(a) Suppose you have just barely loosened a rusty bolt. Your mass is 80 kg and you have a wrench of length L = 50 cm placed as shown in the diagram below, and hung off the end so all your weight was applied, in the downward direction, to the end of the wrench. What is the magnitude and direction of the torque?
magnitude 392 N m
(b) Now suppose you had a bolt that needed to be tightened to 250 N · m. You place the wrench as shown in the diagram below, and hung off the end so all your weight was applied, in the downward direction, to the end of the wrench. What length wrench would you need to tighten the bolt completely?
L = .3189 m
(c) Suppose you had the same wrench as in part (a), but you placed the wrench at an angle θ = 54° with the vertical, as shown below. How much torque is applied to the bolt?
Torque=radius x force (in this case, weight) x sin(theta)
The Attempt at a Solution
I am having difficulty with the 3rd part. If the torque is as the above equation,
T=.5 m x 80kg x 9.8 m/s2 x sin(54)
which magnitude is 219 N m with a clockwise direction
However, this is incorrect. Perhaps this is my angle-do I need to subtract 54 from 90? How do you know what angle to look at? Where do you form the right triangle for the correct trig?