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Homework Help: Newton's laws,solving for tension (smthn wrong with my work)?

  1. Oct 5, 2011 #1
    A flat-topped toy cart moves on frictionless wheels, pulled by a rope under tension The mass of the cart is m1. A load of mass m2 rests on top of the cart with the coefficient of static friction u between the cart and the load. The cart is pulled up a ramp that is inclined at an angle theta above the horizontal. The rope is parallel to the ramp. What is the maximum tension T that can be applied without causing to load to slip?

    Okay. I figure this problem is fairly simple right?
    (i) Fx = m2a
    (ii) ff = m2a
    (iii)Fy = 0
    (iv)Fn - m2gcos = 0
    (v) Fn = m2gcos
    Plug v into (ii)
    (vi) um2gcos = m2a
    (vii) a = ugcos
    Now sum forces for the cart
    (vii) T - ff = (m1+m2)a
    Plug in (vi) and (vii)
    T - um2gcos = (m1+m2)(ugcos)
    Here's my problem. The final answer is simply T = (m1+m2)(ugcos). Meaning there's an obvious problem with my work here...

    What's the problem here? I'm so confused!! My teacher suggested "adding m2gsin" to my fx equation, so like m2a + m2gsin? Because I tried that out and it still didn't work. Any help is great help, thanks in advance
     
  2. jcsd
  3. Oct 5, 2011 #2

    Doc Al

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    Staff: Mentor

    What about gravity?
    OK.
    You'll need to fix this since you left out gravity on m2.
    The cart has mass m1, not m1 + m2. (And you forgot about gravity again.)
     
    Last edited: Oct 5, 2011
  4. Oct 5, 2011 #3
    -------

    Right, so does that mean it's m2a + m2gsin, with gravity added? or am I wrong??
     
  5. Oct 5, 2011 #4

    Doc Al

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    Staff: Mentor

    Adding gravity to your m2 equation means adding -m2gsinθ to ƩFx.
     
  6. Oct 5, 2011 #5
    Okay, thanks ^__^
     
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