(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 15 meter beam jutting out of the side of a building is held by a hinge (at the wall) and a cable at 10 meters from the wall. The angle between the beam and the cable is 60 degrees and the mass of the beam is 250 kg. If a 1000 N object is located on the beam, 7 meters from the wall, what is the reacting forceRfrom the hinge and at what angle is it applied? Assume the system is in equilibrium.

2. Relevant equations

1. ΣF_{x}= R_{x}-TcosΘ = 0

2. ΣF_{y}= R_{y}+TsinΘ - F_{object}- F_{beam}= 0

3.TsinΘ(d_{cable}) - F_{beam}(d_{beam}) - F_{object}(d_{object})

*Use 10 m/s^{2}for the value of gravitational acceleration.

3. The attempt at a solution

Alright, so I just wanted to double check to see if I'm actually doing this correctly.

First I substitute into the third equation in order to find the cable tension.

Tsin60(10 m) - (2500 N)(7.5 m) - (1000 N)(7 m) = 0

T= 2973.44

Then, I would substitute theTvalue into the other equations.

ΣF_{x}= R_{x}- 2973.44cos60 = 0

R_{x}= 1486.72 N

ΣF_{y}= R_{y}+ 2973.44sin60 - 1000 - 2500 = 0

R_{y}= 924.925 N

From here, it appears to be a simple matter of using the Pythagorean Theorem and then just using inverse cosine to find Θ_{R}.

R = [tex]\sqrt{1486.72^2 + 924.925^2}[/tex] = 1750.95 N

cos^{-1}Θ = 1486.72/1750.95

Θ = 31.88°

I was hoping someone would be able to double check to see if my understanding of this matter is correct or otherwise. I was also wondering if someone could tell if my final answerRshould be positive or negative, as that is one thing I haven't a clue about.

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# Basic Torque - Hinge and Cable

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