# The track near the top of your favorite roller coaster is looped with the diameter of 20m. When you are at the top, you feel as if you weight one-third of your true weight.How fast is the roller coaster moving?

Nov 8, 2015

$16.16 \text{m/s}$

#### Explanation:

At the top of the ride the net force experienced will be the difference between the centripetal force and the weight .This is equal to $\frac{m g}{3}$ so we can write:

$\frac{m {v}^{2}}{r} - m g = \frac{m g}{3}$

$\therefore \cancel{m} \left({v}^{2} / r - g\right) = \frac{\cancel{m} g}{3}$

$\therefore {v}^{2} / r = \frac{4 g}{3}$

$v = \sqrt{\frac{4 g r}{3}}$

$v = \sqrt{\frac{4 \times 9.8 \times 10}{3}}$

$v = 11.4 \text{m/s}$