Question

A mechanic unscrews a nut by applying a force of 120 N on a spanner of length 40 cm. What should be the required length of the spanner in order to apply only 40 N force ?

Answer 1

In the 1st case, the force applied,
F = 120 N and the magnitude of the perpendicular distance (called radius vector),
`r=40 cm = (40)/(100)m`
Torque `(tau)=120N xx(40)/(100)=48 N m`.
In the 2nd case, applied force F = 40 N and the length of the radius vector is to be found.
`r=?`
`tau=Fxxr` is the same in both the cases.
Hence,
`48=40xxr`
`:. r = 1.2 m`. Hence, to apply a force of 40 N for the same torque, the mechanic should use a spanner of length 1.2 m.