What you'll learn
This topic explores how forces transfer energy when they move objects, a fundamental concept tested across multiple Edexcel GCSE Physics papers. You'll master calculations involving work done, understand the relationship between forces, distance and energy transfer, and apply these principles to real-world contexts from braking cars to lifting mechanisms.
Key terms and definitions
Work done — the energy transferred when a force moves an object through a distance; measured in joules (J).
Force — a push or pull acting on an object, measured in newtons (N); causes acceleration, deformation or energy transfer.
Displacement — the distance moved by an object in the direction of the applied force, measured in metres (m).
Joule — the SI unit of energy and work; one joule equals the work done when a force of one newton moves an object one metre in the direction of the force.
Energy transfer — the process by which energy moves from one store to another or from one object to another when work is done.
Resultant force — the single force that has the same effect as all the forces acting on an object combined.
Gravitational potential energy — energy stored in an object because of its position in a gravitational field; gained when work is done against gravity.
Power — the rate at which energy is transferred or work is done, measured in watts (W).
Core concepts
The relationship between work, force and distance
Work is done whenever a force causes an object to move. The amount of work done depends on two factors: the size of the force applied and the distance the object moves in the direction of that force.
The equation for work done is:
Work done (J) = Force (N) × Distance (m)
W = F × d
This equation appears frequently on Edexcel GCSE papers and applies only when:
- The force acts in the same direction as the movement
- The force remains constant throughout the movement
- Distance refers to displacement in the direction of the force
When a force acts at an angle or perpendicular to the direction of motion, only the component of force in the direction of movement does work. A satellite in circular orbit experiences a centripetal force perpendicular to its motion — this force does no work because there's no displacement in the direction of the force.
Energy transfers when work is done
Work done represents energy transferred from one store to another. Common energy transfers involving work include:
Mechanical work transfers:
- Lifting an object: chemical energy in muscles → gravitational potential energy in the object
- Pushing a box across a floor: chemical energy → kinetic energy + thermal energy (due to friction)
- Stretching a spring: chemical energy → elastic potential energy
Against resistive forces:
- Friction: kinetic energy → thermal energy in surfaces
- Air resistance: kinetic energy → thermal energy in air and object
- Braking: kinetic energy → thermal energy in brake pads
The principle of energy conservation applies: the total energy before equals the total energy after, though some energy often dissipates to thermal stores due to resistive forces.
Calculating work done in different contexts
Lifting objects vertically:
When you lift an object at constant speed, you do work against gravity. The force required equals the object's weight:
Force = mass × gravitational field strength (F = m × g)
Work done = m × g × h
Where h is the vertical height gained. This work increases the object's gravitational potential energy store.
Moving objects horizontally:
When pushing an object across a surface at constant speed, the applied force equals the friction force. All work done transfers to thermal energy:
Work done against friction = friction force × distance moved
Accelerating objects:
When a resultant force accelerates an object, work done increases the kinetic energy store:
Work done by resultant force = change in kinetic energy = ½mv² - ½mu²
Where u is initial velocity and v is final velocity.
The work-energy principle
The work-energy principle states that the work done by the resultant force on an object equals its change in kinetic energy. This principle helps solve problems involving multiple forces:
- Calculate the resultant force (sum of all forces considering direction)
- Calculate work done by this resultant force: W = F × d
- This work equals the change in kinetic energy
Example: A car accelerates along a level road. The engine provides 5000 N forward thrust, while resistive forces total 1500 N. Over 100 m:
Resultant force = 5000 - 1500 = 3500 N
Work done by resultant force = 3500 × 100 = 350,000 J
This 350 kJ increases the car's kinetic energy.
Work done by varying forces
The GCSE specification requires understanding that when forces vary, work done can be found from the area under a force-distance graph. This appears in contexts such as:
Stretching springs: Force increases linearly with extension (Hooke's law). The work done equals the area of the triangle under the force-extension graph:
Work done = ½ × maximum force × extension = ½ F × x
This work transfers to the elastic potential energy store.
Non-linear relationships: Some materials don't obey Hooke's law. The area under the curve still represents work done, but calculations may require counting squares on graph paper.
Power and work
Power measures how quickly work is done or energy is transferred:
Power (W) = Work done (J) ÷ Time (s)
P = W ÷ t
Alternatively, for objects moving at constant speed:
Power = Force × velocity
P = F × v
This equation proves useful for vehicles moving at steady speed where driving force equals resistive forces.
A 60 W light bulb transfers 60 J of energy every second. A 1500 W kettle does work (heating water) 25 times faster than the bulb.
