Question

A rod is lying on the top of a table. One end of the rod is hinged to the table so that the rod can rotate freely on the table top. Two forces, both parallel to the table top, act on the rod at the same place. One force is directed perpendicular to the rod and has a magnitude of 36 N. The second force has a magnitude of 54 N and is directed at an angle ? with respect to the rod. If the sum of the torques due to the two forces is zero, what must be the angle ??

Answer 1

For the torques to be equal the component of the forces perpendicular to the rod must be equal and in the opposite direction

So 36 = 54*sin(?)

So ? = arcsin(36/54) = 41.81degrees

Answer 2

63*cos? = 35
? = acos(35/63) = 56.25 degs from perpendicular.