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Tension in two wires at unknown angles

  1. Aug 6, 2016 #1
    1. The problem statement, all variables and given/known data
    An object at rest is suspended from two strings (A and B) as shown in the diagram, with A shorter than B. The object pulls on the point O with a force of 20 N. Each of the strings also exerts a force on the Point O. The angle between the strings at O is 90o.

    prob09.gif

    Which of the statements below are true? (If A and E are true, and the others are false, enter TFFFT).

    A) The force exerted by B on point O points downward and to the left.
    B) The magnitude of the force exerted by B on point O must be smaller than that of A.
    C) The magnitude of the vector sum of the forces exerted by A and B is greater than 20 N.
    D) The vector sum of the forces exerted by A and B points upward and to the right.
    E) The magnitude of the force exerted by B must be 20 N or less.

    2. Relevant equations
    F = ma

    3. The attempt at a solution
    I know that the net forces in the horizontal and vertical planes will add up to 0 respectively, and that double angles and trig can be used to narrow down the given data into two unknowns (one value for tension and the angle). I think that the final answer is False, False, False, True, True. I'm at a bit of a loss as to how to think about the problem further.
     
  2. jcsd
  3. Aug 6, 2016 #2

    Merlin3189

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    Perhaps you could give a reason for each answer.
    (BTW I disagree with only one of your answers. One other answer I might say the opposite, but I can see how one could say T and F for it!)
     
  4. Aug 6, 2016 #3
    A) F - In component form, the forces will act up and to the right
    B) F - I think considering cos of this force to the block will make it bigger than A
    C) F - The vector sum should be equal to 20N to keep the system in equilibrium
    D) F? - The forces in the horizontal should be opposite and equal, which means the vector sum should be up in the vertical
    E) T - If B were greater than 20N, there would most likely be movement in this direction
     
  5. Aug 6, 2016 #4

    Merlin3189

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    A) F - In component form, the forces will act up and to the right - force in B is up and right. I'm not sure where components come in?
    B) F - I think considering cos of this force to the block will make it bigger than A - not clear to me. cos of which angle? how big is that angle?
    C) F - The vector sum should be equal to 20N to keep the system in equilibrium - Agree
    D) F? - The forces in the horizontal should be opposite and equal, which means the vector sum should be up in the vertical - Agree
    E) T - If B were greater than 20N, there would most likely be movement in this direction - I don't follow your logic here. If both A and B were greater than 20N pulling mainly sideways, they'd cancel each other and only their smaller vertical components would add to 20N. But I do think B is less than 15N.
     
  6. Aug 6, 2016 #5
    • A: where the resultant B can be resolved into vectors on the x- and y-axes
    • B: I'm sorry, I confused this with determining magnitude of work.
    • E: As far as this goes I know it can be said that Ay + By = 20N to counter the weight, regardless of which one is greater. If this refers to force in the vertical, then B would have to be less than 20N with A making up the difference. It's just the mathematical relationship between B and the acute angle that made me unsure. I understand it now.
    Thank you for sacrificing some of your Saturday night!
     
  7. Aug 6, 2016 #6

    haruspex

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    You need to be careful with B. I draw your attention to two facts:
    • You are not told angle alpha
    • The word "must" in the question
    Write out the balance of forces equations for the horizontal and vertical directions.
    I don't think you do.
    To answer this question you need to use the given 90 degree angle.
     
  8. Aug 6, 2016 #7

    CWatters

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    I note it says A is shorter than B. So the length of A is in the range 0 to slightly less than B.
     
  9. Aug 6, 2016 #8

    CWatters

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    I think that makes statement B true.
     
  10. Aug 6, 2016 #9

    CWatters

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    For statement E.... I think force B would be a maximum when lenght A is a maximum. The max lenght of A is just less than lenght B. Eg the angle is 45 degrees.
     
  11. Aug 6, 2016 #10

    CWatters

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    At the risk of giving too much help.. if A is less than B what does that mean for Tan(alpha) and hence alpha.
     
  12. Aug 6, 2016 #11

    haruspex

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    Yes, I missed that.
     
  13. Aug 8, 2016 #12
    I completely forgot about Pythagoras. Thanks for all the help.
     
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