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 problem, we can use the formula for torque: Torque = Force × Distance × sin(θ), where Torque is given as 12 J, Distance is given as 40 cm (or 0.4 m), and the angle θ is given as 60 degrees.
Step 1: Convert the given distance from centimeters to meters.
- 40 cm = 0.4 m
Step 2: Substitute the given values into the torque formula.
- 12 J = Force × 0.4 m × sin(60 degrees)
Step 3: Solve for the Force.
- Dividing both sides of the equation by 0.4 m and sin(60 degrees), we have:
- Force = 12 J ÷ (0.4 m × sin(60 degrees))
Step 4: Calculate the value of sin(60 degrees).
- sin(60 degrees) = √3/2
Step 5: Substitute the value of sin(60 degrees) into the equation.
- Force = 12 J ÷ (0.4 m × √3/2)
Step 6: Simplify the expression.
- Force = 12 J ÷ (0.4 m × √3/2)
- Force = 12 J ÷ (0.4 m × √3/2)
- Force = 12 J ÷ (0.4 × √3)
- Force = 30 J ÷ √3
- Force = 17.32 J
Now, to find the magnitude of the force used to loosen the bolt, we take the absolute value of the calculated force (since force is always positive).
- Magnitude of the force = |17.32 N| = 17.32 N
Therefore, the correct answer is C) 34.6N.