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Box on Cart (Friction)

  1. Oct 16, 2005 #1
    This is a link to a picture of my problem:

    http://img57.imageshack.us/img57/9382/cart5rh.jpg

    It asks what tension on the rope would give the cart a maximum acceleration. The surface the cart is on is frictionless, while the cart itself is not (the surface the box is on).

    To solve this, I figured that pulling the rope with a force of usN would give the maximum acceleration of the cart. However, this seems too easy; I think I may have not completely answered the question.

    |T| = usN = usmg

    Is my reasoning correct? Thanks.
     
  2. jcsd
  3. Oct 16, 2005 #2

    Doc Al

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    Staff: Mentor

    You really didn't provide your reasoning, just your answer. (No, it's not correct.)

    Instead, think this way: What's the only force directly applied to the cart? What's the maximum acceleration acceleration that that force can give the cart? Use that to find the required tension in the rope.
     
  4. Oct 16, 2005 #3

    Doc Al

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    Staff: Mentor

    What contact force is exerted on the cart?
     
  5. Oct 16, 2005 #4
    Ok this is what I came up with:

    [tex]F_M=\mu_sN\implies a_M=\frac{\mu_sN}{M}[/tex]

    [tex]T=\left(M+m\right)a=\frac{\left(M+m\right)\mu_sN}{M};\quad N=mg[/tex]

    Is this correct?

    Thanks again.
     
  6. Oct 16, 2005 #5

    Doc Al

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    Staff: Mentor

    Now you've got it.
     
  7. Oct 16, 2005 #6
    Thanks Doc Al, I appreciate it.
     
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