Energy questions are a favourite for the longer parts of the Mechanics paper, and they often combine with Newton's laws or kinematics. The reports show that the principle is understood. The marks are lost in the terms that go into the equation and their signs. This guide collects what Cambridge examiners say students get wrong, based on recent reports.
Summarised in our own words from a reading of the examiner reports.
Mistakes that cost marks
- Missing or extra terms. The most repeated comment. In forming PE loss + work done by the engine = KE gain, students omitted one of the three terms, combined them with the wrong sign, or both. Others duplicated potential energy by including both the change in PE and the work done by the weight. In a question where only the potential energy term was used, the kinetic energy was missing.
- Dimensional errors. Students omitted the distance from the frictional force term, leaving a force in an energy equation. One report describes this as an equation that is not dimensionally correct, and it appears more than once.
- Omitting the resistance. The resistance to motion, or the work done against it, was left out or used with the wrong sign. A common error was to subtract the given work done against resistance instead of adding it.
- Wrong component of the force. Using F = 20 sin θ instead of 20 cos θ, or using d cos θ in the work done by friction when friction acts parallel to the plane.
- Work done by a particular force. Students gave the braking force instead of the work done by it, multiplied a force by a distance when the force was at an angle, or included the frictional force in the work done by the pulling force.
- Connected particles. Using the kinetic energy of only one particle, or the potential energy lost by only one of the two. For a car towing a trailer, omitting the work done by the tow-bar force.
- Missing the mass term. In one question, omitting the mg terms was very common, which with rounding often gave the "correct" value to 3 significant figures from incorrect working, and could not be credited.
- Power. Using the wrong force in P = Fv. Some students used the driving force from an earlier part when the question needed a different value. Students also made errors in resistance when the question gave an expression for it.
- Mixing methods. Combining Newton's second law and constant acceleration with errors, or using the wrong tension from an earlier part.
- Premature rounding. One report records that 720 m was sometimes the answer after approximating too early, or after rounding to two significant figures.
What examiners advise
- Write the work-energy equation in words first: initial KE + work done by driving forces = final KE + PE gain + work done against resistance. Then check that every term is present and consistent.
- Check that each term is energy: a force times a distance, not a force alone.
- Include all forces that do work, including the tow-bar force and friction when appropriate.
- Consider the whole system and its parts. In connected particle questions, include the kinetic energy of both particles and the potential energy changes of both.
- Use exact values until the final line.
Habits that help
- List the energy at the start and at the end, and the work done by each force in between.
- State whether each force helps or opposes the motion before assigning a sign.
- If a problem has two phases, write down what you know at the end of the first before starting the second.
Questions students ask
How do I write a work-energy equation without missing terms?
Write it in words first: initial KE + work done by driving forces = final KE + PE gain + work done against resistance. Then check every term is present and has the right sign.
What does it mean for an equation to be dimensionally wrong?
A force appears in an energy equation. Students omitted the distance from the friction term. Check that each term is a force times a distance.
Do I add or subtract the work done against resistance?
It depends on which side of the equation it sits. A common error was subtracting the given work done against resistance instead of adding it. State whether each force helps or opposes the motion before assigning a sign.
Which force do I use in P = Fv?
The driving force at that moment. Students used the driving force from an earlier part when the question needed a different value, or made errors with resistance given as an expression.
How should I treat connected particles in an energy question?
Include the kinetic energy of both particles and the potential energy changes of both. Students used only one. For a car towing a trailer, include the work done by the tow-bar force.
Why did 720 m appear as a wrong answer?
From approximating too early, or rounding to two significant figures. Use exact values until the final line.
Practice this topic
Ready to try some? Work through past paper questions on this topic one at a time. Attempt each question fully first, and open the mark scheme only afterwards.