posted by Jessica on .
A floodlight with a mass of 20.0 kg is used to illuminate the parking lot in front of a library. The floodlight is supported at the end of a horizontal beam that is hinged to a vertical pole. A cable that makes an angle of 30 degrees with the beam is attached to the pole to help support the floodlight. Find the following, assuming the mass of the beam is negligible when compared with the mass of the floodlight:
a. the force provided by the cable
b. the horizontal and vertical forces exerted on the beam by the pole
Add up the horizonal and vertical forces on the floodlamp separately. The cable exerts a tenstion force T and the pole exerts a compression force (push), P.
T sin 30 = M g
T cos 30 = P
Solve these two equations for the two unknowns. Here would be a good way to start:
tan 30 = M g /P
I forgot not address part b or your problem. The horizontal force that the pole exerts on the floodlight is equal and opposite to the force the pole exerts on the beam. There is no vertical force, since the beam is assumed to be weightless and the beam support points are assumed to be frictionless, as if hinged.