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Homework Help: Potential and Kinetic Energy with Time Thrown In

  1. Jan 27, 2010 #1
    1. The problem statement, all variables and given/known data

    A stone weighing 0.2 kilograms is thrown vertically upwards with a velocity of 19.6 meters per second. Neglecting the friction of the air, calculate the kinetic and potential energy it possesses at the end of 1 second and 2 seconds respectively.

    2. Relevant equations



    3. The attempt at a solution
    I found total kinetic energy here:
    Total Kinetic Energy=1/2 times mass times velocity squared
    KE = (1/2)(0.2)(19.2) ^2 = 36.864
    - just not sure how to find it after "1 and 2 seconds respectively."

    I know potential energy =
    Egrav=mgh

    but i dont have a height value so even rearranging doesn't work:
    And rearranging to solve for h=Egrav/mg = ???

    How do you solve for kinetic and potential energy when you have the added component of time and missing components of height?
     
  2. jcsd
  3. Jan 27, 2010 #2

    rl.bhat

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    Homework Helper

    Use h = ut-1/2gt^2 where u is the initial velocity of the body.
    u is given. t is known. Find h at the end of 1 s and 2 s. Then find PE = mgh.
    Then KEf = KEi - mgh.
     
  4. Jan 27, 2010 #3
    This is what i got:
    Use h = ut-1/2gt^2 where u is the initial velocity of the body.
    For 1 second h=(19.6)(1)-1/2(9.8)(1) ^2 = 14.7
    For 2 seconds h = (19.6)(2) – ½(9.8)(2) ^2 =19.6
    PE=mgh
    For 1second = PE=(0.2)(9.8)(14.7) = 28.812
    For 2seconds = PE (0.2)(9.8)(19.6) = 38.416

    For Kinetic Energy-1second
    KEf = 36.864 – (0.2)(9.8)(14.7) = 8.052
    For Kinetic Energy – 2seconds
    Kef = 36.864 – (0.2)(9.8)(19.6) = -1.552

    Is this correct? Can that last kinetic energy value be negative?
     
  5. Jan 28, 2010 #4

    rl.bhat

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    In the second case
    final velocity after 2 second is
    v = u - gt = 19.6 - 2*9.8 = 0.
    So at 2 second KE = 0.
     
  6. Jan 28, 2010 #5
    Ok -thanks. Why does the equation change for the second time-for 2 seconds? Why would you use PE-tgh in the first one and H-gt in the second? Is it b/c at 2 seconds, PE would be 0?
     
  7. Jan 28, 2010 #6
    one more quick thing - why did we use 0.2 for seconds in the first equation but 2.0 in the second?
     
  8. Jan 28, 2010 #7

    rl.bhat

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    0.2 kg is mass, and 2 second is the time.
     
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