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Stupid Stubborn Mule and his Kinetic/Static Friction

  1. Sep 23, 2008 #1

    1. The problem statement, all variables and given/known data
    A stubborn, 120 kg mule sits down and refuses to move. To drag the mule to the barn, the exasperated farmer ties a rope around the mule and pulls with his maximum force of 770 N. The coefficients of friction between the mule and the ground are µs = 0.8 and µk = 0.5. Is the farmer able to move the mule?


    If so, how much force in excess of the required amount did the farmer pull? If not, how much more force does the farmer require?

    2. Relevant equations
    F= Ma
    F(fric)= (Coefficient of friction)*N(normal force)

    3. The attempt at a solution

    I got the answer to the first part of this question through guessing, so I'm not sure if there is actually work invovled there that needs to be used for part 2 that I therefore don't have due to the fact that I guessed. Anyway, I'm not sure how to approach this problem. Using those equations I got answers separately for static friction and kinetic friction, but I don't think either of those is what I'm looking for. My thought is that I can just disregard kinetic for a second because using 770N, only static friction is involved.

    Is there a different way to approach this problem??

    Thank you so much in advance!


    PS- I do realize that my net force is zero, for in my force diagram all the vectors should equal each other. But, then how is one to get the amount of force needed to actually pull the mule?
    Last edited: Sep 23, 2008
  2. jcsd
  3. Sep 23, 2008 #2


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    Science Advisor
    Homework Helper

    Hi Phoenix! :smile:

    Yes, you're right … the kinetic friction is irrelevant.
    In exam questions like this, you should always assume that the acceleration is negligible … the mule moves, but only just … in other words, the acceleration is zero.

    Show us what you think the answer is. :smile:
  4. Sep 23, 2008 #3
    The only relevant equation that involes the acceleration is F=ma. However, showing that the acceleration is zero wouldn't aid us in that equation. Hmmm...

    All right, a different view...

    Using the fact that acceleration is so low would mean that the total force comes out to be zero. Therefore the answer would be zero. But that doesn't seem right at all. 770N could be 1000N away from actually being able to move the mule just an inch.

    µs = 0.8
    Using this seems like a good idea. But when put into the second equation, the maximum static friction comes out to be 96. (.8*120). I have no idea where to go.
    Using this
  5. Sep 23, 2008 #4

    Doc Al

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    Staff: Mentor

    What's the maximum static friction force that the mule can generate? (Correct your equation above. What's the normal force? 120 kg is the mule's mass.)

    Compare this to the applied force of 770N and then decide whether he can move the mule or not.
  6. Sep 23, 2008 #5
    GAR! Darn it! I don't know how many times I've substituted mass for weight.

    In other words, all I have to do is multiply 120*9.8 to get the weight. (Which is 1176) Then multiply that by .8, to give me the maximum static friction. 941-770=171.

    Thank you so much!

    Oh, a friend asked about what would happen if the man could move the mule and we were trying to find how much extra force was exerted. Wouldn't that mean taking the WEIGHT (got it this time) being 1176, then multiplying by .5 (the kinetic energy), equaling 588. 770-588=182. Would that be correct?
  7. Sep 23, 2008 #6

    Doc Al

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    Staff: Mentor

    Exactly. (But that's the coefficient of kinetic friction, not kinetic energy. :wink:)
  8. Sep 23, 2008 #7
    Right, right, of course. :)

    Thank you so much for all of the help.

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