Calculating the Radius of Curvature for a Car on a Hill

[waldvocm]

An automobile moves at a constant speed over the crest of a hill traveling at a speed of 85.7km.h. At the top of the hill a package on a seat in the rear of the car barely remains in contact with the seat. What is the radius of curvature (m) of the hill?

85.7km/h=2.38m.s v=2.38m/s ac=v^2/r r=v^2/a

I know that the only force acting on the package is gravity. Does this mean that the mass of the package is 9.80? mg=m*ac

I am not sure where to go from here

 

[Delphi51]

Error in "85.7km/h=2.38m.s"
In 85.7 km/h you must replace the km with 1000 m and the h with 3600 s.

You are so close when you say "only force acting on the package is gravity"!
Put this into F = ma and realize that the acceleration is centripetal so put that formula in for a. Solve for R.

 

[waldvocm]

So...
F=m*v^2/r

9.80=m*23.8^2/r

How do I solve for r if I don't know the mass of the package?

 

[Delphi51]

F = ma
mg = m*v^2/r
and the m's cancel.