Could someone please explain on how to do this question step-by-step. Thank you!

A bolt is being loosened by a 40 cm wrench. The torque in this situation has a magnitude of 12 J and the force makes an angle of 60 degree with the wrench. What is the magnitude of the force used to loosen the bolt?

a) 2.4N

b) 4.2N

c) 34.6N

d) 60.0N

To solve this question, we can use the formula for torque:

Torque = Force x Lever Arm x sin(theta)

Where:

- Torque is the magnitude of the torque in Newton-meters (Nm),
- Force is the magnitude of the force applied in Newtons (N),
- Lever Arm is the distance from the axis of rotation to the point where the force is applied, and
- Theta (θ) is the angle between the force and the lever arm, measured in degrees.

In this case, we are given the torque (12 J), the lever arm (40 cm), and the angle (60 degrees). We need to find the magnitude of the force.

Step-by-step solution:

1. Convert the lever arm from centimeters to meters: 40 cm = 0.4 m

2. Convert the angle from degrees to radians: θ = 60 degrees * (π/180) ≈ 1.047 radians

3. Rearrange the torque formula to solve for the force:

Force = Torque / (Lever Arm x sin(theta))

4. Substitute the known values into the formula:

Force = 12 J / (0.4 m x sin(1.047))

5. Calculate the sine of the angle:

sin(1.047) ≈ 0.866

6. Substitute the value of sin(1.047) into the formula:

Force = 12 J / (0.4 m x 0.866)

7. Simplify the equation:

Force = 12 J / 0.3464 m

8. Calculate the force:

Force ≈ 34.6 N

Therefore, the magnitude of the force used to loosen the bolt is approximately 34.6N. Hence, the correct answer is option c) 34.6N.