Prove That A Motor Car Moving Over A Convex Bridge Is Lighter Than The Same Car Resting On The Same Bridge.

The moving of the motor car over a convex bridge AB is the motion along the segment of a circle AB.

The centripetal force is provided by the difference of weight mg of the car and the normal reaction FB of the bridge.

Therefore,

$$mg – F_{B} = \frac{mv^{2}}{r}$$

OR

$$F_{B} = mg – \frac{mv^{2}}{r}$$ $$F_{B} < mg$$

Therefore, the weight of the moving car is less than the weight of the stationary car.

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