Question

Why a long spanner is used to unscrew a very tight nut

Answer 1

force is directly proportional to the length of fulcrum

hence longer the spanner more the force is applied

Answer 2

Answer: The moment of force which is torque can be produced with comparatively lesser effort in a long spanner than a spanner with a short handle.

Explanation:

To screw or unscrew a nut , Torque is taken into consideration.

The longer the spanner, lesser the force required to produce the same torque(which is fixed) that is required to unscrew the tight nut.

Longer the spanner, greater the torque.

$l\propto \tau$

$l\propto 1/F$

Torque is defined as the cross product between the distance vector (the distance from the pivot point to the point where force is applied) and the force vector, '$\theta$' being the angle between r and F.

$\tau =r\times F=rFsin\theta$