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Work-Energy Theorem / Finding The Mass

  1. Nov 8, 2009 #1
    1. The problem statement, all variables and given/known data

    It takes 241 kJ of work to accelerate a car from 22.0 m/s to 28.8 m/s. What is the car's mass?

    W = 241000 J

    vo = 22.0 m/s

    vf = 28.8 m/s

    m = ?

    2. Relevant equations

    KE = 1/2 mv2

    W = KEf - KEo

    3. The attempt at a solution

    W = KEf - KEo

    W = 1/2 mvf2 - 1/2 mvo2

    I was trying to solve for m as everything else is known, but I think I got stuck somewhere in the algebra.

    W = 1/2 (mvf2 - mvo2)

    2W = mvf2 - mvo2

    2W / vf2 - vo2 = m - m

    That's as far as I got. I'm wondering if by switching the sides of the equation so that their signs would change if then m - m could become m + m, thus 2m. Then divide both sides by 2.

    Does that seem right?

    Thanks!
     
  2. jcsd
  3. Nov 8, 2009 #2

    jgens

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    Gold Member

    Your work looks fine until the last step. Your equations should read:

    [tex]2W = mv_f^2 - mv_i^2 = m(v_f^2 - v_i^2)[/tex]

    [tex]m = \frac{2W}{v_f^2 - v_i^2}[/tex]
     
  4. Nov 8, 2009 #3
    Thank you! I completely overlooked that! :)
     
  5. Nov 8, 2009 #4

    jgens

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    Gold Member

    You're welcome!
     
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