A force of 6.0 N applied at 30^ to a wrench at a distance of 8 cm from the nut is just sufficient to loosen the nut. Determine the force F that would be required to loosen it if it acts perpendicularly to the wrench at a distance of 16 cm from the nut.

Step-by-step solution

The torque required to loosen the nut remains constant in both cases. The torque produced by a force is given by = r F . For the first case: F₁ = 6.0 N r₁ = 8 cm ₁ = 30^ ₁ = 8 6.0 30^ = 48 1 2 = 24 N cm For the second case: F₂ = F r₂ = 16 cm ₂ = 90^ ₂ = 16 F 90^ = 16F N cm Equating the torques: ₁ = ₂ 24 = 16F F = 24 16 = 1.5 N