What minimum tension must your cable be able to support without having your sign

Question

What minimum tension must your cable be able to support without having your sign come crashing down? You open a restaurant and hope to entice customers by hanging out a sign. The uniform horizontal beam supporting the sign is 1.80 long, has a mass of 15.0 , and is hinged to the wall. The sign itself is uniform with a mass of 35.0 and over-all length of 1.20 . The two wires supporting the sign are each 37.0 long, are 80.0 apart, and are equally spaced from the middle of the sign. The cable supporting the beam is 2.00 long.

Explanation / Answer

First you need to provide units of mass and measurements to your given values so as not to confuse the person who wants to answer your question.

Assuming the unit of mass is "kg" and the units of length and distances are "meter" and "centimeter.
Mass of beam = 15 kg
Length of beam = 1.80 meters
Mass of sign = 35 kg
Length of sign = 1.20 meters
Length of wires = 37 centimeters = 0.37 meter
Distance between wires = 80 centimeters = 0.80 meter
Length of cable = 2 meters

Solve for angle between cable & beam :
@ = arc cosine (1.80/2.00)
@ = 25.842 degrees

Solving for "T" (tension) :
Summation of Moment at Hinge = 0
T sine @ = (15kg x 9.81m/sec^2 x 0.90m) + (35kg x 9.81m/se^2 x 1.40m)
T sine 25.842 = 613.125 N
T = 613.125/sine 25.842
T = 1,406.60 Newtons (Answer)
T = 1.4066 KN (Answer)

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