Question

If the overbridge is concave instead of being convex. What will be the thrust on the road at the lowest position?

Answer 1

Step 1. Given

The overbridge is concave instead of convex.

Step 2. Thrust at the lowest position:

Consider a body lying at the lowest position of the concave path.

We know

$F_C=\frac{m{v}^2}{r}$, Where $F_C$= centrifugal force. $m$=mass, $v$=velocity, $r$= radius of the concave path.

Now $N$=normal reaction( acting upwards).

Then the sum of the centrifugal force on the body and the gravity of the body will be balanced by the normal reaction force on the body due to the road.

So we can write:

$N=mg+F_C$

Putting the value of $F_C$ we get:

$N=mg+\frac{m{v}^2}{r}$

Since this normal reaction force is the thrust on the road,

So Thrust or normal reaction force $\left(N\right)$ = $mg+\frac{m{v}^2}{r}$