Applying the Work–Energy Theorem

Strategy

The work–energy theorem can be applied to the problem. Write the equation for the theorem and simplify it if possible.

W = Δ KE = \frac{1}{2} m v_{2}^{2} - \frac{1}{2} m v_{1}^{2}

Simplify to W = \frac{1}{2} m (v_{2}^{2} - v_{1}^{2})

Solution

Identify the variables. m = 50 kg,

v_{2} = 12 \frac{m}{s}, and v_{1} = 8 \frac{m}{s}

9.1

Substitute.

W = \frac{1}{2} 50 (12^{2} - 8^{2}) = 2, 000 J

9.2

Discussion

Tips For Success

This problem illustrates a general technique for approaching problems that require you to apply formulas: Identify the unknown and the known variables, express the unknown variables in terms of the known variables, and then enter all the known values.