KCSE 2025 Physics P1 Q7 — Moments (why a longer spanner needs less force)
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The Question
“Two spanners are used to loosen the same nut. Spanner B has a longer handle than spanner A. Explain why spanner B needs less force to loosen the nut.”
Identify the turning effect as a moment
The nut is loosened by the turning effect of the applied force about the nut. That turning effect is called the moment, and it depends on two things: the size of the force and how far from the nut the force is applied — the perpendicular distance. A longer handle lets you push much further from the nut.
Fix the moment and compare the two spanners
The same nut needs the same moment to break it loose, whichever spanner you use. Because moment is the product of force and distance, keeping the moment fixed while making the distance d larger means the force F must fall. Spanner B, with its longer handle, provides the larger distance, so the required force is smaller — that is why it takes less effort.
Final Result
Because moment = F × d, spanner B's longer handle gives a larger perpendicular distance d. To produce the same moment needed to loosen the nut, a larger d means a smaller force F, so spanner B needs less force.
Why this method works
The turning effect of a force is not set by the force alone but by the product of the force and its perpendicular distance from the pivot. For a given job — here, overcoming the friction that holds the nut — the moment required is fixed. Since that fixed moment equals F times d, force and distance trade off against each other: increasing one lets you decrease the other. Lengthening the spanner is simply a way of buying a bigger lever arm d, so the hand needs to supply proportionally less force. This is the same principle behind crowbars, wheelbarrows and door handles being placed far from the hinge.
Double the handle length and d doubles, so the force needed halves for the same moment — consistent with F = moment ÷ d.