Normal Force - Car over a Circular Arc

[nicknaq]

Homework Statement

An 1850 kg car passes over a bump in a road that follows the arc of a circle of radius 40.60 m as seen in the figure below.

a) What force does the road exert on the car as the car passes the highest point of the bump if the car travels at 14.9 m/s?

b) What is the maximum speed the car can have as it passes this highest point before losing contact with the road?

Homework Equations

N-mg=mv^2/r
mg=mv2/r

The Attempt at a Solution

I tried using the equation above and got 28246N, but that was not correct.
For part b) I got 6.37m/s. Also not correct.

 

[Doc Al]

N-mg=mv^2/r

This equation is not quite correct. Hint: What's the direction of the acceleration?

 

[nicknaq]

This equation is not quite correct. Hint: What's the direction of the acceleration?

Do I need a negative sign?
So like this? mg-N=mv^2/r

 

[Doc Al]

Do I need a negative sign?
So like this? mg-N=mv^2/r

Yes.

Using your previous convention of positive for up, I'd write it as:
N - mg = - mv^2/r

The centripetal acceleration (magnitude v^2/r) points toward the center of the circle, which in this case means it points down. Thus it should have a minus sign.

 

[nicknaq]

Yes.

Using your previous convention of positive for up, I'd write it as:
N - mg = - mv^2/r

The centripetal acceleration (magnitude v^2/r) points toward the center of the circle, which in this case means it points down. Thus it should have a minus sign.

Thanks a lot for the help Doc Al!
If you have time to answer https://www.physicsforums.com/showthread.php?t=440062"too, that'd be great: