O-Level Pure Physics: Forces, Work, Energy and Power — One Framework for Every Energy Transfer Question

Why This Topic Quietly Costs Students Marks

Forces, Work, Energy and Power sits in almost every O-Level Pure Physics paper, often disguised as a "real-world" question about a crane, a cyclist, a lift, or a ball rolling down a ramp. Students who have memorised the formulas W = Fd, E_k = ½mv², E_p = mgh, and P = W/t still lose marks — not because they don't know the formulas, but because they don't know which formula the question is actually asking for, or which quantity (mass, weight, distance, height) belongs in which equation.

The good news is that almost every question in this topic is really asking one thing: where did the energy come from, and where did it go? Once a student can answer that in words, the correct formula almost writes itself. This post lays out that framework, works through the calculation types students meet most often, and flags the traps that quietly cost marks even when the physics is understood.

The Core Framework: Energy In, Energy Out

Step 1 — Work Done: the Bridge Between Force and Energy

Work done is simply the amount of energy transferred when a force moves an object through a distance, in the direction of the force:

W = F × d

where W is work done (in joules, J), F is the force applied (in newtons, N), and d is the distance moved in the direction of the force (in metres, m). This last condition is the one students forget: if a crane pulls a load up a slope, the relevant distance for the lifting force is not the length of the slope — it's the vertical height. This single distinction is behind more lost marks than any other in this topic.

Step 2 — The Two Energy "Accounts" You Must Track

Almost every problem in this topic is a transfer between two accounts:

• Gravitational Potential Energy (GPE): E_p = mgh, where m is mass (kg), g is gravitational field strength (usually 10 N/kg at O-Level), and h is the vertical height risen or fallen.
• Kinetic Energy (KE): E_k = ½mv², where v is speed (m/s).

A useful habit: before touching any formula, write a one-line energy sentence. For example: "GPE lost by the ball becomes KE gained by the ball, minus energy lost to friction and air resistance." That sentence tells you exactly which formulas to set equal to each other, and it's often worth a method mark on its own in "explain" questions.

Step 3 — Power: Two Formulas, One Meaning

Power is the rate of doing work — how quickly energy is transferred:

P = W / t (work done per unit time)

There is a second, equally important form derived from it. Since W = Fd, and d/t = v (average speed), we get:

P = F × v

Students often don't realise these are the same equation in disguise. Use P = W/t when you're given total work/energy and total time. Use P = Fv when you're given a force and a constant speed — this is the version examiners love for "car travelling at constant velocity" or "motor pulling at steady speed" questions, because no time value is given at all.

Step 4 — Efficiency: Where the "Missing" Energy Goes

No real machine transfers 100% of input energy to useful output — some is always lost, usually as heat (from friction) or sound. Efficiency is simply the fraction that made it to where you wanted it:

Efficiency = (useful energy output / total energy input) × 100%

The same relationship works with power instead of energy, since both are measured over the same time interval:

Efficiency = (useful power output / total power input) × 100%

In exam questions, "energy lost as heat" is simply total input − useful output. Students frequently try to calculate this with a separate formula that doesn't exist — it's just subtraction once you've correctly identified the two energy accounts.

Worked Examples: Applying the Framework

Example 1 — Lifting a Load (Work Done Against Gravity)

A motor lifts a 50 kg crate vertically through 4 m in 5 s. Calculate (a) the work done, (b) the power developed by the motor. (Take g = 10 N/kg.)

(a) The force needed to lift the crate at constant speed equals its weight: F = mg = 50 × 10 = 500 N. Work done: W = Fd = 500 × 4 = 2000 J.

(b) Power: P = W/t = 2000 / 5 = 400 W.

Notice the two-step structure: convert mass to weight (force) first, then apply W = Fd. Students who skip the mass-to-weight conversion and use F = 50 N directly lose the entire question — always check whether you've been given a mass (kg) or a force/weight (N).

Example 2 — A Falling Object (GPE to KE)

A 2 kg ball is dropped from rest from a height of 5 m. Assuming air resistance is negligible, calculate its speed just before hitting the ground.

Energy sentence: GPE lost = KE gained (nothing else to account for, since air resistance is negligible).

GPE lost: E_p = mgh = 2 × 10 × 5 = 100 J.

