Question

A car is traveling on a road in hilly terrain, see figure to the right. Assume the car has speed v and the tops and bottoms of the hills have radius of curvature R. The driver of the car is most likely to feel weightless: 

(A) at the top of a hill when v > √R 

(B) at the bottom of a hill when > √R  

(C) going down a hill when  = √R  

(D) at the top of a hill when <√R 

(E) at the bottom of a hill when  < √R 

Answer 1

Correct option (A) at the top of a hill when v > √R

Feeling weightless is when the normal force goes to zero, which in only possible going over the top of the hill where mg (inward) – F_N (outward) = mv²/R. Setting F_N  to zero gives a maximum speed of √gR.