1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Statics Problem

  1. May 31, 2013 #1
    1. The problem statement, all variables and given/known data
    Two cables are tied together at C and loaded as shown. Determine the range of values of P for which both cables remain taut.
    FAyAUGD.png


    2. Relevant equations
    [itex]\Sigma F_x=0[/itex]
    [itex]\Sigma F_y=0[/itex]


    3. The attempt at a solution
    [itex]\Sigma F_x=\frac{ 4 }{ 5 }*P-\frac{ 600 }{ 650 }*T_{AC}=0[/itex]
    [itex]\Sigma F_y=\frac{ 250 }{ 200 }*T_{AC}+T_{BC}+\frac{ 3 }{ 5 }*P-480=0[/itex]

    I am ending up with 2 equations and 3 unknowns. How can I eliminate the variables?
     
  2. jcsd
  3. May 31, 2013 #2

    rock.freak667

    User Avatar
    Homework Helper

    You'll need to take moments about a point then. Try about point A.
     
  4. May 31, 2013 #3
    My knowledge on this is a bit rusty. Taking the moment about point A, I know for BC I would have: 600*T_(BC)
    I am not sure about the others, but here is my guess: [itex]ƩM_A=0.6*T_{BC}+0.6*(600/650)*T_{AC}-0.6*480+0.6*(2/5)*P=0[/itex]

    Is this correct?
     
  5. May 31, 2013 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    You need to use the critical condition that the cables remain taut. If P is too small for that, which cable will go slack? What if P is too great?
     
  6. May 31, 2013 #5
    Setting P=0, it seems that cable AC will go slack. I am not sure about if P is too great. It looks like it would be BC. I am still confused.
     
  7. May 31, 2013 #6

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    You may be confused, but you're getting there :smile:. So what equation do you get for BC going slack?
     
  8. May 31, 2013 #7
    This is where I'm confused. I took an arbitrarily large number and set it equal to P. Plugging this into both equations, T_(BC) becomes a large negative value. Not sure if I'm doing this correctly.
     
  9. May 31, 2013 #8
    Your coefficient of TAC in the y force balance is incorrect. It should be 250/650.

    Solve this pair of equations for TAC and TBC as a function of P. Make a graph or a table of TAC and TBC versus P. Each of the cables will go slack if the tension in the cable is less than zero. Find out the range of P that makes this happen for each of the cables. For example, you can immediately see from the x- force balance that cable AC will go slack if P is less than zero.
     
  10. May 31, 2013 #9

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    You don't need to try plugging in an arbitrary value for P. As P increases from 0, what will TBC be at the point where BC goes slack?
    (Also, note the correction Chestermiller mentions to your Fy equation.)
     
  11. May 31, 2013 #10
    Thank you!! I did this and got the correct answer. Here is what I did:

    I rearranged the equations like this:
    [itex]T_{AC}=P*\frac{4}{5}*\frac{650}{600}[/itex]
    [itex]T_{BC}=480-\frac{250}{650}*T_{AC}-\frac{3}{5}*P[/itex]


    Then I created these tables:
    T89jO50.png

    Since T_BC is positive at P=514 and negative at P=515, 514 must be the maximum value of P.

    Is this the only way to do this problem? Is there any easier method that takes less time?
     
  12. May 31, 2013 #11

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Yes - answer my question in post #9.
     
  13. Jun 1, 2013 #12
    TBC would be 0 where BC goes slack. But then what do I set TAC equal to?
     
  14. Jun 1, 2013 #13

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    With TBC = 0 you now have two equations and two unknowns. Solve them.
     
  15. Jun 1, 2013 #14
    Ah, right, I wasn't thinking :redface:

    Indeed this yields the same answer. Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Statics Problem
  1. Statics Problem (Replies: 1)

  2. Statics problem (Replies: 15)

  3. Statics table problem (Replies: 5)

Loading...