Question

A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is $20m$. The speed of the car at the top of the hill should be between

• A. $14m/s$ and $15m/s$
• B. $15m/s$ and $16m/s$
• C. $16m/s$ and $17m/s$
• D. $13m/s$ and $14m/s$

Answer 1

The correct option is A $14m/s$ and $15m/s$

Balancing the forces, we get
$Mg-N=M\frac{v^2}{R}$
For weightlessness, $N=0$
$\therefore \frac{M{v}^2}{R}=Mg$
where $R$ is the radius of curvature and $v$ is the speed of car.
Therefore, $v=\sqrt{Rg}$
Putting the values, $R=20m,g=10.0m/s^2$
So, $v=\sqrt{20\times 10.0}=14.14m/s^2$
Thus, the speed of the car at the top of the hill is between $14m/s$ and $15m/s$
Note: The roller coaster is a popular amusement ride developed for amusement parks and modern theme parks.