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Homework Help: Determine the angle which will cause the greatest torque

  1. Sep 18, 2010 #1
    1. The problem statement, all variables and given/known data
    Given F, b, and h, determine the angle θ which will cause the greatest strain.
    http://img844.imageshack.us/img844/5595/cusersjoshappdatalocalt.th.png [Broken]


    3. The attempt at a solution
    I know to break it up into components so that I get Ma = F(bcosθ+hsinθ). But after that I'm at a loss for what to do.
    Intuitively I think the answer is 45, but I'm at a loss for how to prove that mathematically.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 18, 2010 #2
    find the answer keeping it [tex]\theta[/tex] only and then look for the value of [tex]\theta[/tex] which can give the maximum value to answer. I'm also very new in engineering so can't say for sure but this method should work.
     
    Last edited: Sep 18, 2010
  4. Sep 18, 2010 #3
    see, Cos [tex]\theta[/tex] + Sin [tex]\theta[/tex] is to be made maximum
     
    Last edited: Sep 18, 2010
  5. Sep 18, 2010 #4
    I'm not seeing what you're getting at. Maybe its just the wording of your response.
     
  6. Sep 18, 2010 #5
    Moment about point A should be maximum to produce maximum strain to the body (okay)

    Now resolve the force F:
    1. F Cos [tex]\theta[/tex] along vertically downward direction (-Y)
    2. F sin [tex]\theta[/tex] along +X direction

    Moment about point A = F Cos [tex]\theta[/tex]. b + F sin [tex]\theta[/tex]. h
    (clock wise rotation is taken as positive)

    Now calculate the value of [tex]\theta[/tex] for which the moment will be maximum.
     
  7. Sep 18, 2010 #6
    I was able to get that far, but I'm just having trouble with finding that value for [tex]\theta[/tex]. The way it is right now I can't see any way forward other than just factoring out the F...but that doesn't get me any closer.
     
  8. Sep 18, 2010 #7

    nvn

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    wannawin: Do you currently use calculus in this course? Or no calculus yet?
     
  9. Sep 18, 2010 #8
    We don't use it in the course, but it did cross my mind to take a look at the first derivative and go from there. I guess thats looking more and more like the way to go.
     
  10. Sep 18, 2010 #9

    nvn

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    wannawin: You might be able to do it without calculus. Perhaps think of it this way (without calculus). Any component of F toward or away from point A causes no harm. Use that concept to figure out what is the worst direction for force F.
     
  11. Sep 18, 2010 #10
    oh there's another way to solve this problem very easily

    Resolve the force in such a way that it's one component passes through point A. For that you need to find an angle. Since b and h are given, you can do it easily.
     
  12. Sep 18, 2010 #11
    Answer: tan [tex]\theta[/tex] = b/h. If b and h will be equal you'll get [tex]\theta[/tex] = 45 degree but that's not given, I think.
     
  13. Sep 18, 2010 #12

    nvn

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    snshusat161: Did you know, we are not allowed to solve the problems for the student. The powers that be only allow us to check math, and occasionally give small hints. Also, your answer is incorrect.
     
  14. Sep 19, 2010 #13
    we don't have to give complete solution. I had only given answer for the problem. I had not solved the whole problem for him. I solved it in my notebook and I myself is in first semester so I'm trying to solve this question along with him sharing my some thoughts and accepting some thoughts from him. It's known as group learning.
     
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