A nut has been tightened by a force of 200 N using a 10 cm long spanner. What length of a spanner is required to loosen the same nut with 150 N force? (13.3 cm)
Difficulty: Medium
Solution:
Force = $F_{1}$ = 200 N
Length = $L_{1}$ = 10 cm = $\frac{10 }{100}$= 0.1 m
Length of the spanner to tighten the same nut:
Force = $F_{2}$ = 150 N
Length = $L_{2}$ = ?
Since $Τ_{1} = Τ_{2}$
$F_{1} \times L_{1}$ = $F_{2} \times L_{2}$
$200 \times 0.1$ = $150 \times L_{2}$
20 = $150 \times L_{2}$
$L_{2}$ = $\frac{20}{150}$ = 0.133 m = $0.133 \times 100$ = 13.3 cm
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