Tension in two ropes supporting a hanging weight

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Homework Statement



Two ropes are connected to a steel cable that supports a hanging weight as shown in the figure.

http://session.masteringphysics.com/problemAsset/1000050931/2/YF-05-59.jpg

Draw a free-body diagram showing all of the forces acting at the knot that connects the two ropes to the steel cable.

Based on your force diagram, which of the two ropes will have the greater tension?

Homework Equations



n/a

The Attempt at a Solution



rope.jpg


So Vector length: C<A<B

or should the length of C equal the length of A+B?

So vector A will have the greater tension than vector B because it is shorter?

Does this look and sound correct?

thank you :)
 
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Discussion

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Also could i get a little help with the last part of this question:

If the maximum tension either rope can sustain without breaking is 4000 N, determine the maximum value of the hanging weight that these ropes can safely support. You can ignore the weight of the ropes and the steel cable.

so i found the weight each rope can hold.

4000sin(60)= 3464

4000sin(4)= 2571

then i added these two together to get 6035 N but this is incorrect?

does anyone know where i went wrong?

thank you
 
Since the knot isn't accelerating, all forces acting on it have to balance each other.

To break this problem down, what you want to do is consider the components of each vector in the horizontal (x) and vertical (y) directions. Once you do this, you can determine the magnitudes of A and B in terms of C.

For the second part of the question, you first consider which rope will have the most tension on it and that's the one that would be first to break. Then, with a tension of slightly less than 4000 N, go back to the relative magnitudes of each vector you determined in the first part.
 
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so since its just hanging wouldn't i only need to deal with the y components of the vectors A and B?

so if this is true then the y component of A and the y component of B would have equal the length of the vector C?