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Moving a box with a force that is less than gravity

  1. Oct 3, 2012 #1
    1. The problem statement, all variables and given/known data
    The object is a box with a given mass m. Our person has the choice between pushing the box with a horizontal force, or pulling the box with a wire with an angle of θ=30o. The magnitude of Fo is the force vector he affects the box with in both cases.

    Is it possible (If you can freely choose a value for θ) to keep the box moving without using a force fo that is greater than the gravity on the box


    2. Relevant equations
    A drawing of the situation:
    http://myupload.dk/handleupload/64d68oBb8KHy8

    I believe I need an equation that describes the force Fo of θ, which I've found is given as:
    [itex]F_o(θ)=\frac{\mu_k mg}{cos(θ)-μ_k sin(θ)}[/itex]

    3. The attempt at a solution

    I could choose to solve F'o(θ)=0 for theta which gives θ=arctan(μk)

    This would describe the minimum force required but I don't know how to relate that to Fg
     
  2. jcsd
  3. Oct 3, 2012 #2

    Simon Bridge

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    What is the relationship between friction and the weight of the box?

    But what would the turning point tell you?
    Don't you want to know where F0 < Fg
     
  4. Oct 4, 2012 #3
    So if I use that Fnet(x)=Fo*cos(θ)-μn

    And that Fnet(x)<0, then the value of θ<arctan(μ), and therefor I'm applying a force Fo that is less than gravity? Wouldn't that technically mean the box is not moving and is being held back by the friction?
     
  5. Oct 5, 2012 #4

    Simon Bridge

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    Why would that be? Gravity is mg.... and force less than mg would be less than gravity. To overcome friction it just has to overcome μmg.cos(θ) ...
     
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