TPR AP Work, Energy, and Power Example 1 11716

You slowly lift a book of mass $2\ \mathrm{kg}$ at constant velocity a distance of $3\ \mathrm{m}$.

How much work did you do on the book?

$W=60\ \mathrm{J}$

In this case, the force you exert must balance the weight of the book (otherwise the velocity of the book wouldn’t be constant), so

$$F=mg$$

$$F=(2\ \mathrm{kg})\left(10\ \mathrm{\frac{m}{\ s^2}}\right)$$

$$F=20\ \mathrm{N}$$

Since this force is straight upward and the displacement of the book is also straight upward, $\textbf F$ and $\textbf d$ are parallel, so the work done by your lifting force is

$$W = Fd$$

$$W=(20\ \mathrm{N)(3\ m)}$$

$$W=60\ \mathrm{N\cdot m}$$

$$\mathrm{or}$$

$$W=60\ \mathrm{J}$$