Could you answer this question for me please? It is the hardest question one may get about young modulus, elasticity ecc.

Roddilla - we are not going to take your exam for you! I suggest you work through each step of the problem, and if you get stuck along the way please show us what you tried and how you got stuck - then we can help point the way.

We can help, but have you worked out ANY of the answers yourself? Parts a and b, for example, are simple trigonometry.

Yes I worked it all out and in fact got a value of 2.36 x 10^-11 for Young's Modulus but I don't know if I worked it out correctly

Your value for Young's Modulus should not have a negative sign in the exponent. It should be on the order of the reciprocal of what you got. What did you calculate for the stress and elongation?

my mistake 2.36 x 10^11 not -11

could you check if it is good

Hm... may I ask you to post the stress and extension you got?

I'm not getting what you got.

That seems just about right. I get the same answer if I round the extension up to 0.08, but I would suggest you keep at least one more significant digit.

Jerry, how different was your answer? I think I'm right, but I must admit I'm not entirely sure if I'm off by a factor of two. You've probably done this sort of problem much more recently than I have! ;)

JC: I Think you're correct. I'm getting E=2.45 x 10^11 Pa, or 245 GPa. By the way, Young's Modulus for steel is on the order of 200 GPa (depending on the particular alloy), so this seems reasonable.

I calculate a stress of 18.8 GPa and strain of 7.7%.

Oh, you had more posts going in the meantime :p

Yes, the last post I saw was the negative power :o

Yes, now it's good :)

So for the force which is extending the wire you take the tension of each half of the wire
My teacher is saying that in order to calculate extension you have to use the tension of one half of the wire only which surely doesn't make sense

Could you plase post the working of the question so that I can compare it to mine

Quote:

---

Originally Posted by Roddilla

So for the force which is extending the wire you take the tension of each half of the wire
My teacher is saying that in order to calculate extension you have to use the tension of one half of the wire only which surely doesn't make sense

---

OK, now I'm embarrassed. I'm afraid I forgot to divide by 2 and I'm off by a factor of 2.

From the symmetry of the problem you can see that half of the 175N is carried by each half of the wire. So the tension in the wire is found from:



So T = 235.6N, and Stress = 235N/(.025 mm^2) x 10^6 mm^2/m^2 = 9.42 x 10^9 Pa

Strain is 7.7%, so

E = Stress/Strain = 9.42 x 10^9 Pa/0.077 = 122 GPa.

Sorry for the previous error.

EB, that was exactly the factor of two I was unsure about. In fact, that was my first way of calculating it, but then I looked up the Young's Modulus of steel (and saw Rodilla's answer) and decided it must be wrong.

I definitely agree with your answer now though. And the fact that it's low compared to the book value for E is not surprising since the wire is assumed to have gone beyond its elastic limit.

But if two tensions are acting from the centre, why don't you take the force acting on the wire as 235 x 2?

In my opinion it is like 1 half of the wore is receiving 236N of force while the other half is also receiving 236N of force so the total length of the wore is receiving 236*2

If you take 236N only then you must take one half of the wire only, no?

Why do you divide by two if the every tension is acting on a half of the string?

Darn I must have been asleep while doing this :(

I got 1.22338... × 10^11 and saw the same thing on the screen... =/

Okay Rodilla, for your comments now (please, use the answer box below the page instead of using the comments options please.

Quote:

---

In my opinion it is like 1 half of the wore is receiving 236N of force while the other half is also receiving 236N of force so the total length of the wore is receiving 236*2

---

No, if you use the whole wire and double the extension the tension that you use has to be the same.

Quote:

---

If you take 236N only then you must take one half of the wire only, no?

---

As per above, you take 236 N when taking the whole wire too.

Quote:

---

why do you divide by two if the every tension is acting on a half of the string?

---

The tension is divided by two because the portion of the wire that he is working with is half the total length of the wire.

