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Maximum force so object on top wouldn't start sliding back

  1. Dec 13, 2016 #1
    1. The problem statement, all variables and given/known data
    Box B is on top of box A. Box A has a mass of 1 kg, B has 0.3 kg. Coefficient of friction between ground and box A is 0.5, between box A and B : 0.75. With what maximum force can I pull box A without box B sliding back ?

    m1 = 1 kg
    m2 = 0.3 kg
    u1 = 0.5
    u2 = 0.75

    2. Relevant equations
    Ffr = umg
    F = ma

    3. The attempt at a solution
    I got that the force of friction between box A and ground is 6.5 N ( (m1 + m2)u1g )
    Between box A and B friction is 2.25 N. ( m2u2g )
    So the total force of friction box A receives is 8.75 N. But I can't work out what is the maximum force with which I can pull box A without having box B falling off.
     
  2. jcsd
  3. Dec 13, 2016 #2

    Doc Al

    User Avatar

    Staff: Mentor

    That's the key.
    Hint: What's the max acceleration that box A can have before it starts to slide?
     
  4. Dec 13, 2016 #3
    I got acceleration 7.5 m / s2. Then :
    F = Ffr + ma = 6.5 + 9.75 = 16.25 N ( for friction I used friction between box A and ground, and m = 1.3 kg)

    Is this correct ?
     
  5. Dec 13, 2016 #4

    Doc Al

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    Staff: Mentor

    Looks good to me. (Assuming it's OK for you to use g = 10 m/s^2.)
     
  6. Dec 13, 2016 #5
    Yeah, it's ok. Thank you !
     
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