An explanation is complete when it says what it depends on. Reading your own answer with a short checklist shows where a hidden assumption sits.
This lesson is part of the SPM subjects and learning resources section. The examples are original and conceptual; follow your teacher for the depth your syllabus expects.
What does the checklist ask?
- Direction: does the force act at the angle I assumed?
- Losses: have I ignored friction or weight of parts?
- Size: does the claim hold for a much larger or smaller load?
- Condition: does it only hold at steady speed or at rest?
Worked example: two gears
A student writes: “Gear A has 20 teeth and drives gear B with 40 teeth, so gear B turns at half the speed of gear A.”
Check the claim. Gears in mesh move the same number of teeth past the contact point each turn. Gear A turns once for 20 teeth, and gear B needs 40 teeth for one turn, so gear B turns once for every two turns of gear A. Half the speed is correct.
Find the assumptions.
- The teeth are in mesh without slipping.
- Gear A is the driver and gear B is the driven gear.
- The speed ratio is about turns per minute, not the force or torque.
Corrected answer. “If the teeth mesh without slipping, gear B, with 40 teeth, turns once for every two turns of gear A, which has 20 teeth. If gear A turns at 60 revolutions per minute, gear B turns at 60 × 20 ÷ 40 = 30 revolutions per minute. This describes speed only; the torque on B is larger, which I am not calculating here.”
The corrected answer states the no-slip condition, gives a number and names what it does not cover.
The mistake that costs marks
The common slip is to state a conclusion as if it held in all cases, and then to lose a mark when a case in the question breaks it.
| Claim | Hidden assumption | Better wording |
|---|---|---|
| “B turns at half the speed.” | Teeth mesh without slipping | “With no slipping, B turns at half the speed.” |
| “A longer lever needs less force.” | Force is perpendicular | “When the force is perpendicular to the lever, a longer lever needs less force.” |
Check yourself
A student writes: “A pulley lets you lift a 100 N load with only 50 N of force.” Name two assumptions that must hold for the claim to be true, and rewrite it.
Answer
Assumptions: the pulley system has two supporting rope sections sharing the load equally, and friction and the weight of the pulley are ignored.
Rewrite: “In a two-rope pulley system with negligible friction and pulley weight, a 50 N pull lifts a 100 N load, because each rope section carries half of the load. In practice friction makes the pull somewhat larger.”
What to study next
Practise applying these ideas with the Mechanical Engineering original practice set. If the models still feel slippery, return to link an observation to a mechanical model.
The structured answer self-review can prompt you to state assumptions. A teacher can review your explanations in online one-to-one Mechanical Engineering tuition.