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# Why does a spanner have a long handle?

Last updated date: 14th Jun 2024
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Hint We need to investigate the force required to operate a (hypothetical) short handled spanner with respect to a long handled spanner. Torque is proportional to the distance between the force and the point (or centre) of rotation. So from here we can find the reason for a spanner to have a long handle.
Formula used: In this solution we will be using the following formulae;
$T = Fr$ where $T$ is the torque applied about a point, $F$ is the force generating the torque and $r$ is the perpendicular length between the force and the point of rotation.

Alternatively, we may reason mathematically as follows: The relationship between forces and torque is given by $T = Fr$ where $T$ is the torque applied about a point, $F$ is the force generating the torque and $r$ is the perpendicular length between the point of application of the force and the axis of rotation of the object.
Assuming for a torque $T$ required to rotate a bolt, we must apply a force $F = \dfrac{T}{l}$ applied at its end (where $l$ is the length of the spanner). Hence, for a short length $l$ the force required is larger. But for a long length $l$ the force required is little. Thus, a longer handle will be preferred, so it requires the minimum amount of force.