Work-Energy Theorem / Finding The Mass

AI Thread Summary
To find the mass of a car accelerated from 22.0 m/s to 28.8 m/s with 241 kJ of work, the work-energy theorem is applied. The equation W = KEf - KEo is used, where KE is the kinetic energy. Rearranging gives m = 2W / (vf^2 - vo^2). The correct approach clarifies that the mass can be directly calculated from the work done and the change in velocity. This method effectively resolves the algebraic confusion encountered in the initial attempt.
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Homework Statement



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 = ?

Homework Equations



KE = 1/2 mv2

W = KEf - KEo

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

2W = mv_f^2 - mv_i^2 = m(v_f^2 - v_i^2)

m = \frac{2W}{v_f^2 - v_i^2}
 
Thank you! I completely overlooked that! :)
 
You're welcome!
 

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