Find the terminal speed of a ball rolling on an inclined desk.
Equipment:
- a ball
- 2 wooden blocks
- ???
At the top of the desk, the ball has only potential energy [[$ E_{\text{pot}} = mgh $]]. As the ball rolls downhill, it loses its potential energy and gains kinetic energy [[$ E_{\text{liike}} = \frac{1}{2}mv^2 $]] in return. As energy is conserved, we must have [[$ E_{\text{liike}} = E_{\text{pot}} $]], which implies:
[[$$ \frac{1}{2}mv^2 = mgh \quad ||:m$$]]
[[$$ \frac{1}{2}v^2 = gh \quad || \cdot2$$]]
[[$$ v^2 = 2gh \quad || \sqrt{} $$]]
[[$$ v = \sqrt{2gh} $$]]