Worked examples
Example 1: Lifting a load (Foundation/Higher tier)
Question: A crane lifts a 2500 kg steel beam vertically upwards through 15 m at constant speed. Calculate the work done by the crane. (g = 10 N/kg) [3 marks]
Solution:
Step 1: Calculate the weight of the beam (force required)
Force = mass × gravitational field strength
F = 2500 × 10 = 25,000 N ✓
Step 2: Calculate work done
Work done = force × distance
W = 25,000 × 15 ✓
W = 375,000 J or 375 kJ ✓
Mark scheme points:
- Correct calculation of weight (1 mark)
- Correct substitution into work equation (1 mark)
- Correct answer with unit (1 mark)
Example 2: Work against friction (Higher tier)
Question: A 1200 kg car brakes and decelerates uniformly from 25 m/s to rest over a distance of 80 m.
(a) Calculate the work done by the braking force. [3 marks] (b) Calculate the average braking force. [2 marks]
Solution:
(a) The work done removes the car's kinetic energy.
Initial kinetic energy = ½mv²
KE = ½ × 1200 × 25² ✓
KE = ½ × 1200 × 625 = 375,000 J ✓
Work done by brakes = 375,000 J or 375 kJ ✓
(b) Using W = F × d
375,000 = F × 80 ✓
F = 375,000 ÷ 80 = 4687.5 N or 4700 N (2 s.f.) ✓
Mark scheme points:
- (a) Correct kinetic energy equation used (1 mark)
- Correct calculation (1 mark)
- Correct answer with unit (1 mark)
- (b) Correct rearrangement (1 mark)
- Correct answer (1 mark)
Example 3: Power calculation (Foundation/Higher tier)
Question: An electric motor does 45,000 J of work lifting boxes in 30 seconds.
(a) Calculate the power of the motor. [2 marks] (b) A more powerful motor transfers energy at 2000 W. How long would it take to do the same work? [2 marks]
Solution:
(a) Power = work done ÷ time
P = 45,000 ÷ 30 ✓
P = 1500 W ✓
(b) Rearranging: time = work done ÷ power
t = 45,000 ÷ 2000 ✓
t = 22.5 s ✓
Common mistakes and how to avoid them
• Mistake: Using distance travelled instead of displacement in the direction of the force. Correction: Work is only done when movement occurs in the direction of the applied force. If you push horizontally on a wall and it doesn't move, zero work is done regardless of how hard you push.
• Mistake: Forgetting that work done equals energy transferred, treating them as separate concepts. Correction: Work and energy transfer are equivalent — 500 J of work means 500 J of energy has moved from one store to another. Always identify which energy stores are involved.
• Mistake: Confusing force with work done, especially stating units incorrectly (e.g., "work = 500 N"). Correction: Force is measured in newtons (N), work is measured in joules (J). You must multiply force by distance to find work: W = F × d.
• Mistake: Calculating work done using the applied force when multiple forces act, instead of using the resultant force for kinetic energy changes. Correction: When finding change in kinetic energy, use the resultant force. When finding total work done by one specific force (like friction), use that individual force value.
• Mistake: Omitting units or using incorrect units in final answers. Correction: Work is always in joules (J) or kilojoules (kJ). Power is in watts (W) or kilowatts (kW). Include units in your final answer — many mark schemes award a separate mark for correct units.
• Mistake: Assuming all work done increases kinetic energy, ignoring energy dissipated by friction. Correction: When friction acts, some work transfers to thermal energy stores. Only work done by the resultant force changes kinetic energy. Always account for resistive forces.
Exam technique for "Energy and Forces Doing Work"
• Command word "Calculate" requires you to show numerical working. Edexcel mark schemes typically award one mark for correct equation/method, one for substitution, and one for the answer with units. Never write just a final number — always show: equation, substitution with units, answer with units.
• "Describe the energy transfers" questions (usually 2-3 marks) require you to name specific energy stores and state clearly where energy moves from and to. Use precise terminology: "kinetic energy store", "gravitational potential energy store", "thermal energy store" rather than vague phrases like "movement energy" or "heat energy".
• Multi-step problems often combine work calculations with other equations (like kinetic energy, power, or speed calculations). Read the question carefully to identify which quantities you have and which equation links them. Write down known values before selecting your equation.
• Rearranging equations is essential for higher marks. If asked to find distance when given work and force, rearrange W = F × d to give d = W ÷ F. Show this rearrangement in your working. Marks are often awarded for correct method even if the final numerical answer contains an arithmetic error.
Quick revision summary
Work done (measured in joules) occurs when a force moves an object: W = F × d. This transfers energy between stores — lifting increases gravitational potential energy, friction converts kinetic to thermal energy. Only force components in the direction of movement do work. The work-energy principle states work done by the resultant force equals change in kinetic energy. For springs, work done equals ½Fx. Power measures the rate of doing work: P = W ÷ t or P = Fv. Always show working, include units, and identify energy stores clearly in exam answers.