Prove that a motor car moving over a convex bridge is lighter than the same car resting on the same bridge.

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Solution

The moving of the motor car over a convex bridge AB is the motion along the segment of a circle AB (Figure); The centripetal force is provided by the difference of weight mg of the car and the normal reaction $F_{B}$ of bridge.
$∴ m g - F_{B} = \frac{m v^{2}}{r}$ or $F_{B} = m g - \frac{m v^{2}}{r}$
Clearly $F_{B} < m g$ , i.e. the weight of the moving car is less than the weight of the stationary car.

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