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Tension Force problem involving friction

  1. Sep 29, 2008 #1
    1. A horizontal rope pulls a 20kg wood sled across frictionless snow. A 5 kg wood box rides on the sled. The coefficient of static friction for wood on wood is 0.5. What is the largest tension force for which the box doesn't slip?

    m = 5 kg box, 20 kg sled
    mu = .5
    T = ?

    2.
    F = ma
    Ff= mu x n

    3.
    F = ma
    a of box is zero since it is not moving

    T - mu x (20 + 5) x (9.8) = 0
     
  2. jcsd
  3. Sep 29, 2008 #2

    Doc Al

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    Staff: Mentor

    No, both sled and box are accelerating. (They're being pulled by a rope.)

    Hint: What is the maximum static friction between box and sled?
     
  4. Sep 29, 2008 #3
    I partially get it. If Tension force is greater than the static friction force, then the box will move. So just find friction force.

    Ff = mu x n
    Ff = .5(9.8)(5)

    But that isn't the right answer.
     
  5. Sep 29, 2008 #4

    Doc Al

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    Staff: Mentor

    That's just one step toward the answer. Now that you know the maximum friction force on the box, what is the maximum acceleration that the sled can have without the box slipping?

    To get the final answer, you'll need to apply Newton's 2nd law twice.
     
  6. Sep 29, 2008 #5
    So:

    sum of F = ma
    Ff = ma
    .5(9.8)(5) = 5(a)

    a = 4.9

    Tension of rope: T = ma

    T = (10 + 5)(4.9)
    T = 73.5

    Thanks a lot. I got it correct.
     
  7. Sep 29, 2008 #6

    Doc Al

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    Staff: Mentor

    Excellent!
     
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