Science Puzzle
Which Spanner Loosens the Stuck Nut?
A rusty nut won't budge. You have two spanners: one 15 cm long and one 45 cm long. Either way, you can push down on the end of the handle with the same force, about 100 newtons, roughly the weight of a 10 kilogram bag of potatoes.
Which spanner gives you the better chance of loosening the nut?
The Answer
Spanner B. The long handle gives you three times the turning effect for exactly the same push.
What turns a nut isn't the force alone but the force multiplied by its distance from the centre of the turn. Physicists call this the moment, or torque. On spanner A it's 100 newtons × 0.15 metres = 15 newton metres. On spanner B it's 100 × 0.45 = 45 newton metres. Same muscles, three times the twist.
It's the reason door handles sit on the side away from the hinges. Push a door right next to its hinges and it barely moves; push at the handle and it swings easily. Mechanics use the same trick when they slide a length of pipe over a spanner to free a seized bolt.
There's no free lunch, though. To turn the nut the same amount, your hand on the long spanner has to travel three times as far round its circle. You trade a smaller force for a longer movement, just like a low gear on a bike.
The principle: Moments. The turning effect of a force is the force multiplied by its distance from the pivot, so a longer lever turns the same push into a bigger twist.