A crate of mass 523 kg is hanging at the end of a uniform beam of mass 112 kg. I

Question

A crate of mass 523 kg is hanging at the end of a uniform beam of mass 112 kg. If the angle between the cable and the beam is ?=30.0 A crate of mass 523 kg is hanging at the end of a uniform beam of mass 112 kg. If the angle between the cable and the beam is ?=30.0 A crate of mass 523 kg is hanging at the end of a uniform beam of mass 112 kg. If the angle between the cable and the beam is ?=30.0 degree as shown, find (a) the tension T in the cable, (b) the magnitude of force F supporting the beam by wall, and (c) the directional angle ? of F.

Explanation / Answer

a)tension = Mg = 523*9.8 = 5125.4 N

b)by equating all the vertical forces on the beam Fcos(alpha) - Tsin(theta) = mg = 112*9.8 = 1097.6 N

Fcos(alpha) = 1097.6 + 5125.4*(1/2) = 3660.3 N

By equating horizontal forces , Fsin(alpha) = Tcos(30) = 5125.4*sqrt(3)/2 = 4438.73 N

F = sqrt(3660.3^2 +4438.73^2) = 5753.267 N

alpha = tan^-1(4438.73/3660.3) = 50.5 degrees.

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