GCSE Combined Science Work, energy and momentum revision

Work done is the energy a force transfers as it moves its point of application: W = F s, where s is the distance moved along the line of action. Push a sofa with 340 N through 6.0 m and you transfer 340 × 6.0 = 2 040 J. One joule is one newton-metre. No movement, no work: holding a heavy box motionless is tiring but transfers no energy mechanically.

Where the energy lands depends on the job. Lifting an 18 kg box 1.5 m (g = 10 N/kg) banks W = 270 J in its gravitational store; dragging the same box along a rough floor transfers the work to the thermal store of the floor and box — they warm up. Friction never destroys the account; it just books everything under heating.

Power prices the speed of the job: P = E ÷ t, in watts (1 W = 1 J/s). A motor shifting 4 800 J in 40 s works at 120 W; a 150 W motor out-performs a motor doing 900 J in 5.0 s? Compare: 900 ÷ 5.0 = 180 W — so the second motor wins. Climbers price their effort the same way: 55 kg gaining 6.0 m in 30 s does mgh = 55 × 10 × 6.0 = 3 300 J of useful work, at 3 300 ÷ 30 = 110 W.

Drawing a bow is a work job: your muscles pull against the rising resistance of the bent limbs, and the energy is banked in the elastic potential store (for a spring, E = ½ k e² — met in chapter 21; a spring with k = 250 N/m drawn 0.20 m holds ½ × 250 × 0.20² = 5.0 J). Release the string and the store pays out almost instantly into the kinetic store of the arrow. Catapults, trampolines and pogo sticks all run the same story: work done stretching → elastic store → kinetic store.

The pattern generalises. Work done is just the currency; stores are where the joules sit. Any force multiplied by the distance it moves its point of application tells you the transfer — and if the force is friction, the destination is thermal. That single sentence is most of the marks in "explain the energy transfers" questions.

Momentum is mass in motion: p = m v, measured in kilogram metres per second (kg m/s) — and it is a vector, so direction is signed: rightwards positive, leftwards negative. An 85 kg cyclist at 12 m/s carries p = 85 × 12 = 1 020 kg m/s. A 0.045 kg golf ball at 40 m/s carries just 1.8 — small mass, fast speed.

In a closed system (no external forces), total momentum is conserved: the total before equals the total after. A 3.0 kg trolley at 4.0 m/s coupling with a stationary 1.0 kg trolley carries 12 kg m/s in; the joined 4.0 kg pair must leave with the same 12, so they roll at 12 ÷ 4.0 = 3.0 m/s. Recoil is the same law backwards: a 3.0 kg cannon firing a 0.012 kg ball at 250 m/s (momentum 3.0 kg m/s forwards) must itself drift backwards at 3.0 ÷ 3.0 = 1.0 m/s — the total stays at zero.

The bridge between force and momentum: F t = Δ(m v) — the force multiplied by the time it acts equals the change in momentum it produces. Rearranged, F = Δ(m v) ÷ t: for a fixed momentum change, more time means less force. A 1 200 kg car braking from 15 m/s to rest changes momentum by 18 000 kg m/s; over 2.0 s the force averages 9 000 N, but an unbelted passenger stopping in 0.10 s inside the cabin experiences a devastating 180 000 N.

Every crash safety feature is an impact-time stretcher. Crumple zones fold so the car takes longer to stop; air bags let the head decelerate through a soft cushion instead of a hard wheel; seat belts spread the stop over the strongest parts of the body while extending the time; cycle helmets crush gradually; gym mats turn a hard floor into a longer, gentler arrest. None of them changes the momentum change — physics is not negotiable — they only stretch t, so F drops.