Question

If the torque required to loosen a nut that holds a wheel on

a car has a magnitude of 58 N∙m, what force must be exerted at the
end of a 0.35 m lug wrench to loosen the nut when the angle is
56.

Answer 1

To loosen a nut with a required torque of 58 N·m using a 0.35 m lug wrench at a 56· angle, a force of approximately 200 Newtons must be exerted perpendicular to the wrench.

Step-by-step explanation:

The student's question pertains to the concept of torque and how it is applied using a lug wrench to loosen a nut on a car's wheel. Torque (τ) can be calculated using the formula τ = r * F * sin(θ), where 'r' is the distance from the pivot point, 'F' is the force applied, and 'θ' is the angle between the force vector and the lever arm. Given that the torque required is 58 N·m, the length of the wrench is 0.35 m, and the angle of the force is 56°, the force needed can be found by rearranging the formula to F = τ / (r * sin(θ)).

Thus, the necessary force to loosen the nut is:

F = 58 N·m / (0.35 m * sin(56°)) ≈ 58 N·m / (0.35 m * 0.829) ≈ 58 N·m / 0.29015 m ≈ 199.9 N.

Therefore, to loosen the nut, a force of approximately 200 Newtons must be exerted at the end of a 0.35 m lug wrench at an angle of 56 degrees to the wrench's handle.