A rod of length L is pivoted about its left end and has aforce F applied perpend

Question

A rod of length L is pivoted about its left end and has aforce F applied perpendicular to the other end. The force F is nowremoved and another force F' is applied at the midpoint of the rod.If F' is at an angle of 30° withrespect to the rod, what is its magnitude if the resulting torqueis the same as when F was applied? Equation? A rod of length L is pivoted about its left end and has aforce F applied perpendicular to the other end. The force F is nowremoved and another force F' is applied at the midpoint of the rod.If F' is at an angle of 30° withrespect to the rod, what is its magnitude if the resulting torqueis the same as when F was applied? Equation?

Explanation / Answer

Torque T = F r sin In case I , F = F , r = r and = 90 degrees In case II , F ' = F ' , r ' = r / 2 , = 30degrees Given both cases torques are equal , So, F r sin 90 = F ' r ' sin 30                      = F ' ( r / 2 ) sin 30 from this F r = F ' r / 4 from this   F ' = 4 F

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