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Derived values not satisfying equations.

  1. Feb 10, 2009 #1
    I derived some values from 2 equations...the values are such that its not complying with one of the equations -

    Considering scenario of 2 colliding bodies, in this case both move in the same direction but one is much faster.
    u1 = 80
    u2 = 500
    v1 = ?
    v2 = ?
    m1 = 100
    m2 = 10

    Forming equation for law of conservation of K.E -

    m1*u1^2 + m2*u2^2 = m1*v1^2 + m2*v2^2

    100*6400 + 10*250000 = 100*v1^2 + 10*v2^2

    640000 + 2500000 = 100*v1^2 + 10*v2^2

    314000 = 10*v1^2 + v2^2...............1

    Forming equation for law of conservation of Momentum -
    m1*u1 + m2*u2 = m1*v1 + m2*v2

    8000 + 5000 = 100v1 + 10v2

    13000 = 100v1 + 10v2

    13000 = 100v1 + 10v2

    1300 = 10v1 + v2...............2

    130 - v2/10 = v1

    Substitute v1 in 1 -

    314000 = 10*(130 - v2/10)^2 + v2^2

    314000 = 10*(16900 + (v2^2)/100 - 26v2) + v2^2

    31400 = 16900 + (v2^2)/100 - 26v2 + v2^2

    31400 = 16900 - 26v2 + 1.01v2^2

    0 = -14500 - 26v2 + 1.01v2^2

    0 = 14500 + 26v2 – 1.01v2^2

    By quadratic equation formula -

    v2 = 107.6364125 and -133.3789860

    The negative value will be correct since the body will recoil.
    Taking negative value and substituting it in equation 2-

    1300 = 10v1 - 133.3789860

    v1 = 143.3378986

    Values do not comply with conservation of K.E

    Taking positive value -

    1300 = 10v1 – 107.6364125

    v1 = 140.7636412

    Error was pointed out by jtbell...and is now fixed.
     
    Last edited: Feb 10, 2009
  2. jcsd
  3. Feb 10, 2009 #2

    jtbell

    User Avatar

    Staff: Mentor

    Do you see your error now?
     
  4. Feb 10, 2009 #3
    Thanks for that man...I edited that question...and the problem still persists after correction.
     
  5. Feb 10, 2009 #4

    jtbell

    User Avatar

    Staff: Mentor

    I haven't got time to go back over the details right now, but I can suggest a "sanity check." When you solve the quadratic equation to get v2, one of the roots should equal the original u2. This corresponds to the two objects "passing through each other" without interacting, in which case the total momentum and total KE are obviously conserved.
     
  6. Feb 10, 2009 #5
    I think something's wrong with the quadratic equation...the sanity check has failed.

    But I don't know whats wrong.
     
  7. Feb 11, 2009 #6
    Problem solved...one of my many careless errors.

    Considering scenario of 2 colliding bodies, in this case both move in the same direction but one is much faster.
    u1 = 80
    u2 = 500
    v1 = ?
    v2 = ?
    m1 = 100
    m2 = 10

    Forming equation for law of conservation of K.E -

    m1*u1^2 + m2*u2^2 = m1*v1^2 + m2*v2^2

    100*6400 + 10*250000 = 100*v1^2 + 10*v2^2

    640000 + 2500000 = 100*v1^2 + 10*v2^2

    314000 = 10*v1^2 + v2^2...............1

    Forming equation for law of conservation of Momentum -
    m1*u1 + m2*u2 = m1*v1 + m2*v2

    8000 + 5000 = 100v1 + 10v2

    13000 = 100v1 + 10v2

    1300 = 10v1 + v2...............2

    130 - v2/10 = v1

    Substitute v1 in 1 -

    314000 = 10*(130 - v2/10)^2 + v2^2

    314000 = 10*(16900 + (v2^2)/100 - 26v2) + v2^2

    314000 = 169000 + (v2^2)/10 – 260v2 + v2^2

    314000 = 169000 – 260v2 + 1.1v2^2

    0 = -145000 – 260v2 + 1.1v2^2

    0 = +145000 + 260v2 – 1.1v2^2

    v2 = 500
    v2 = -263.63636363 or -2900/11
    alternative -

    v1 by eq. 2 = 156.3636363636363636 or 1720/11

    Equations satisfied.
     
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