004 (part 1 of 3) 10.0 points A floodlight with a mass of 26 kg is used to illum

Question

004 (part 1 of 3) 10.0 points A floodlight with a mass of 26 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, as shown. A cable that makes an angle of 39? with the beam is attached to the pole to help support the floodlight. Assume the mass of the beam is negligible when compared with the mass of the floodlight.

005 (part 2 of 3) 10.0 points Find the horizontal force exerted on the beam by the pole. Answer in units of N. 006 (part 3 of 3) 10.0 points Find the vertical force exerted on the beam by the pole. Answer in units of N.

006 (part 3 of 3) 10.0 points Find the vertical force exerted on the beam by the pole. Answer in units of N.

Explanation / Answer

Let the Tension in the cable = T
T*cos(39) = Fh
Fh = T * cos(39) ---------1

Fv + T*sin(39) = 26 * 9.8 -------2

At equilibrium, Torque about the hinge = 0
T*L*sin(39) = 26.0*9.80*L
T*sin(39) = 254.8 N
T = 404.9 N

Tension in the cable, T = 404.9 N

Fh = T * cos(39)
Fh = 404.9 * cos(39) N
Fh = 314.7 N
Horizontal force exerted on the beam by the pole, Fh = 314.7 N

Fv + T*sin(39) = 26 * 9.8
As T*sin(39) = 254.8 N
Fv = 0
Vertical force exerted on the beam by the pole, Fv = 0 N

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