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Work and Energy-Combining equations

  1. Jul 27, 2009 #1
    Work and Energy--Combining equations

    Hi, I have the following sample problem that I am having difficulty combining equations:

    The power expended in lifting an 825-lb girder to the top of a building 100 ft. high is 10.0 hp. How much time is required to raise the girder.

    So the data is:

    F= 825
    s= 100 ft
    P= 10.0
    t= ?

    Now the following two equations contain all the values we need:

    P=W/t and W= Fs

    In the text the combined equations are shown as:

    t= W/P = Fs/P ----- How was this found and combined?


    Thanks.
     
  2. jcsd
  3. Jul 27, 2009 #2

    Dick

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    Re: Work and Energy--Combining equations

    Well, combining the equations is just minor league algebra. P=W/t is the same as saying t=W/P, right? Then put W=Fs. Is that really what your question is? To really finish the problem you need to look up what a horsepower is in ft*lb/s.
     
  4. Jul 27, 2009 #3
    Re: Work and Energy--Combining equations

    Well, woudn't P=W/t translate to: t=PxW and where does Fs/P come from?
     
  5. Jul 27, 2009 #4

    Dick

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    Re: Work and Energy--Combining equations

    How would P=W/t turn into t=P*W?? Take P=W/t, and multiply both sides by t, getting P*t=(W/t)*t=W. Now divide both sides by P, getting (P*t)/P=t=W/P. You have a wrong idea about algebra. What is it?
     
    Last edited: Jul 27, 2009
  6. Jul 27, 2009 #5
    Re: Work and Energy--Combining equations

    I see, yeah it has never been my strong point, but how is FS/P found?
     
  7. Jul 27, 2009 #6

    Dick

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    Re: Work and Energy--Combining equations

    Take t=W/P. You know W=Fs. Just substitute Fs for W. You can always substitute equal quantities for equal quantities. You aren't exaggerating about algebra being a weak point. No offense, but it's REALLY weak. Problems like this are going to take more than you've got. Can you take some time to review and practice?
     
  8. Jul 27, 2009 #7

    cepheid

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    Re: Work and Energy--Combining equations

    W = Fs

    EDIT: Nevermind. Somebody got there before me.
     
  9. Jul 27, 2009 #8
    Re: Work and Energy--Combining equations

    Yeah, I know they are and it hasn't bothered me until now. Ok, so because they are equal quantities it becomes just FS. Where does the P come from if it wasn't previously in the equation.
     
  10. Jul 27, 2009 #9

    cepheid

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    Re: Work and Energy--Combining equations

    What??? The P was in the equation previously!

    t = W/P [1]

    W = Fs [2]

    THEREFORE SUBSTITUTING Fs for W in [1],

    t = Fs/P
     
  11. Jul 27, 2009 #10

    diazona

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    Re: Work and Energy--Combining equations

    It was previously in the equation. You see the P in t=W/P? It's that P.
     
  12. Jul 27, 2009 #11
    Re: Work and Energy--Combining equations

    Got it. Thanks, both of you very much. I haven't had to use algebra in so long, and I was never really good at it. I will do some practicing.

    Thanks again.
     
  13. Jul 27, 2009 #12
    Re: Work and Energy--Combining equations

    Actually I have one more question.

    With the values

    P= known
    s= known
    t= known
    F= unknown

    and the equations P= W/t and W= Fs

    how does the working equation become F= Pt/s


    I was doing it this way F= s * W then after this point I was lost.
     
  14. Jul 27, 2009 #13
    Re: Work and Energy--Combining equations

    Your equation is wrong....
    You can look from the previous post that W = F*s , not F = s*W

    W = F*s
    F = W/s

    Do you get it?
     
  15. Jul 27, 2009 #14
    Re: Work and Energy--Combining equations

    Ok substitute again that W=Fs into P=W/t.
    This gets P=Fs/t. Got it? To get F by itself we multiply both sides by t, Pt=Fs, and then you divide by s on both sides. Pt/s=F or F=Pt/s.
     
  16. Jul 27, 2009 #15
    Re: Work and Energy--Combining equations

    See, that's what I was doing before isolating f by dividing both sides by s ,but

    how come P=W/t solving for t = t=W/P when using the above approach multiplying both sides by W gets PxW=t


    What is the difference with these two problems that makes calculating the answer different?
     
  17. Jul 27, 2009 #16
    Re: Work and Energy--Combining equations

    Oh sorry! I didn't know the equations were wrong! I just saw two equations and you needed help to get a third one. I don't know the equations or what they mean. Sorry for your trouble.
     
  18. Jul 27, 2009 #17
    Re: Work and Energy--Combining equations

    P =W/t, multiplying both sides by W, we get :

    P x W = W^2 / t , not PxW=t
     
  19. Jul 28, 2009 #18

    Dick

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    Re: Work and Energy--Combining equations

    W=F*s does NOT turn into F=s*W when you solve for F. It turns into F=W/s. You have to DIVIDE both sides by s. There's really no point in asking these question until you review your algebra.
     
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