Normal force of a body over a circular bridge

[Shashwat02]

TL;DR Summary

Hi! Can somebody please explain me the concept of normal force over convex and concave bridge?

I am not able to understand why normal force on top in a vertical circular motion the least.
Also please help me with normal force of a body over convex and concave bridges.
Why do we get these equations:
N=mg-mv²/r (convex bridge)
N=mg+mv²/r (concave bridge)

 

[PhanthomJay]

Are you familiar with centripetal acceleration, free body diagrams, and Newton's 2nd law? At the top of the circle (convex curve), draw a free body diagram of the forces acting on the body, with the body in contact with the surface on the outside of the circle. Do the same at the bottom of the circle (concave curve), with the body in contact with the surface on the inside of the circle. In each case, what is the direction of the two forces that act on the body?

 

[Shashwat02]

The normal force acts upwards and force due to gravity and centripetal force act downward in convex bridge.
In concave bridge normal force acts upwards along with centripetal force and force due to gravity acts downwards.
Please explain me why normal force at topmost point in vertical circular motion is least and highest at bottom.

 

[A.T.]

Please explain me why normal force at topmost point in vertical circular motion is least and highest at bottom.

How are the three forces you named related quantitatively? Have you looked at Newton's 2nd Law?

 

[Shashwat02]

How are the three forces you named related quantitatively? Have you looked at Newton's 2nd Law?

Consider FBD of a vehicle on the top of a convex and concave bridge.

 

[Shashwat02]

Are you familiar with centripetal acceleration, free body diagrams, and Newton's 2nd law? At the top of the circle (convex curve), draw a free body diagram of the forces acting on the body, with the body in contact with the surface on the outside of the circle. Do the same at the bottom of the circle (concave curve), with the body in contact with the surface on the inside of the circle. In each case, what is the direction of the two forces that act on the body?

The normal force acts upwards and force due to gravity and centripetal force act downward in convex bridge.
In concave bridge normal force acts upwards along with centripetal force and force due to gravity acts downwards.
Please explain me why normal force at topmost point in vertical circular motion is least and highest at bottom

 

[jbriggs444]

The normal force acts upwards and force due to gravity and centripetal force act downward in convex bridge.
In concave bridge normal force acts upwards along with centripetal force and force due to gravity acts downwards.
Please explain me why normal force at topmost point in vertical circular motion is least and highest at bottom

Please realize that "centripetal" and "centrifugal" are not types of forces. They are directions in which a force can act: toward the center or away from the center.

On a surface that is concave, the normal force from the surface against an object is a centripetal force. On a convex surface, the normal force from the surface against an object is a centrifugal force.

[Confusingly, the term "centrifugal" is often applied to a very specific force -- the apparent outward inertial force associated with the adoption of a rotating frame of reference]

 

[PhanthomJay]

The normal force acts upwards and force due to gravity and centripetal force act downward in convex bridge.
In concave bridge normal force acts upwards along with centripetal force and force due to gravity acts downwards.
Please explain me why normal force at topmost point in vertical circular motion is least and highest at bottom

Please note that in your example problem, the body rides above (on top of) the convex surface and above the concave surface, and your direction of the normal and weight forces are correct for each case. The sum of these two forces must equal mv^2/r, per Newton’s 2nd Law. This would be an example of a typical roller coaster ride. The coaster can’t be going too fast at the top of the convex surface or else it would fly off the rail (without safety features).
Now a “loop-the-loop” roller coaster, where you ride on the inside of the loop, upside down when on top, is a bit different. At the top, gravity force still acts down, but which way does the normal force act? You can’t be going too slow on top, or else you’d fall off the track(without safety features).
In both cases, the speed is greater at the bottom because of conservation of energy principle, with which hopefully you are familiar.