Question

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

Answer 1

The motion of the motor car over a convex bridge is the motion along the segment of a circle. The centripetal force is provided by the difference of weight "mg" of the car and the normal reaction R of the bridge.

Thus mg - R = mv²/r

or R = mg - mv²/r

Clearly, R < mg, i.e., the weight of the moving car is less than the weight of the stationary car.