Question

A roller coaster is travelling on a flat track with a minimum radius of curvature of $15\text{m}$ and the train car has a maximum velocity of $15\text{m/s}$. What should be the friction coefficient between the train car and the track for the ride to be safe?
$(g=10{\text{m/s}}^2)$

• A. $0.5$
• B. $1.5$
• C. $2.5$
• D. $1.0$

Answer 1

The correct option is B $1.5$

For safe ride, the friction between the track and the train car should be able to provide the required centripetal force.

$\therefore \frac{m{v}^2}{r}=f\le \mu mg$
Since $v=v_{max}$ (given),
$\frac{m{v}_{max}^2}{r}=\mu mg$
$\Rightarrow \mu =\frac{v_{max}^2}{rg}=\frac{{15}^2}{15\times 10}=\frac{225}{150}$
$\Rightarrow \mu =1.5$