Question

A nut has been tightened by a force of 180 N using 8 cm long spanner. What length of a spanner is required to loosen the same nut with 150 N force.

Answer 1

Given:

A nut has been tightened by a force of 180 N using 8 cm long spanner.

To Find:

What length of a spanner is required to loosen the same nut with 150 N force.

Solution:

First condition:

$\mathbf{ Force(F_{1})=180\ N }$

$\mathbf{ Perpendicular\ distance(L_{1})=8 \ cm}$

Second condition:

$\mathbf{ Force(F_{2})=150\ N }$

For same value of torque:

$\mathbf{ F_{2}\times L_{2}=F_{1}\times L_{1}}$

$\mathbf{ 150\times L_{2}=180\times 8}$

$\mathbf{ 5\times L_{2}=6\times 8}$

$\mathbf{ L_{2}=9.6 \ cm}$

Means length of a spanner is 9.6 cm to loosen the same nut with 150 N force.