Question

A person using a 50 cm long handle spanner can open a nut by applying a 120 N force.What should be the length of the handle if he wants to open the nut by applying a force of 80 N?​

Answer 1

Given data : A person using a 50 cm long handle spanner can open a nut by applying a 120 N force.

case : If a person wants to open the nut by applying a force of 80 N, then the length of the handle should be ?

Solution : According to given data,

• force, F = 120 N
• perpendicular distance/length of the handle spanner, r = 50 cm = 0.5 m

Now, we need to calculate the torque created by the handle spanner the length, 0.5 m and force, 120 N.

⟹ τ = F * r

⟹ τ = 120 * 0.5

⟹ τ = 60 Nm. ----{1}

Now,

• force, F' = 80 N
• perpendicular distance/length of the handle spanner, r' = ?

⟹ τ' = F' * r'

⟹ τ' = 80 * r'

We know that, a person needs 60 Nm of torque to open the nut (form {1}).

Therefore, τ = τ'

Now,

⟹ τ' = 80 * r'

⟹ 60 = 80 * r'

⟹ r' = 60/80

⟹ r' = 0.75 m

Answer : The length of the handle spanner 0.75 m or 75 cm is needed to open the nut by applying a force of 80 N.