TPR AP Work, Energy, and Power Example 8 11784

Consider the box sliding down the inclined plane in Example 4.

If it starts from rest at the top of the ramp, with what speed does it reach the bottom?

$v=7.6\ \mathrm{\displaystyle \frac{m}{s}}$

It was calculated in Example 4 that $W_{\mathrm{total}}=1,019\ \mathrm{J}$. According to the Work–Energy Theorem,

$$W_{\mathrm{total}}=\Delta K$$

$$W_{\mathrm{total}}=K_{\mathrm{f}}-K_{\mathrm{i}}$$

$$W_{\mathrm{total}}=K_{\mathrm{f}}$$

$$W_{\mathrm{total}}=\frac{1}{2}mv^2$$

$$v=\sqrt{\frac{2W_{\mathrm{total}}}{m}}$$

$$v=\sqrt{\frac{2(1,019\ \mathrm{J})}{35\ \mathrm{kg}}}$$

$$v=7.6\ \mathrm{\frac{m}{s}}$$