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# Knowing that α = 55° and that boom AC exerts on a pin C a force directed along line AC, determine a) the magnitude of that force b) The tension in cable BC.

Question-AnswerCategory: Engineering MechanicsKnowing that α = 55° and that boom AC exerts on a pin C a force directed along line AC, determine a) the magnitude of that force b) The tension in cable BC.
Tuntun asked 1 year ago

Knowing that α = 55° and that boom AC exerts on a pin C a force directed along line AC, determine
a) the magnitude of that force
b) The tension in cable BC.

2 Answers
Sazid Ahmad answered 1 year ago

Sazid Ahmad answered 1 year ago

Step: 1

Draw free body diagram at point C as shown:

Step: 2

From the Lami’s theorem, write the equilibrium equation of forces as follows:
…… (1)
Here,  is the tension in the cable BC and  is the force in the member AC.

Step: 3

(a)
Calculate the force in the member AC as follows:
From equation (1),

Here, the negative sign indicates that the original direction is opposite to that of assumed direction.
Therefore, the force in the member AC is

Step: 4

(b)
Calculate the tension in the cable BC as follows:
From equation (1),

Therefore, the tension in the cable BC is .

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