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Homework Help: Work and energy: find the total mechanical energy at the max. height of a projectile.

  1. Jan 19, 2010 #1
    1. The problem statement, all variables and given/known data
    A 32 kg cannon ball is fired from a cannon with muzzle speed of 1360 m/s at an angle of 44◦ with the horizontal. The acceleration of gravity is 9.8 m/s2 . What is the total mechanical energy at the maximum height of the ball? Answer in units of J.

    2. Relevant equations
    Mechanical energy = KE + UG + US (ignore spring potential energy)
    UG = mgh
    KE = (1/2)mv2

    3. The attempt at a solution
    I actually thought I understood the concepts behind this one fine, but I keep getting the wrong answer.

    First I found the height:
    Theoretically, mechanical energy is conserved, so E at launch = E at top of flight (w/ max height)
    KE + UG = KE + UG
    no UG at launch, and no KE at top of flight in the y-direction -- motion is changing direction -- so
    KE in the vertical direction = UG
    (1/2)(32 kg)(1360sin44 m/s) = (32 kg)(9.8 m/s2)h
    h = 45536.98701 m

    Then, I attempted to find the mechanical energy at the top of the flight.
    Known facts:
    * the mass has a vertical acceleration and a horizontal velocity of 1360cos44 m/s
    * the mass has both kinetic energy (it is moving) and potential gravitational energy.
    * I guessed that the total mechanical energy would be the resultant of these two using the Pythagorean theorem since the two energies are perpendicular to each other.

    E at top = KE in the x-direction + UG in the y-direction
    KE = (1/2)(32)(1360cos44)2 = 15313200.87 J
    UG = (32)(9.8)(45536.98701) = 14280399.13 J

    KE2 + UG2 = resultant2
    resultant = 20938574.93 J

    But... that's the wrong answer.
    Do the directions of the vectors not matter? Can someone provide an explanation for this?
     
  2. jcsd
  3. Jan 20, 2010 #2

    ehild

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    Homework Helper

    Re: work and energy: find the total mechanical energy at the max. height of a project

    Energy is scalar, has no direction, you simply have to add the different kinds of energy.

    "KE2 + UG2 = resultant2" this is wrong.

    As for your method, you overcomplicate the calculations. Conservation of the mechanical energy means that the total energy E= KE + PE at the muzzle is the same as at the maximum height.

    ehild
     
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