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    Hard physics question

    Asked Jun 16, 2011, 08:19 AM — 31 Answers
    Could you answer this question for me please? It is the hardest question one may get about young modulus, elasticity ecc.

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    ebaines's Avatar
    ebaines Posts: 11,827, Reputation: 1272
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    #2

    Jun 16, 2011, 08:38 AM

    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.
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    jcaron2's Avatar
    jcaron2 Posts: 984, Reputation: 204
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    #3

    Jun 16, 2011, 09:42 AM
    We can help, but have you worked out ANY of the answers yourself? Parts a and b, for example, are simple trigonometry.
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    Roddilla's Avatar
    Roddilla Posts: 145, Reputation: 3
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    #4

    Jun 16, 2011, 10:11 AM
    Comment on jcaron2's post
    Quote Originally Posted by jcaron2 View Post
    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
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    jcaron2's Avatar
    jcaron2 Posts: 984, Reputation: 204
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    #5

    Jun 16, 2011, 10:53 AM
    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?
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    Roddilla's Avatar
    Roddilla Posts: 145, Reputation: 3
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    #6

    Jun 16, 2011, 10:57 AM
    Comment on jcaron2's post
    Quote Originally Posted by jcaron2 View Post
    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
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    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #7

    Jun 16, 2011, 11:03 AM

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

    I'm not getting what you got.
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    jcaron2's Avatar
    jcaron2 Posts: 984, Reputation: 204
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    #8

    Jun 16, 2011, 11:15 AM
    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! ;)
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    ebaines's Avatar
    ebaines Posts: 11,827, Reputation: 1272
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    #9

    Jun 16, 2011, 11:43 AM

    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%.
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    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #10

    Jun 16, 2011, 11:49 AM

    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 :)
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    Roddilla's Avatar
    Roddilla Posts: 145, Reputation: 3
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    #11

    Jun 16, 2011, 11:52 AM
    Comment on ebaines's post
    Quote Originally Posted by ebaines View Post
    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%.
    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
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    ebaines's Avatar
    ebaines Posts: 11,827, Reputation: 1272
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    #12

    Jun 16, 2011, 12:04 PM
    Quote Originally Posted by Roddilla View Post
    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.
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    jcaron2's Avatar
    jcaron2 Posts: 984, Reputation: 204
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    #13

    Jun 16, 2011, 12:20 PM
    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.
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    Roddilla's Avatar
    Roddilla Posts: 145, Reputation: 3
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    #14

    Jun 16, 2011, 10:10 PM
    Comment on jcaron2's post
    Quote Originally Posted by jcaron2 View Post
    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?
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    Roddilla's Avatar
    Roddilla Posts: 145, Reputation: 3
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    #15

    Jun 16, 2011, 10:11 PM
    Comment on jcaron2's post
    Quote Originally Posted by jcaron2 View Post
    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.
    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
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    Roddilla's Avatar
    Roddilla Posts: 145, Reputation: 3
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    #16

    Jun 16, 2011, 10:24 PM
    Comment on jcaron2's post
    Quote Originally Posted by jcaron2 View Post
    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.
    If you take 236N only then you must take one half of the wire only, no?
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    Roddilla's Avatar
    Roddilla Posts: 145, Reputation: 3
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    #17

    Jun 17, 2011, 01:08 AM
    Comment on ebaines's post
    Quote Originally Posted by ebaines View Post
    Quote Originally Posted by Roddilla View Post
    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.
    Why do you divide by two if the every tension is acting on a half of the string?
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    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #18

    Jun 17, 2011, 05:13 AM

    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.

    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.

    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.

    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.
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    Roddilla's Avatar
    Roddilla Posts: 145, Reputation: 3
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    #19

    Jun 17, 2011, 06:26 AM
    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
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    Roddilla's Avatar
    Roddilla Posts: 145, Reputation: 3
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    #20

    Jun 17, 2011, 06:27 AM
    Comment on Roddilla's post
    Quote Originally Posted by Roddilla View Post
    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
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