Question

Experiment by loosening lug nuts from an automobile tire with a lug wrench, a lug wrench with a short extension on the handle, and a lug wrench with a longer extension on the handle. Write a paragraph explaining your findings and draw a free body diagram showing the applied force, resistance, and axis of rotation. What provides the resistance? Please don't forget to provide the "Free Body Diagram"

Explanation:

Answer 1

In the figure below, there are two wrenches with lengths and forces are applied respectively. Also, there is a resisting torque or loosening torque required to loosen the lug. So loosening torque will be provided by the applied forces at the wrench arms.

We found that we will need smaller force with longer arm wrench while a larger force with smaller arm wrench. This is in consistence with the following mathematical interpretation.

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The resistance is provided by the friction force developed between the threads of the lug. The external threads of the lug meshes with internal threads of the hole. But when we keep on tightening the lug a normal force on the threads develop in the axial direction. Since there is friction between threads, this frictional force (due to friction and normal force) acts as a resisting force at the threads. This resiting force creates a resiting torque, which needs to be overcome when we try to loosen the lug.