Calculating tension in a wire?

[BlueCB]

Homework Statement

A wing on a light aircraft experiences an upward thrust of 10 kN.
This is counteracted by two steel wires each set at an angle of 30 degrees from the horizontal and of length of 4 meters.
The diameter or the wire is 10 mm, and Young's modulus for steel is 2.05*10^11 N/m^2.

What is the tension in each wire?

The Attempt at a Solution

10,000 / sin(30 = 20,000
Tension = 20 kN?

Apparently this is wrong according to my teacher?

 

[voko]

The entire force of tension is 20 kN, that is correct. But you have two wires. Using ordinary statics, you cannot determine how much tension each wire experiences, but it is reasonable to assume that it is distributed equally.

 

[BlueCB]

So am I right in saying that the answer is 10 kN of tension in each tie, if the total is 20 kN?

 

[voko]

So am I right in saying that the answer is 10 kN of tension in each tie, if the total is 20 kN?

I think so.

 

[siddharth23]

Yup..10 kN in each wire.

 

[haruspex]

Since the modulus is given, it is conceivable that the wires stretch enough to change the geometry. Not sure how difficult the question is supposed to be. However, seems to me the stretch is only about 0.05%. Or maybe there are more parts to the question.

 

[siddharth23]

Tension and tensile stress are two different things. If tensile stress is to be calculated, then yes, E needs to be used.

 

[haruspex]

Tension and tensile stress are two different things. If tensile stress is to be calculated, then yes, E needs to be used.

If the stretch were 10%, say, then it would change the geometry sufficiently to affect the tension.

 

[siddharth23]

Tension will depend on the force, won't it? Stretch will change the cross sectional are, which will change the Tension/Area ratio (Stress), not the tension.

 

[voko]

Since the modulus is given, it is conceivable that the wires stretch enough to change the geometry. Not sure how difficult the question is supposed to be. However, seems to me the stretch is only about 0.05%. Or maybe there are more parts to the question.

Yes, this is a good point. I thought that the modulus was given for a next step, but its is definitely true that as the wires stretch due to tension, the geometry changes.

However, the change in the geometry affects the wing and probably the force acting on it, and there is no information in the problem on that.

 

[haruspex]

Tension will depend on the force, won't it? Stretch will change the cross sectional are, which will change the Tension/Area ratio (Stress), not the tension.

If it stretches enough to change the angle significantly then it will also change the forces.

 

[siddharth23]

To change the angle, the position of the wing or other pivot would have to change.

 

[haruspex]

To change the angle, the position of the wing or other pivot would have to change.

If the cable stretches, something else must change. Maybe the wing flexes, or maybe it stays straight and pivots freely at the point of attachment. Either way, the angle will change.

 

[siddharth23]

If the wing flexes, who purpose of using cable is being lost.