Question 196: Work, Energy and Power & Circular Motion

Question

A vehicle is moving with uniform speed along 3 different shaped roads as horizontal, concave and convex. The surface of road on which, the normal reaction on vehicle is maximum is

Accepted Answer

$$ 	ext { Horizontal road } $$
$$ \begin{aligned} &\mathrm{N}=\mathrm{mg}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(i)\ &	ext { Concave road } \end{aligned} $$
$$ \begin{array}{ll}  & \mathrm{N}=\frac{\mathrm{mv}^2}{\mathrm{r}}+\mathrm{mg} \cos 	heta \ 	herefore \quad & \mathrm{~N}_{\max }=\frac{\mathrm{mv}^2}{\mathrm{r}}+\mathrm{mg}\,\,\,\,\,\,\, \ldots 	ext { (ii) } \end{array} $$
Ã¢ÂÂ¦. (When $\cos 	heta=1$ )
Convex road
$$ \begin{aligned} & N+\frac{m v^2}{r}=m g \cos 	heta \ 	herefore & N=m g \cos 	heta-\frac{m v^2}{r} \ 	herefore \quad & N_{\max }=m g-\frac{m v^2}{r}\,\,\,\,\,\,\,\ldots 	ext { (iii) } \ & \,\,\,\,\, \,\,\,\,\, \,\,\,\,\, \,\,\,\,\, \,\,\,\,\, \,\,\,\,\, \,\,\,\,\, \,\,\,\,\, \,\,\,\,\,\ldots(	ext { When } \cos 	heta=1) \end{aligned} $$
From equations (i), (ii) and (iii), we get: Normal reaction on the vehicle is maximum for a concave shaped road.

Answer

convex

Answer

concave

Answer

horizontal

Answer

same on all the 3 surface

Work, Energy and Power & Circular Motion

A vehicle is moving with uniform speed along 3 different shaped roads as horizontal, concave and convex. The surface of road on which, the normal reaction on vehicle is maximum is

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