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Dropping two balls, one with twice the mass

  1. Feb 9, 2015 #1
    1. The problem statement, all variables and given/known data
    Two masses are placed on top of a building. The mass of one is twice the mass of the other. Both are dropped at the same time. Neglecting air resistance, which statements are true?
    1. Both objects have the same potential energy at the top
    2. Both objects fall with the same acceleration
    3. Both objects have the same kinetic energy before hitting the ground
    4. Both objects have the same speed when they hit the ground

    A. 1, 2
    B. 1, 3
    C. 2, 4
    D. 1
    E. 2

    2. Relevant equations

    3. The attempt at a solution
    I know 1 and 2 are definitely true.
    But I also thought 3 and 4 were true since for 4, I could use the kinematic equation
    v2 = v02 + 2ay
    And since a and y and v0 are the same for both, I thought they'd have the same final velocity and thus, the same kinetic energy.
    But is that not true?
     
  2. jcsd
  3. Feb 9, 2015 #2

    Nathanael

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    Are you saying kinetic energy only depends on speed?

    Double check your thinking on this, too.
     
  4. Feb 9, 2015 #3
    Oh wait, never mind, the twice as heavy ball would have a greater kinetic energy since it has twice the mass.

    I still think 1 and 2 are both right though.
     
  5. Feb 9, 2015 #4
    2 and 4 are related, 1 and 3 are related. Can you think how?
     
  6. Feb 10, 2015 #5
    Oh I see how they're related. So if I use 1 and 3 first, the potential energy should be equal to the kinetic energy at the bottom. So then, that means that they both have the same kinetic energy and since their masses differ, their velocities would have to differ.

    But I don't see why using the kinematic equation tells me that the velocities at the bottom will be the same.
     
  7. Feb 10, 2015 #6

    Nathanael

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    Okay then let's trust the kinematics and say the speed is the same at the bottom. Therefore the smaller ball has less kinetic energy at the bottom. What does this mean about the potential energy at the top?
     
  8. Feb 11, 2015 #7
    Oh, wow, I was really stupid....
    The potential energies at the top aren't the same..... because they have different masses.
    Wow, thanks.

    So the answer should be 2 and 4?
     
  9. Feb 11, 2015 #8

    Nathanael

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    Yep
     
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