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Two masses hanging from a pulley (conservation of energy)

  1. Mar 6, 2015 #1
    1. The problem statement, all variables and given/known data
    Two masses are connected by a string that hangs over a frictionless pulley with mass 8kg, radius .25m, and moment of inertia .5mr^2. One mass lays on the ground and has mass 15kg. The other mass is 22.5 kg and is 2.75 m above the ground. Use conservation of energy to determine the speed of the 22.5 kg mass when it hits the ground

    2. Relevant equations
    Ke final = pe initial
    Ke=.5mv^2 + .5Iw^2

    3. The attempt at a solution
    I found the pe of the 22.5 mass using pe=mgh. I made that equal the ke equation but I'm not sure whether to combine masses or what to use
     
  2. jcsd
  3. Mar 6, 2015 #2

    PeroK

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    The system loses gravitational PE. The first question is to ask where does this energy go?
     
  4. Mar 6, 2015 #3

    haruspex

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    There are three elements to the system, the two masses and the pulley. Consider the total energy (KE and PE) of each at start and again at the moment of impact.
     
  5. Mar 6, 2015 #4
    Kinetic energy of each mass and the rotation of the pulley
     
  6. Mar 6, 2015 #5

    PeroK

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    Can you write down an energy equation involving all the energies gained and lost?
     
  7. Mar 6, 2015 #6
    Ke=.5mv^2 of mass 1 + .5mv^2 of mass 2 + .5Iw^2 of pulley
     
  8. Mar 6, 2015 #7

    PeroK

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    OKay, but there's no PE there.

    You're also going to have to find a relationship between the various KE's. So, you need to think about that as well.
     
  9. Mar 6, 2015 #8
    Would the pe just be the mgh of the weight above the ground?
     
  10. Mar 6, 2015 #9

    PeroK

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    There are two masses involved.
     
  11. Mar 6, 2015 #10
    But why does it have pe if it's on the ground
     
  12. Mar 6, 2015 #11

    PeroK

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    Does it stay on the ground?
     
  13. Mar 6, 2015 #12
    No but in the beginning it has no pe
     
  14. Mar 6, 2015 #13

    haruspex

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    Right (assuming ground is taken as the reference point for PE). So post the initial energy = final energy equation.
     
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