched spring stores elastic potential energy; when released, it transfers energy to kinetic energy of a moving object and some thermal energy to the surroundings. A battery transfers chemical energy to electrical energy, which can then be transferred to thermal energy in a resistor. In every transfer, the total energy is conserved. To analyse a process, identify the initial store, the transfer pathway and the final store, then apply conservation of energy. Energy transfer diagrams or Sankey diagrams can help visualise the transfers and any energy dissipated to the surroundings.
(e) transfer of energy is equal to work done.
The transfer of energy to or from an object is equal to the work done on or by that object. When a force moves its point of application, the work done by the force equals the energy transferred. For example, lifting a mass m through a height h requires work done against gravity equal to mgh, which equals the increase in gravitational potential energy. Accelerating a body from rest to speed v requires work done equal to ½mv², which equals the increase in kinetic energy. If friction acts, the work done against friction equals the thermal energy transferred to the surroundings. This relationship links mechanics to energy conservation: work is the mechanical transfer of energy, and the total energy transferred equals the work done by all forces. In calculations, equate work done to the change in energy stores.
Your focus
- Define work done by a force and state the equation W = Fs for a constant force along the displacement.
- Define the joule and use 1 J = 1 N m in calculations.
- Calculate work done when a force acts at an angle to the displacement and relate work to energy transfer.
Show all 15 objectives
- Apply W = Fx cos θ to calculate work done by a constant force at an angle to the displacement.
- Identify the correct angle θ between the force and displacement vectors in a given physical situation.
- Interpret the sign of work done as the direction of energy transfer.
- State the principle of conservation of energy accurately.
- Apply the principle to solve problems involving energy transfers in mechanical systems.
- Account for thermal energy transfers when resistive forces are present.
- Identify and name different energy stores and forms.
- Describe energy transfers between stores using appropriate pathways.
- Apply conservation of energy to multi-step transfers, including dissipated energy.
- State that work done equals energy transferred.
- Calculate energy transfers using work done for gravitational, kinetic and frictional processes.
- Apply the relationship between work done and energy transfer to solve mechanics problems.
Work and conservation of energy exam tips
Marking Points
- States that work is done when a force moves its point of application through a displacement.
- Applies W = Fs for a constant force acting along the displacement.
- Defines the joule as the work done by a one-newton force moving an object one metre in the direction of the force, so 1 J = 1 N m.
- Uses W = Fs cos θ when the force is at an angle θ to the displacement.
- Links work done to energy transfer, recognising that work done on an object increases its energy store.
- State that work done equals the product of force, displacement and the cosine of the angle between them: W = Fx cos θ.
- Identify θ as the angle between the force vector and the displacement vector, not the angle to the horizontal unless that is the same direction.
- Use the component of force along the displacement: F cos θ, then multiply by displacement x.
- Recognise that when θ = 90°, cos 90° = 0, so the force does no work on the object.
- Recognise that when θ = 180°, cos 180° = −1, so the work done is negative and energy is transferred away.
- Calculate work in joules using consistent SI units: force in newtons, displacement in metres.
- Substitute values correctly, including evaluating cos θ in degrees or radians as appropriate.
- State that energy cannot be created or destroyed, only transferred between forms or stores.
- State that the total energy of a closed system is constant.
- Apply conservation of energy by equating total energy before and after a process, accounting for all energy transfers.
- Recognise that in the absence of resistive forces, gravitational potential energy lost equals kinetic energy gained for a falling object.
- Recognise that when resistive forces act, some energy is transferred to thermal energy, but the total energy is still conserved.
- Use the principle to set up equations such as mgh = ½mv² for a falling object with no air resistance.
- Identify the system and check whether energy is transferred across its boundary before applying conservation.
- List different forms or stores of energy, such as kinetic, gravitational potential, elastic potential, thermal, chemical, nuclear, electrostatic and magnetic.
- Describe energy transfers between stores, for example gravitational potential to kinetic, or chemical to electrical to thermal.
- State that energy is conserved during any transfer: the total energy before equals the total energy after.
- Identify the transfer pathway, such as mechanical work, electrical work, heating or radiation.
- Use energy transfer diagrams or Sankey diagrams to represent inputs, useful outputs and dissipated energy.
- Recognise that in real transfers, some energy is often dissipated to the surroundings as thermal energy, but the total remains constant.
- Apply conservation of energy to calculate unknown quantities in multi-step transfers.
- State that the work done by a force equals the energy transferred to or from the object.
- Use W = ΔE, where W is work done and ΔE is the change in energy of the system.
- Calculate work done against gravity as mgh, equal to the change in gravitational potential energy.
- Calculate work done to accelerate an object as ½mv², equal to the change in kinetic energy.