SO as you are saying unknown008 the answer would still come to be 2 * 10^11 approximately since total extension of wire is 0.008, the original length is 0.10, the total force acting on the whole wire is 236 * 2 and the area is 2.5 * 10^-8
E = 1.89 * 10^10 (stress) * 0.10/0.008 = 2.36 * 10^11

not 2 * 10^11 but 2.36 * 10^11

No no no, I'm saying

I got 1.22338 × 10^11 Nm^-2

Hmm... I forgot one detail >.<

F = ke

If the length is doubled (the k constant doubles), the extension is doubled, and doubling the force too is wrong.

Hence, if you use the total length of the wire, you don't double the tension in the wire. I'm changing it now.

To be sure, just take the part of the wire that is under the tension which you got. You got the tension in half the wire, take the length and extension of that half wire.

Quote:

---

Originally Posted by Roddilla

SO as you are saying unknown008 the answer would still come to be 2 * 10^11 approximately since total extension of wire is 0.008, the original length is 0.10, the total force acting on the whole wire is 236 * 2 and the area is 2.5 * 10^-8
E = 1.89 * 10^10 (stress) * 0.10/0.008 = 2.36 * 10^11

---

Let's talk through this one more time: Instead of a single wire spanning across from left to right, picture the weight suspended from two separate wires, which happen to be tied to the weight at the same point. The forces, tensions, etc. are all exactly the same in this scenario as in the given one where the wire is continuous. Now, however, it's a little more intuitive to just consider one of the wires. Whatever tension, stress, elongation, and modulus we calculate for one wire will be exactly the same for the other wire, since everything is symmetrical in this problem.

Since the weight is held up by two wires, each one carries half the weight, or 87.5N. This 87.5N of upward force provided by the wire is accompanied by a 218.75N horizontal force pulling the weight toward the wall. This equates to a tension of ~235.6N in the wire. Given the cross-sectional area of the wire, this equates to a stress of around 9.424 GPa. Meanwhile, the strain of the wire is 0.077. Thus, the Young's modulus is around 122 GP.

The one thing which I still cannot understand is why working with 1 piece gives me one answer but working with two pieces the answer is different

1 half is experiencing 1 force and the other half is experiencing another force with same value

But if one each half there is a force of 236N acting, on the whole wire the total force acting is 236 x 2

THANK you all for your patience but I am not yet getting the point

The point that working with one half gives me one answer and working with whole wire gives me a different answer

Don't worry; you're not the first person to be confused by the concept of tension. It's confusing because intuitively it always seems like it should be double. I'll give another example:

Suppose you have a wire connected to an immovable object. You pull on the end of the wire with 200N of force. The tension in the wire is then 200N, of course. If you were to focus on one specific point on the wire (let's pick the middle), however, you'd find that it was experiencing a force of 200N in one direction as a result of you pulling on it, and it was experiencing a force of 200N in the opposite direction as a result of the equal and opposite reaction from the wall (Newton's third law). So it seems like each point on the wire is getting pulled by 200N in both directions. But by definition, that's still 200N of tension.

So in your case, yes, it seems that the wire is getting pulled by 236N in both directions, but that, by definition, is 236N of tension.

For a more familiar analogy, let's say you weigh around 70kg. That means that your body presses down on the bottoms of your feet with a force of around 700N. Meanwhile, the ground is pushing up on your feet with an equal and opposite reaction of 700N. Does that mean the bottoms of your feet are experiencing 1400N of total compression? No. Pushing down on something with 700N of force results in 700N of compression. Tension is the same; pulling on something with 236N of force results in 236N of total tension.

I hope that makes it a little clearer. :)

Very helpful indeed - you have solved a problem which I had ages ago as well I think
So the fact that half of the wire is getting pulled by 200N of force and the other half getting pulled by 200N of force still means that the wire is getting pulled by 200N of force overall

Jcaron - big thanks for your ingenious explanation

I'm glad that helped. It's not a very intuitive concept!

One last thing to conclude:
If rwo people are pulling a rope, one from each end, with 100N the total tension is 100N not 200N and if area is known and so is extension and original length one can find Young Modulus by: 100/area * length/extension

Yes that's right :)

For the first part, you could also replace one person by a pole while the other person pulls on with 100 N, the pole will exert 100 N too, but you only consider the force that you are applying and ignore the pole and this is the tension! :)