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Force, Mass and Acceleration Problem

  1. Nov 21, 2012 #1
    1. The problem statement, all variables and given/known data
    A block of mass m1 on a rough horizontal surface is connected to a ball of mass m2 by a light weight cord over a light weight, friction-less pulley, as shown in the figure below. A force of magnitude F at an angle θ with the horizontal is applied to the block as shown. The coefficient of kinetic friction between the block and surface is uk. Determine the magnitude of the acceleration of the two objects.


    2. Relevant equations
    Refer to attachment


    3. The attempt at a solution
    I would just like to confirm my answer. Better still if anyone can suggest a shorter way of solving it would be nice. Please find my complete solutions on pdf attached. Thanks
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Nov 21, 2012 #2

    jedishrfu

    Staff: Mentor

    We can't help yet until you show us what you've done.

    Is that your answers written in the Pdf and hilighted in turquoise? and is that your work shown above the hilighting?

    It looked like this was a PDF question/answer from the book?
     
  4. Nov 21, 2012 #3

    haruspex

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    If you look at the legend at top left of page 2 you can see it is not out of a book. More tellingly, it's wrong.
    blondii, your force diagram for the block omits the tension in the string. Also, using F for the string tension in the second free body diagram creates confusion. Put, say, T for the tension in both diagrams and try again.
     
  5. Nov 22, 2012 #4
    Thanks for your response haruspex.

    I have reworked the problem with tensions added as specified. See my new attached diagram. Here is my new working out also. Please confirm if my answer is correct this time or any other suggested approaches. Thanks:

    Let:
    fk = Kinetic Friction
    uk = Coefficient of Kinetic friction
    g = Gravitational Acceleration
    n = Normal
    T = Tension


    Force acting on block
    ƩFx = Fcos - fk - T = m1a
    Eq (1)
    ∴ Fcos - fk - T = m1a

    ƩFy = Fsinθ + n - w1 = 0
    ∴ n = w1 - Fsinθ
    Eq (2)
    = m1g - Fsinθ (2)

    Substitute (2) into (1)
    Fcosθ - uk(m1g - Fsinθ) - m1a
    Eq (A)
    ∴T = Fcosθ - uk(m1g - Fsinθ) - m1a

    Force acting on ball
    ƩFy = T -w2
    = T - m2g = m2a
    Eq (B)
    ∴ T = m2a + m2g

    Calculate Acceleration
    Substitute (B) into (A)
    m2g + m2a = Fcosθ - uk(m1g-Fsinθ) - m1a
    a(m1 + m2) = Fcosθ - uk(m1g - Fsinθ) - m2g
    ∴ a = (Fcosθ - uk(m1g - Fsinθ) - m2g) / (m1 + m2)
     

    Attached Files:

  6. Nov 22, 2012 #5

    Please find attached also my revised answer on PDF and confirm if I am on the right track now. Thanks
     

    Attached Files:

  7. Nov 22, 2012 #6
    Your final answer is ok.
     
  8. Nov 22, 2012 #7
    Thanks for confirming grzz. Much appreciated
     
  9. Nov 22, 2012 #8

    jedishrfu

    Staff: Mentor

    how did you do the drawings? they look very professional.
     
  10. Nov 22, 2012 #9
    I did the drawings using Adobe Illustrator
     
  11. Nov 22, 2012 #10

    jedishrfu

    Staff: Mentor

    Okay, thanks.
     
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