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Task with spring, energy, velocity and angle

  1. Feb 17, 2013 #1
    1. The problem statement, all variables and given/known data
    A projectile is loaded into a spring cannon.

    Find its velocity as it leaves the spring.

    The cannon is angled at 38 degrees above the horizontal. (θ=38)

    m=0.025kg
    k=100 N/m
    x0=0.13m
    x1=0.05m

    (We press the spring down 13 cm when we load it. When it stops expanding, it still has 5 cm of winding left. Bit ambiguous in the text, but I interpret this to mean there is some mechanism that stops it from expanding the full 13 cm)


    2. Relevant equations

    0.5*k*x^2
    0.5*m*v^2
    mgh

    E(initial) = E(final)

    3. The attempt at a solution

    Do I have to account for the angle to find the velocity as it leaves the spring?

    Please correct me on this:

    1) The energy contribution from the spring does not need to be vectorized, because it is angled in parallell with the angle of the velocity we're measuring.

    2) The contribution from gravity also does not need to be vectorized, because when there is no friction, all the gravity will push against the spring direction regardless of angle. This one I am really unsure of..

    If I pretend the cannon points completely vertically:

    Njuw3yV.jpg

    0cgyBEH.jpg

    3) If statement 3 is correct: all angles for the cannon between 90 and 0 will give the same velocity.
    If statement 3 is incorrect, and the retarding contribution from gravity changes with angle, surely 90 degrees (completely vertical) will give the lowest velocity, and 0 degrees with give the highest.

    This conflicts with my calculations of 7.69 m/s for vertical, because the answer given is only 7.53 m/s

    What am I doing wrong? Any help whatsoever would be appreciated, spent.. 4 hours on this simply task now hah!
     
    Last edited: Feb 17, 2013
  2. jcsd
  3. Feb 17, 2013 #2

    haruspex

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    The gain in gravitational PE is only related to the change in height, so, yes, you do need to multiply by the sine of the angle. Your mistake is that you are adding the gain in gravitational PE instead of subtracting it. (.05-.13 will be negative.)
     
  4. Feb 17, 2013 #3
    Thanks.

    I am learning physics in a language other than English.

    What is PE an acronym for?

    Are you using the term "gain" in the same sense I am using the word "contribution"?

    Actually, I see that if g= -9.81 that takes care of itself... Which makes sense.

    And then I need to do some trigonometry work to modify the impact of gravity taking into account the angle.

    Gonna give that a go tomorrow, way past midnight here heh.
     
  5. Feb 17, 2013 #4

    haruspex

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    Potential Energy. In the present problem there is PE in the spring and gravitational PE.
    As the spring expands, there is a loss of PE in the spring, a gain (increase) of gravitational PE, and a gain of KE (kinetic energy).
     
  6. Feb 18, 2013 #5
    Thanks again. I should have understood PE stands for potential energy. I know how that works.

    I have made the changes to the calculations now and it looks good to me, uploading it in case somebody else wonders about this problem in the future:

    VzRGLpP.jpg
     
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