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Homework Help: Finding normal force with momentum

  1. Oct 29, 2006 #1
    Water falls without splashing at a X kg/s from a height H into a bucket of mass M. The bucket sits on a sacle. Determine the reading of the sacle as a function of time.

    I know the the sum of all forces is equal to the derivative of momentum with respect to time.

    Mg is the force at time = 0.

    The correct answer is mg + xtg + x*SQRT(2gH)

    I know

    F = dp / dt
    dp = F dt

    but I don't know what to do.
  2. jcsd
  3. Oct 29, 2006 #2
    Since p = mv, the expression F = dp/dt can be expanded for situations involving changing masses: F = m dv/dt + v dm/dt.
  4. Oct 29, 2006 #3

    Andrew Mason

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    The scale is going to measure the downward force. There are two things that contribute the downard force. What are they?

  5. Oct 29, 2006 #4
    The total force measured by the bucket is the weight of the bucket + weight of water + force of collision.

    So, I understand mg + xtg which gives me force. But where did the x * SQRT(2gH) come from. SQRT(2gH) is equivalent to time, meaing that x * SQRT(2gH) is a mass. Why is a mass included in an equation for force?
    Last edited: Oct 29, 2006
  6. Oct 29, 2006 #5

    Andrew Mason

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    The rate of change of momentum is the rate of mass flow x the speed of the water when it hits the bucket.

    [tex]dp/dt = vdm/dt[/tex]

    In order to determine the speed, use the fact that potential energy is converted to kinetic energy. So, for an element of mass, [itex]\Delta m[/itex]:

    [tex]\Delta mgh = xtgh = \frac{1}{2}\Delta mv^2 = \frac{1}{2}xtv^2[/tex]

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