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Pebble Shot with Spring Constant - how to setup?

  1. Mar 29, 2009 #1
    1. The problem statement, all variables and given/known data
    You shoot a 49 g pebble straight up with a catapult whose spring constant is 320 N/m. The catapult is initially stretched by 0.30 m. How high above the starting point does the pebble fly? Ignore air resistance.


    2. Relevant equations
    Unsure?


    3. The attempt at a solution
    49g pebble = 0.049kg
     
  2. jcsd
  3. Mar 29, 2009 #2

    rock.freak667

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    When the spring is stretched how much elastic potential energy does it have?

    This is the energy that is converted to gravitational potential energy to raise it to the maximum height.
     
  4. Mar 29, 2009 #3
    Uelastic = (.5)(320N/m)(0.3m2) = 14.4.

    But then what? How do I turn this into a height?
     
  5. Mar 29, 2009 #4

    rock.freak667

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    what is the formula for gravitational potential energy?
     
  6. Mar 29, 2009 #5
    Ugrav = mg[tex]\Delta[/tex]y
     
  7. Mar 29, 2009 #6
    I can find U grav, but i don't see what that would get me?

    Ug = (0.049kg)(9.8)(0.3)
    = 0.144
     
  8. Mar 29, 2009 #7

    rock.freak667

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    0.3 is not the height. if y is the height and U=mgy, and you know the energy it has is equal to the elastic potential energy (which you found to be 14.4J) can you find the height y?
     
  9. Mar 29, 2009 #8
    Yep. It was y that I was looking for...duh. So I just leave it blank, set Ug equal to 14.4, and solve for y, giving me roughly 30m as an answer.

    Thanks!
     
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