- Recognise that work done against friction equals the thermal energy transferred to the surroundings.
- Apply the relationship to solve problems involving forces, distances and energy changes.
- Account for all forces when determining the total work done on an object.
Examiner Tips
- 💡Check that the force and displacement are along the same line; if not, resolve the force before multiplying.
- 💡Write the unit as J and remember 1 J = 1 N m, which helps you check equations by unit analysis.
- 💡For a force perpendicular to the motion, such as a centripetal force, state that no work is done because cos 90° = 0.
- 💡Sketch the force and displacement vectors and mark the angle θ between them before substituting into W = Fx cos θ.
- 💡Check whether the force is constant and the displacement is along a straight line; the equation applies to a constant force over a straight-line displacement.
- 💡If the force and displacement are in the same direction, use W = Fx; if perpendicular, state that no work is done by that force.
- 💡Keep the sign of cos θ: a negative result means energy is transferred away from the object, not that the calculation is wrong.
- 💡State the principle in full when asked, using the wording 'energy cannot be created or destroyed, only transferred'.
- 💡When solving problems, write an energy balance equation: total energy before = total energy after, including all forms.
- 💡If a process involves friction or air resistance, include a thermal energy term in your equation.
- 💡Check that your answer is physically sensible: for example, a speed calculated from energy conservation should not exceed the speed of light or be negative.
- 💡When describing an energy transfer, name the initial store, the pathway and the final store.
- 💡Use a Sankey diagram to show the proportion of energy transferred usefully and dissipated.
- 💡In calculations, write down the conservation of energy equation before substituting numbers.
- 💡Check that all energy forms are accounted for, including thermal energy to the surroundings.
- 💡Write down the energy balance equation: work done = change in energy stores.
- 💡For lifting problems, equate work done to mgh; for acceleration problems, equate work done to ½mv².
- 💡If friction is present, include the work done against friction as a thermal energy transfer.
- 💡Check the sign of work done: positive work increases the object's energy, negative work decreases it.
Common Mistakes
- Using the total force when it acts at an angle: the error is ignoring the direction, and the correction is to use the component along the displacement, F cos θ.
- Treating work as a vector: the error is giving work a direction, and the correction is to recognise that work and energy are scalar quantities measured in joules.
- Assuming a force does work even when there is no displacement: the error is forgetting the displacement condition, and the correction is to note that no work is done if the point of application does not move.
- Using the full force F instead of the component F cos θ when the force is at an angle to the displacement; correct by resolving along the displacement first.
- Taking θ as the angle between the force and the horizontal rather than the angle between the force and the displacement; correct by identifying the displacement direction and measuring the angle from it.
- Forgetting that cos 90° = 0, so a force perpendicular to motion does no work; correct by checking the angle before calculating.
- Treating negative work as impossible or as a mistake; correct by interpreting W = −Fx as energy transferred away from the object, for example by friction.
- Mixing units, such as using force in N and displacement in cm without converting; correct by converting all lengths to metres before multiplying.
- Thinking that energy is 'used up' or disappears; correct by stating that energy is transferred to other forms, often thermal energy to the surroundings.
- Applying conservation of energy without including all energy transfers, such as ignoring thermal energy when friction is present; correct by listing all energy stores and transfers.
- Assuming that mechanical energy (kinetic plus potential) is always conserved; correct by noting that it is only conserved when resistive forces do no work.
- Confusing conservation of energy with conservation of momentum; correct by keeping the two principles separate and applying each where appropriate.
- Forgetting that the principle applies to a closed system; correct by defining the system and checking for external energy transfers.
- Treating energy as a substance that can be used up; correct by describing energy as transferred between stores, with the total conserved.
- Confusing energy forms with energy transfer pathways; correct by distinguishing stores (kinetic, potential, thermal, chemical) from pathways (work, heating, radiation).
- Ignoring dissipated energy in real processes; correct by including thermal energy transferred to the surroundings in energy balance calculations.
- Assuming that energy transfer is always 100% efficient; correct by recognising that some energy is always dissipated in practical devices.
- Mixing up gravitational potential energy and elastic potential energy; correct by identifying the store based on the physical situation.
- Thinking that work done and energy transferred are different quantities; correct by stating that work done is the mechanical transfer of energy, so they are equal.
- Forgetting to include the work done against friction when calculating total energy transfer; correct by adding the thermal energy term.
- Using the wrong energy store when equating work done; correct by identifying the relevant store, such as gravitational potential or kinetic.
- Assuming that work done is always positive; correct by recognising that work done by a force opposite to displacement is negative, reducing the object's energy.
- Confusing work done with power; correct by noting that power is the rate of doing work, not the total work done.