A car of mass m moving over a concave bridge of radius r. Find the normal reaction acting on a car when it is at the lowest point of the bridge.

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Solution

The motion of the motor car over a concave bridge AB ai the motion along the segment of a circle AB.
The centripetal force is provided by the difference of normal reaction R of the bridge and weight mg of the car.
$∴ R - m g = \frac{m v^{2}}{r}$
or $R == m g + \frac{m v^{2}}{r}$
Clearly R> mg, i.e., the weight of the moving car is greater than the weight of the stationary car.

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