Physics · Paper 2

CP7 · Energy — forces doing workTopic 8 — Energy - Forces doing work

Work done, kinetic and gravitational energy, power and efficiency.

Revise the key ideas

Forces doing work

  • When a force moves an object through a distance in its direction, it transfers energy mechanically. This energy transfer is called work done and is measured in joules (J).
  • For a constant force acting along the movement, work done = force × distance moved in the direction of the force, E = Fd. Use force in N and distance in m; 1 J = 1 N m.
    Work along displacementA 20 N force moves a crate 3 m horizontally and does 60 J of work.CrateF = 20 Nd = 3 mE = Fd = 20 × 3 = 60 J
    Both force and displacement are along the same direction.
  • Pushing a crate with 20 N through 3 m in the force direction transfers 60 J. Do not multiply by distance in an unrelated direction.
  • If an object does not move, no mechanical work is done on it by the supporting force, even though a person's muscles may still transfer energy internally.
  • A force at right angles to an object’s movement does no work on it. For example, the inward force on an object moving in a circle at constant speed changes its direction but not its speed.
  • Work done against friction transfers energy to thermal stores of the surfaces and surroundings. This can be useful in brakes but unwanted in machinery.
  • Measure force using a newton meter and displacement using a ruler or tape. A constant-force experiment needs the force direction aligned with the measured movement.

Energy stores and conservation

  • Energy can be stored kinetically, thermally, chemically, gravitationally, elastically, magnetically, electrostatically or nuclearly. Transfer pathways include mechanical work, electrical transfer, heating and radiation.
  • Energy is conserved: it cannot be created or destroyed. In a closed system, transfers move energy between stores or places, but the total stays the same.
  • A motor lifting a load transfers energy electrically to the motor and mechanically to the load’s gravitational potential store. Some energy spreads to thermal stores in the surroundings (is dissipated).
    Lifting energy transfersElectrical energy supplied to motor → Mechanical work raises the load → GPE increases; thermal stores also increaseElectrical energy supplied to motorMechanical work raises the loadGPE increases; thermal stores also increase
    Useful gravitational energy plus unwanted transfers equals input energy.
  • When a falling object speeds up, its gravitational potential store decreases while its kinetic store increases. Drag adds thermal transfers, so the kinetic gain may be smaller than the gravitational decrease.
  • Dissipation spreads energy into less useful thermal stores; sound can carry energy away. “Wasted” describes usefulness for the task, not failure of conservation.
  • Energy-flow diagrams identify input, useful output and unwanted transfers. For quantitative diagrams, the total output must equal input.

Gravitational and kinetic energy calculations

  • Change in gravitational potential energy = mgΔh. Use mass in kg, gravitational field strength in N/kg and vertical height change in m to calculate energy in J.
  • A 5 kg mass raised 2 m where g = 10 N/kg gains 100 J. The change depends on vertical rise, not the length of an inclined path.
  • Kinetic energy = ½mv², using mass in kg and speed in m/s. Doubling mass doubles kinetic energy; doubling speed quadruples it.
  • A 2 kg object at 4 m/s has kinetic energy ½ × 2 × 16 = 16 J. To find speed, rearrange v = √(2E/m).
  • If all lost GPE becomes kinetic energy, mgΔh = ½mv². The mass cancels; ignoring drag, the speed gained from a height depends on g and height.
    GPE to kinetic energyAn object falls from rest through height h without drag; mg h becomes half m v squared.At restInitial store: mghHeight lost: hFinal store: ½mv²No drag: mgh = ½mv²
    Conservation connects the two energy stores.
  • To stop an object, its kinetic energy must be transferred. For a constant braking-force magnitude, Fd = ½mv²; larger speed increases required stopping distance strongly.
  • For a load raised at constant speed, lifting force equals its weight and work done = weight × vertical distance = mgΔh. Acceleration or other losses may change input requirements.

Power and measuring it

  • Power is the rate of energy transfer or work done: P = E/t. Power is measured in watts (W); 1 W = 1 J/s.
  • A machine doing 600 J of work in 3 s has power 200 W. Two machines can do equal work but have different power if they take different times.
  • Rearrange to E = Pt and t = E/P. Convert minutes to seconds and kilowatts to watts before using SI units.
  • To investigate power while climbing stairs, measure mass, vertical height gained and time; calculate useful power = mgΔh/t. Use safe walking/running conditions and repeat.
    Stair power measurementMeasure the vertical height of stairs, mass and time; use mgh divided by time.Verticalheight hUseful power = mass × g × height ÷ time
    Use vertical height, not the sloping staircase length.
  • To investigate lifting power, time raising a known weight through a measured vertical height. Control the load and height when comparing machines or people.
  • Measured useful lifting power may be smaller than total input power because energy is also transferred to surroundings. State whether a calculation uses input or useful output.

Efficiency and improving performance

  • Efficiency = useful energy output ÷ total energy input. The same ratio applies to useful power ÷ input power when comparing the same operating interval.
  • Efficiency is a fraction from 0 to 1 or a percentage from 0% to 100%. A 60% efficient motor gives 60 J useful output for every 100 J input.
    Efficiency accountingInput, Useful, Unwanted; 100 J, 60 J, 40 J; 500 J, 300 J, 200 JInputUsefulUnwanted100 J60 J40 J500 J300 J200 J
    Both examples have efficiency 60%; energy totals balance.
  • Useful output = efficiency fraction × input. Total input = useful output ÷ efficiency fraction; use 0.6 rather than 60 in these equations for 60%.
  • Lubrication can reduce frictional heating. Insulation reduces unwanted heating of the surroundings; the improvement depends on the intended task.
  • For a kettle, heating the water is useful, while heating the room is unwanted. For a lamp, light is useful while most heating is unwanted. Identify the task before classifying transfers.

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