P4.114SD0 · Section P4: Energy resources and energy transfers

Work, power and energy

Key learnings

Work done W = F x d equals the energy transferred
Work done is the energy transferred when a force moves an object: force multiplied by the distance moved in the direction of the force, $W = F \times d$ , in joules (J). One joule is done when a force of 1 N moves an object 1 m in the force's direction. Work done equals energy transferred — lifting a box does work against gravity and adds to its gravitational potential energy store. Energy is conserved: transferred between stores, never created or destroyed.
Kinetic energy = ½mv² (square v); gravitational PE = mgh
Two store formulas to recall exactly. Kinetic energy (energy of motion): $\text{KE} = \tfrac{1}{2}mv^{2}$ , with $m$ in kg and $v$ in m/s — the speed is squared, so doubling the speed makes the KE four times larger. Gravitational potential energy (energy of height): $\text{GPE} = mgh$ , with $g = 9.8$ N/kg on Earth and $h$ the vertical height in m. Both are measured in joules (J). Use $g = 9.8$ N/kg unless told otherwise.
Conservation links GPE and KE; power P = W/t is the rate
In a fall or rise (air resistance ignored) energy moves between the gravitational and kinetic stores but the total is unchanged: $mgh = \tfrac{1}{2}mv^{2}$ . A dropped object speeds up as GPE becomes KE; a ball thrown up slows as KE becomes GPE — so you can find a speed from a height without knowing the time. Power is the rate of energy transfer (rate of doing work): $P = W/t$ , in watts, where 1 W = 1 J/s. A more powerful device transfers the same energy in less time.

Common mistakes

Drawn from real examiner reports.

Spot the KE ↔ GPE swap

In a fall or a projectile, kinetic energy comes from gravitational potential energy; in a rise it is the reverse. Candidates who miss this link cannot complete the linked calculation and lose marks. Whenever height and speed both appear (air resistance ignored), set $mgh = \tfrac{1}{2}mv^{2}$ and let the mass cancel to move between them.

Nov 2024 1P Q2a(iii)

Square the speed in kinetic energy

In $\text{KE} = \tfrac{1}{2}mv^{2}$ the speed is squared before multiplying. Two linked slips: writing $\tfrac{1}{2}mv$ (forgetting the square), and squaring the wrong thing, e.g. $\tfrac{1}{2}(mv)^{2}$ — only the speed is squared, not the mass. Safe order: find $v^{2}$ first, then multiply by the mass and halve. Because of the square, doubling the speed quadruples the KE.

Nov 2024 1P Q2a(ii)

Substitute before you rearrange

Examiners award a mark for a correct substitution even if the later algebra slips. Candidates who rearrange the formula first and get it wrong often score zero, whereas putting the given data in first secures that method mark. Habit: write the formula ( $W = Fd$ , $\text{GPE} = mgh$ , $P = W/t$ ), substitute the known values, then rearrange for the unknown.

Jun 2024 1P Q3c

Power is a rate, not an amount of energy

Power is the rate of energy transfer, $P = W/t$ , measured in watts; it is not an energy. Writing "the power is 500 J" is wrong — joules measure energy or work, watts measure power. Two devices that transfer the same energy have different powers if one is faster. Keep the units distinct: J for work and energy, W for power.

Work needs distance in the force's direction

Work done uses the distance moved in the direction of the force, $W = Fd$ . A force acting at right angles to the motion does no work — for example the tension holding a load level as it is carried sideways. Using the full distance when part of the motion is perpendicular to the force overstates the work done.

No movement means no kinetic energy

A stationary object has zero energy in its kinetic store, however heavy it is — KE depends on speed, and $v = 0$ gives $\text{KE} = 0$ . Candidates sometimes credit a resting object with kinetic energy. It may still hold gravitational potential energy (from its height) or elastic energy, but not kinetic energy.

Jun 2023 1P Q7a

Exam tips

Work/energy/power scaffold
Pick the right formula — $W = Fd$ , $\text{KE} = \tfrac{1}{2}mv^{2}$ , $\text{GPE} = mgh$ , or $P = W/t$ — then convert to SI units (kg, m, s, N, J, W), substitute before rearranging, and state the unit on the answer. Remember to square the speed for KE.
Link height and speed by conservation
For a fall or a rise with air resistance ignored, equate the stores: $mgh = \tfrac{1}{2}mv^{2}$ . The mass cancels, giving $v = \sqrt{2gh}$ or $h = v^{2}/(2g)$ . This lets you find a speed from a height (or a height from a speed) without knowing the time. Use $g = 9.8$ N/kg.
Tidy units and standard form
Work in kg, m, s, N, J and W throughout — never leave a mass in grams or a distance in cm. Keep numbers in standard form neat on the calculator to avoid power-of-ten errors, and round only at the end, to the significant figures the question asks for.

Revision notes