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Newton's Laws - friction, tension, acceleration

  1. Oct 2, 2009 #1
    Newton's Laws -- friction, tension, acceleration

    A block of mass m1 = 2 kg and a block of mass m2 = 3 kg are tied together and are pulled from rest across the floor by a force of Fp = 24 N. The coefficient of friction of the blocks with the floor is μ = 0.27.

    a) What is the acceleration of the two blocks?

    b) What is the tension in the string between the blocks?


    I think that this can be solved by setting up two equations:


    m1a = T - μm1g

    and

    m2a = Fp - T - μm2g


    The unknowns in those two equations are exactly what I need -- acceleration and tension.


    Anybody know how to solve this?!
     
  2. jcsd
  3. Oct 2, 2009 #2

    Doc Al

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    Staff: Mentor

    Re: Newton's Laws -- friction, tension, acceleration

    What have you tried so far to solve them? Hint: Try adding them together.
     
  4. Oct 2, 2009 #3
    Re: Newton's Laws -- friction, tension, acceleration

    Yes, I tried adding the two together by solving for T and plugging that equation into the other. Unfortunately, after crunching the numbers, I did not come to the correct answer.
     
  5. Oct 2, 2009 #4

    Doc Al

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    Staff: Mentor

    Re: Newton's Laws -- friction, tension, acceleration

    Show what you did.

    (Just add the two equations. What happens to the T terms?)
     
  6. Oct 2, 2009 #5
    Re: Newton's Laws -- friction, tension, acceleration

    The two equations are:

    m1a = T - μm1g

    m2a = Fp - T - μm2g

    I solved for T as such:

    T = m1a + μm1g



    Substituting this T value into the second equation, I got:

    m2a = Fp - (m1a + μm1g) - μm2g


    So,

    3a = 24 - (2a + (0.27)(2)(9.8)) - (0.27)(3)(9.8)

    Solving for a, I got 5a = 21.35, or a = 4.27 m/s^2. Unfortunately, I do not believe that this is the correct answer.

    (Thanks for helping me with this!!)
     
  7. Oct 2, 2009 #6

    Doc Al

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    Staff: Mentor

    Re: Newton's Laws -- friction, tension, acceleration

    No, not correct. Your equation is fine, just check your arithmetic. (Careful with parentheses and signs.)
     
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