Set this equal to KE gained: ½mv² = 100

½ × 2 × v² = 100 → v² = 100 → v = 10 m/s

This "GPE = KE" substitution, done directly without calculating an intermediate numeric value for GPE, is a useful shortcut once students are confident: mgh = ½mv² lets the mass cancel entirely, giving v = √(2gh) directly. Both methods are acceptable, but writing the energy sentence first prevents students from guessing whether to add or subtract KE and GPE.

Example 3 — A Ramp With Friction (Work-Energy With Losses)

A worker pushes a 20 kg trolley up a ramp of length 5 m, rising a vertical height of 3 m, applying a constant force of 150 N along the ramp. Calculate (a) the work done by the worker, (b) the GPE gained by the trolley, (c) the energy "lost" to friction, and (d) the efficiency of this process. (Take g = 10 N/kg.)

(a) Work done by the worker: W = Fd = 150 × 5 = 750 J. Here, d is the distance along the ramp (5 m), because that is the direction the 150 N force actually acts.

(b) GPE gained: E_p = mgh = 20 × 10 × 3 = 600 J. Here, h is the vertical height (3 m), not the ramp length — a completely different distance from part (a), and the single most common point of confusion in this topic.

(c) Energy lost to friction = total input − useful output = 750 − 600 = 150 J.

(d) Efficiency = (600 / 750) × 100% = 80%.

This question is a complete miniature of the whole topic: two different distances doing two different jobs, and efficiency as nothing more than a subtraction and a fraction.

Example 4 — Constant Speed, No Time Given

A car engine exerts a driving force of 900 N while the car travels at a constant speed of 20 m/s. Calculate the power output of the engine.

No time or distance is given, and the question doesn't need them — "constant speed" is the signal to reach for P = Fv directly:

P = Fv = 900 × 20 = 18 000 W (18 kW).

Trying to force this into P = W/t by inventing a time value is a common panic response — recognising which power formula the given quantities point to is itself the skill being tested.

Exam Traps to Watch For

• Mass vs weight. mgh and Fd both require a force in newtons. If you're given a mass in kg, convert it to weight (F = mg) before using it as a force. Forgetting this is the single most common error in this topic.
• Ramp length vs vertical height. Work done by a pushing/pulling force uses the distance along the direction of that force (often the ramp length). GPE gained uses the vertical height only. These are frequently two different numbers in the same question, as in Example 3.
• Unit conversions hiding in the question. Grams must become kilograms, centimetres must become metres, and minutes must become seconds before any formula is applied. A correct method with an unconverted unit still loses the final answer mark.
• "Energy lost" is not a separate formula. It is always (total energy input) − (useful energy output). Students sometimes hunt for a formula that doesn't exist instead of simply subtracting.
• Efficiency is always less than 100%. If a calculation gives an efficiency above 100%, a value has been read wrong or two quantities have been swapped — this is a useful self-check during the exam, not just after.
• Choosing between P = W/t and P = Fv. If the question gives total energy/work and total time, use P = W/t. If it gives a force and a constant/steady speed, use P = Fv. Reading which quantities are actually provided prevents wasted time trying to force the wrong formula.
• KE and GPE are only equal when nothing else takes energy away. The moment friction, air resistance, or sound is mentioned (or implied by a ramp, a rough surface, or a real vehicle), GPE lost is no longer equal to KE gained — the energy sentence must include a third term.

How to Practise This Topic Systematically

Because every question in this topic is a variation on the same energy-bookkeeping structure, the most effective practice isn't grinding more questions blindly — it's practising the same four-step sequence until it becomes automatic:

1. Identify what's given: mass or weight? Distance along the force, or vertical height? Time, or a constant speed?
2. Write the one-line energy sentence before touching a formula — what energy account is losing, what account is gaining, and is anything "leaking" to friction or heat?
3. Convert units first, especially mass to weight and any non-SI units to SI units.
4. Choose the formula that matches the quantities you actually have, not the formula you remember most confidently.

Students who work through a mixed set of questions — a lifting question, a falling/rolling question, a ramp-with-friction question, and a constant-speed power question — in one sitting, using this exact four-step sequence every time, tend to stop making the mass/weight and ramp-length/height errors within a couple of sessions. That's the "aha moment" this topic is really waiting for: once the bookkeeping clicks, the formulas were never the hard part.

In our small-group Pure Physics classes at Intuitional in Teck Whye, we walk students through exactly this framework using past-year exam questions, so that Work, Energy and Power stops being a topic they hope not to see on the paper and becomes one of their reliable, high-confidence marks.