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Block on block problem

  1. Jan 30, 2017 #1
    1. The problem statement, all variables and given/known data
    A block of mass m = 0.500 kg rests on top of a block of mass M = 2.50 kg which is on the
    floor. A string attached to the block of mass M is pulled so that its tension is T = 7.00 N
    at a 25.0o angle to the horizontal as shown. The blocks move together across the
    horizontal surface. The coefficient of static friction at the surface between the blocks is
    μs = 0.410. There is no friction at the surface between block M and the floor.

    a) What is the acceleration of the two-block system?

    b) What is magnitude and direction of the total force (combination of normal force
    and frictional force) on block m due to block M?

    c) The tension T is now increased - what is the maximum tension, Tmax, with which
    the string can be pulled such that the blocks continue to move together (i.e. that
    the block of mass m does not start to slide on top of the block of mass M)?



    2. Relevant equations


    3. The attempt at a solution
    I solved part a and got 2.11 m/s^2 but i have no clue about part b and c. please help me.
     
  2. jcsd
  3. Jan 30, 2017 #2

    PeroK

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    For part b): what is happening to block m?
     
  4. Jan 30, 2017 #3
    Since there is friction, block m is not moving. Only M is moving.?
     
  5. Jan 30, 2017 #4

    PeroK

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    When the question says "the blocks move together ...", how do you interpret that?
     
  6. Jan 30, 2017 #5
    An analysis that comes to mind is pulling a sled with a child on it...except there is no incline
     
  7. Jan 30, 2017 #6

    PeroK

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    Is block m accelerating?
     
  8. Jan 30, 2017 #7
    no
     
  9. Jan 30, 2017 #8

    PeroK

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    You might want to revise your answer to part a), where I imagine you calculated the acceleration of the two block system. You should recalculate for acceleration of mass M only?

    How did you get 2.11m/s/s if block m doesn't move?
     
  10. Jan 30, 2017 #9
    I found the x and y components of the tension with the angle. Since acceleration is horizontal and not vertical, only the x component is considered. I used Newton's 2nd Law, 7cos25=ma, and when I solved for a, I got 2.11m/s^2. This is only for mass M (the one without friction). Was I supposed to include both blocks? If mass m is not moving, then shouldn't it be fine that we only consider block M?
     
  11. Jan 30, 2017 #10

    PeroK

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    I reckon cos25 is about 0.9, so the horizontal force is about 6.3N.

    That would accelerate block M - mass 2.5kg - at about 2.6 m/s/s.

    Or, it would accelerate the system of block M and m - combined mass 3kg - at about 2.1m/s/s.

    So, how did you get 2.1m/s/s assuming only block M moves?
     
    Last edited: Jan 30, 2017
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