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Crates on a Ramp with Friction and a spring at bottom. Finding the spring constant.

  1. Jul 14, 2009 #1
    You are designing a delivery ramp for crates containing exercise equipment. The crates weighing [itex]F_1[/itex] will move at a speed of v at the top of a ramp that slopes downward at an angle [itex]\phi[/itex]. The ramp exerts a kinetic friction force of [itex]F_2[/itex] on each crate, and the maximum static friction force also has this value. Each crate will compress a spring at the bottom of the ramp and will come to rest after traveling a total distance of L along the ramp. Once stopped, a crate must not rebound back up the ramp.

    Calculate the force constant of the spring that will be needed in order to meet the design criteria.

    http://img269.imageshack.us/img269/1397/asdfbjl.png [Broken]

    This is what I've tried so far:
    initial energy: [itex](Lsin\phi)F_1+1/2*mv^2[/itex]
    final energy: [itex]1/2*kx^2[/itex]
    lost energy: [itex]F_2L[/itex]

    initial= final + lost
    [itex](Lsin\phi)F_1+1/2*mv^2 = 1/2*kx^2 + F_2L[/itex] (we shall call this equation 1)

    From the free body diagram of the crate resting on the spring at the bottom of the ramp:
    [itex]kx=F_1sin\phi+F_2[/itex] (we shall call this equation 2)

    I'm not quite sure all of the above is correct, but if so.. I don't think there's supposed to be the variable of m in there. Should I substitute [itex]F_1/g[/itex] ?
    Then, am I supposed to solve for x in equation 2 then plug that into equation 1?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jul 14, 2009 #2

    LowlyPion

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    Re: Crates on a Ramp with Friction and a spring at bottom. Finding the spring constan

    Looks like a plan.

    F1/g looks workable.

    2 equations, 2 unknowns ...
     
  4. Jul 15, 2009 #3
    Re: Crates on a Ramp with Friction and a spring at bottom. Finding the spring constan

    Edit: I found what I was doing wrong. Thanks.
     
    Last edited: Jul 15, 2009
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