38. We will start by assuming that the normal force (on the car from the rail) points up. Note that gravity
points down, and the yaxis is chosen positive upwards. Also, the direction to the center of the circle
(the direction of centripetal acceleration) is down. Thus, Newton’s second law leads to
N−mg =m−v2
r.
(a) When v= 11 m/s, we obtain N=3.7×103N. The fact that this answer is positive means that
N
does indeed point upward as we had assumed.
(b) When v= 14 m/s, we obtain N=−1.3×103N. The fact that this answer is negative means that
Npoints opposite to what we had assumed. Thus, the magnitude of
Nis 1.3 kN and its direction
is down.