The board is used to hold the end of a four-way lug wrench in position. A torque

Question

The board is used to hold the end of a four-way lug wrench in position. A torque of 40 N.m about the x-axis is required to tighten the nut (note that the system of coordinates has the origin placed in the center of the wrench). 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) and ?.
b) Does all of Mo act to turn the nut? Explain.
c) Determine the magnitude of the force required to tighten the nut if ? = 50o.

d) Which angle would require the least amount of force? What would be the corresponding mag- nitude of the force?
e) What is/are the benefit(s) from using a board to hold the end of a four-way lug wrench?

Explanation / Answer

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) and ?.

bold letters indicate vectors

Mo = Frcos?

r is the distance that nut got moved

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

No,some will be used in turning the wrench
c) Determine the magnitude of the force required to tighten the nut if ? = 50o.

Mo = 40 * 0.6428* r

= 25.712r N

d) Which angle would require the least amount of force? What would be the corresponding mag- nitude of the force?

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

it acts as fulcrum and reduces the force needed (archimedes law about)

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