Question

A civil engineer wishes to redesign the curved roadway in such a way that a car will not have to rely on friction to round the curve without skidding. In other words, a car moving at the designated speed can negotiate the curve even when the road is covered with ice. Such a ramp is usually banked, which means that the roadway is tilted toward the inside of the curve. Suppose the designated speed for the ramp is to be 10.0 m/s and the radius of the curve is 20.0 m. At what angle should the curve be banked?

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$\sum F_r=Nsin\theta =\frac{m{v}^2}{r}$
$\sum F_g=Ncos\theta -mg=0$
$\Rightarrow tan\theta =\frac{v^2}{rg}$
$\Rightarrow \theta =ta{n}^{-1}\left(\frac{{10}^2}{\left(20\right)\left(10\right)}\right)=ta{n}^{-1}\left(\frac{1}{2}\right)$