Question

If the torque required to loosen a nut that holds a wheel on a car has a magnitude of 80 N·m, what force must be exerted at the end of a 0.38 m wrench to loosen the nut when the angle is 60°?

a) 80 N

b) 110 N

c) 135 N

d) 154 N

Answer 1

To loosen the car wheel nut using the wrench at a 60° angle, we calculate the required force using the equation F = τ / (r * sin(θ)). The resultant force is approximately 288.01 N, which does not match any of the provided options.

Step-by-step explanation:

To determine the force needed to loosen the nut with a specified torque using a wrench at an angle, we use the torque equation τ = rFsin(θ), where τ is the torque, r is the lever arm length, F is the force, and θ is the angle between the force vector and the lever arm. Given that the torque required is 80 N·m, the length of the wrench is 0.38 m, and the angle is 60°, we can rearrange the formula to solve for F: F = τ / (rsin(θ)).

By substituting the values into the equation, we get F = 80 N·m / (0.38 m x sin(60°)). Using the sine of 60°, which is approximately 0.866, we calculate the force to be approximately 288.01 N. However, none of the options (a) 80 N, (b) 110 N, (c) 135 N, (d) 154 N match this value, which suggests there might have been a mistake in the given options or in the initial conditions of the problem.