A worker applies a torque to a nut with a wrench 0.430 m long. Because of the cramped space, she must exert a force upward at an angle of 59.5° with respect to a line from the nut through the end of the wrench. If the force she exerts has magnitude 81.0 N, what magnitude torque does she apply to the nut?

Question

A worker applies a torque to a nut with a wrench 0.430 m long. Because of the cramped space, she must exert a force upward at an angle of 59.5° with respect to a line from the nut through the end of the wrench. If the force she exerts has magnitude 81.0 N, what magnitude torque does she apply to the nut?

____N · m

Answer 1

To find the torque applied to the nut, we can use the equation:

Torque = Force * Lever Arm

The lever arm is the perpendicular distance from the axis of rotation (the nut) to the line of action of the force applied by the worker. In this case, the length of the wrench is the lever arm.

Given:
Force = 81.0 N
Lever Arm = 0.430 m

Now, we need to find the component of the force that is perpendicular to the lever arm. The force is applied at an angle of 59.5° with respect to the line from the nut through the end of the wrench.

Using trigonometry, we can find the perpendicular component of the force using the equation:

Perpendicular Force Component = Force * sin(angle)

Perpendicular Force Component = 81.0 N * sin(59.5°)

Next, we can substitute the values into the torque equation:

Torque = Perpendicular Force Component * Lever Arm

Torque = (81.0 N * sin(59.5°)) * 0.430 m

Calculating this expression will give us the magnitude of the torque applied to the nut in units of N · m.