One end of a heavy beam of mass M = 46.7 kg is hinged to a vertical wall, and th

Question

One end of a heavy beam of mass M = 46.7 kg is hinged to a vertical wall, and the other end is tied to a steel cable of length 3.00 m, as shown in the figure. The other end of the cable is also attached to the wall at a distance of 4.00 m above the hinge. A mass m = 15.3 kg is hung from one end of the beam by a rope. a) Determine the tension in the rope. b) Determine the tension in the cable. c) Find the force the hinge exerts on the beam. Here is a link to the diagram http://gyazo.com/f3f3c3e1b3e4e07e1dc4f7ec3ffe97df

Explanation / Answer

balancing vertical force on heavy beam

Ry -Mg - Trope = 0

Trope = mg = 15.3*9.8 = 149.94 N

a. Tension is rope = 149.94 or 150N

Ry = 607.6 N

horizontal force on beam

Rx = Tcable

balancing moment about hinge,

4*Tcable- (3/2 *Mg) - (3*mg) = 0

4Tcable - 1136.31 = 0

b. Tcable = 284.08 N

Rx = 284.08N

Fhinge = (Rx^2 +Ry^2)^1/2

= (607.6^2 + 284.08^2)^1/2

c. Force due hinge = 670.73 N

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