A 45-kg woman is riding a Ferris wheel of radius 15 m at a constant speed.The speed of the Ferris wheel that would make her weightless at the top is
A)12.1 m/s.
B)9.8 m/s.
C)7.5 m/s.
D)3.2 m/s.
E)1.9 m/s.

Question

Quizplus · Accepted Answer

At the top of the Ferris wheel, for the woman to feel weightless, the only force acting on her must be the centripetal force, which is equal to the gravitational force at that point. The formula for centripetal force is $F_c = \frac{mv^2}{r}$, where $m$ is the mass, $v$ is the velocity, and $r$ is the radius. The gravitational force is $F_g = mg$, where $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$). Setting $F_c = F_g$, we get $\frac{mv^2}{r} = mg$. Simplifying, $v^2 = rg$, and solving for $v$, we get $v = \sqrt{rg}$. Substituting $r = 15 m$ and $g = 9.8 m/s^2$, we find $v = \sqrt{15 \times 9.8} \approx 12.1 m/s$.

A 45-Kg Woman Is Riding a Ferris Wheel of Radius