Given speed/mass find R (centripetal)

[jybe]

Homework Statement

1) A 50kg person drives a car at 8.3m/s over a hump in the road. At the top of the hump, the driver feels a force of 143 N from the seat. What is the radius of the hump?

2) At what speed will the car need to move over the hump for the person to feel weightless at the top?

Homework Equations

F_c = (mv²)R

The Attempt at a Solution

1)

F_c = ma_c
mg - F_N = (mv²)/R
R = (mv²)/(mg - F_N)
R = 9.93 m

2)

g = v²/R (total centripetal acceleration must be equal to gravity)
v = (gR)^0.5
v = 9.86 m/s

Pretty sure #2 is right, but did I get the correct radius in #1?

 

[Doc Al]

did I get the correct radius in #1?

Yes, you did.