The board is used to hold the end of a four-way lug wrench in position. A torque T = -30 i N.m is required to tighten the nut (note that the system of coordinates has the origin placed in the center of the wrench and the nut is located at position <-d1,0,0> m). You decided to step at the end of the wrench in order to turn it. Assume that the force provided by your foot can be modeled as a concentrated force at point A with magnitude F. We also assume that the force vector F lies in the vertical plane y-z and makes an angle ? with the y-axis.

a) Determine the moment Mo of the force F about a point located at the nut. Write your answer as a function of F (force magnitude), d1, d2, and ?.

b) Does all of Mo act to turn the nut? Explain.

c) Find the magnitude of the force required to tighten the nut if ? = 40o and d1 = d2 = 0.15 m. d) Which angle would require the least amount of force? What would be the corresponding mag- nitude of the force given d1 = d2 = 0.15 m ?

e) What is/are the benefit(s) from using a board to hold the end of a four-way lug wrench?