Work-Energy Theorem / Finding The Mass

[crono_]

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

v_o = 22.0 m/s

v_f = 28.8 m/s

m = ?

Homework Equations

KE = 1/2 mv²

W = KE_f - KE_o

The Attempt at a Solution

W = KE_f - KE_o

W = 1/2 mv_f² - 1/2 mv_o²

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 (mv_f² - mv_o²)

2W = mv_f² - mv_o²

2W / v_f² - v_o² = 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!

 

[jgens]

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

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

$$m = \frac{2W}{v_f^2 - v_i^2}$$

 

[crono_]

Thank you! I completely overlooked that! :)

 

[jgens]

You're welcome!