Question

A vehicle is crossing a vertical convex bridge.The force exerted by vehicle on mid-point of the bridge with convex curvature (moving at constant speed) will be​

Answer 1

Force = mg at the midpoint of the bridge

Explanation:

Given: A vehicle is crossing a vertical convex bridge. The vehicle is moving at constant speed.

Find: The force exerted by the vehicle on the mid-point of the bridge.

Solution:

Let F be the net force exerted by the vehicle. At the mid-point of the convex bridge, F will act downwards, and it will be equal to product of its mass m and g the acceleration due to gravity.

F = mg

Answer 2

The force acting downwards on the bridge = $M\frac{v^2}{R}$

Explanation:

Assuming that the mass of the vehicle is M and the radius of the convex bridge is R

Let the velocity of the vehicle be v

When the vehicle is in the middle of the convex bridge, its weight Mg will act downwards and a normal reaction N will act upwards

If the bridge were flat then the weight Mg would have been equal to the normal reaction N

but since the bridge has convex curvature, a net resultant force Mg - N will provide the necessary centripetal acceleration required for navigating the bridge

Thus,

$Mg-N=M\frac{v^2}{R}$

Therefore,

The force acting downwards on the bridge = $M\frac{v^2}{R}$

It will be same at the mid point and at the ends if the vehicle is moving with constant velocity because the value of the centripetal acceleration will always be Mv²/R

Hope this answer is helpful.

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