Normal force at the top of a loop the loop

[BikeSmoth]

Homework Statement

A car drives over a hill that is shaped as a circular arc with radius 65.0 m. The car has a constant speed of 14.0 m/s and a mass of 423 kg. What is the magnitude of (a) the centripetal force on the car at the top of the hill and (b) the normal force exerted on the car by the road at this point?

Homework Equations

F=(mv^2)/r
(mv^2)/r=mg+N

The Attempt at a Solution

so i have answered (a) correctly with F=1275.5N, but I am not sure if I have the correct equation for (b) with the equation above I got N=-2869.9N

 

[Mindscrape]

You're algebra is good, so your numbers should be good too.

 

[jpas]

(mv^2)/r=mg+N

No,

$$m \frac{v^2}{r} = N - mg$$

Try drawing a picture and the equation becomes clear.

 

[Mindscrape]

Good catch, I didn't notice the wrong sign, my bad.