# Calculating tension in a wire?

1. Jul 27, 2013

### BlueCB

1. The problem statement, all variables and given/known data

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?

3. The attempt at a solution

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

Apparently this is wrong according to my teacher?

2. Jul 27, 2013

### 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.

3. Jul 27, 2013

### BlueCB

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

4. Jul 27, 2013

### voko

I think so.

5. Jul 28, 2013

### siddharth23

Yup..10 kN in each wire.

6. Jul 28, 2013

### 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.

7. Jul 28, 2013

### siddharth23

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

8. Jul 28, 2013

### haruspex

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

9. Jul 28, 2013

### 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.

10. Jul 28, 2013

### voko

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.

11. Jul 28, 2013

### haruspex

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

12. Jul 28, 2013

### siddharth23

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

13. Jul 28, 2013

### haruspex

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.

14. Jul 29, 2013

### siddharth23

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