Energy & Fields: stores, work, fields and power
Key idea: Track energy transfers consistently, connect work to kinetic and potential-energy change, then apply power and efficiency.
Before you start: Forces & DynamicsMotion & Forces
By the end, you can
- Describe energy stores and transfers and apply conservation of energy.
- Define work, derive kinetic energy from work and uniformly accelerated motion, and use Eₖ = ½mv².
- Represent gravitational and electric fields and relate field work to potential-energy change.
- Distinguish gravitational, electric and elastic potential energy and use force–extension graph area.
- Apply energy-transfer rate, mechanical power and efficiency, including practical energy losses.
Starting-point self-check
1. Check your starting point
Attempt all three groups without notes and mark the first equation or energy transfer you could not justify. Use the recorded topic diagnostic above when you want scoring and a personalised repair plan.
Potential energy, power and efficiency 4(j)–(n)
Question 1
A spring’s force rises linearly from 0 to 40 N over 0.20 m. Find its elastic potential energy. Name the other two potential-energy types in Topic 4.
Check the model response
Elastic energy is graph area = ½(40)(0.20) = 4.0 J. The other types are gravitational and electric potential energy.
Question 2
A motor receives 500 W and delivers a 350 N force at 1.0 m s⁻¹ in the force direction. Find useful power and efficiency.
Check the model response
Mechanical power = Fv = 350 W. Efficiency = useful output/input = 350/500 = 0.70 or 70%.
repair
2. Repair the six common breaks
Use only the repair matching an error, then repeat the corresponding diagnostic model.
Potential energy, power and efficiency 4(j)–(n)
Check this idea
Misconception: Elastic energy is always force multiplied by extension.
Repair: Elastic energy is the area under the force–extension graph. The triangular result ½Fx applies only to a straight line from the origin.
Check this idea
Misconception: Efficiency is useful output divided by wasted output.
Repair: Efficiency is useful output divided by total input, using energy or power consistently. It cannot exceed 1 or 100%.
worked example
3. Follow three worked models
Track the system, transfer, direction and graph area before substituting values.
Potential energy, power and efficiency 4(j)–(n)
Model 1
A nonlinear force–extension graph is a triangle from 0 to 0.10 m and 30 N, then a trapezium to 0.16 m and 42 N. Find stored elastic energy.
Check the model response
Energy is total area: ½(0.10)(30) + ½(30 + 42)(0.06) = 1.50 + 2.16 = 3.66 J. Do not use ½Fx for the whole nonlinear graph.
guided practice
4. Guided practice
Use each hint only to select the governing relationship.
Potential energy, power and efficiency 4(j)–(n)
Question 1
A 600 N force drives a vehicle at 12 m s⁻¹ in the same direction. Its engine input is 9.0 kW. Find mechanical power and efficiency.
Hint: Calculate Fv before comparing output with input.
Check the model response
Useful power = Fv = 600(12) = 7200 W. Efficiency = 7200/9000 = 0.80 or 80%.
independent practice
5. Independent practice
Solve without repair notes and state every energy store, transfer and sign convention used.
Potential energy, power and efficiency 4(j)–(n)
Question 1
Distinguish gravitational, electric and elastic potential energy. Then explain why a 65%-efficient device still conserves energy.
Check the model response
They arise from position in gravitational or electric interactions, or deformation of a material. At 65% efficiency, 65% of input reaches the useful output and 35% reaches less useful stores; total energy remains conserved.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Potential energy, power and efficiency 4(j)–(n)
Question 1
A motor receives 1.5 kW and pulls with 180 N at 6.0 m s⁻¹. Find useful power, efficiency and wasted energy transferred in 20 s.
Check the model response
Useful power = Fv = 1080 W. Efficiency = 1080/1500 = 0.72 or 72%. Wasted power = 420 W, so wasted energy in 20 s is 8400 J.
Re-test practice
7. Delayed re-test practice
Return after at least three days and solve these fresh contexts without reopening earlier responses. The recorded plan enforces the delay and uses a separate re-test family for selected-response skill-group evidence.
Potential energy, power and efficiency 4(j)–(n)
Question 1
A spring graph is linear to 24 N at 0.12 m. It releases all stored energy to a 0.18 kg cart. Find the energy and cart speed.
Check the model response
Elastic energy = graph area = ½(24)(0.12) = 1.44 J. With 1.44 = ½(0.18)v², v = 4.0 m s⁻¹.