TPR AP Work, Energy, and Power Example 8

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,

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

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

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

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

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

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

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