Determine the tension developed in wires CA and CB 2


Determine the tension developed in wires CA and CB required for equilibrium of the 10-kg cylinder. Take ϴ = 40°.

Determine the tension developed in wires CA and CB

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

Solution:

The first step is for us to draw a free body diagram like so:

Determine the tension developed in wires CA and CB

Next we will choose which sides to be positive. We will assume forces going \rightarrow^+ to be positive and \uparrow+ to be positive.

 

Now, we can write our equations of equilibrium for the x-axis forces and y-axis forces.

\sum \text{F}_\text{x}=0

F_{CB}\text{cos}\,(40^0)\,-\,F_{CA}\text{cos}\,(30^0)=0 —————–(eq.1)

 

\sum \text{F}_\text{y}=0

F_{CB}\text{sin}\,(40^0)\,+\,F_{CA}\text{sin}\,(30^0)\,-\,98.1=0 —————–(eq.2)

Show me the free body diagram again

 

Next we will solve for F_{CA} and F_{CB}. First we will isolate for F_{CB} in eq.1.

F_{CB}=\frac{F_{CA}\text{cos}\,(30^0)}{\text{cos}\,(40^0)}

(simplify by getting numerical values for cosine values)

F_{CB}\,=\,1.13F_{CA} —————–(eq.3)

 

Substitute the value of F_{CB} we found into eq.2.

1.13F_{CA}\text{sin}\,(40^0)\,+\,F_{CA}\text{sin}\,(30^0)\,-\,98.1=0

(Solve for F_{CA})

F_{CA}=80 N

 

Substitute the value of F_{CA} into eq.3 to find F_{CB}.

F_{CB}\,=\,(1.13)(80)

F_{CB}\,=\,90.4 N

This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 3, question 3-10.

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2 thoughts on “Determine the tension developed in wires CA and CB

    • questionsolutions Post author

      Well, tension is a type of force. Please read up on it here: https://goo.gl/jvhdjZ

      Remember, you can’t push on a rope, so the force on the rope is tension force. Also, not sure what you mean by “solved it based on force?” I think you have a misunderstanding between what type of force a rope can carry, in this case, its always tension force.