Chapter 12, Problem 12.129RP

Telemetry technology is used to quantify kinematic values of a 200-kg roller-coaster cart as it passes overhead. According to the system, $r=25\text{m},\stackrel{.}{r}=-10\text{m}/\text{s},\stackrel{..}{r}=-2{\text{m}/\text{s}}^2,\theta =90°,\stackrel{.}{\theta }=-0.4\text{rad}/\text{s},$ and $\stackrel{..}{\theta }=-0.32{\text{rad}/\text{s}}^2$ . At this instant, determine (a) the normal force between the cart and the track, (b) the radius of curvature of the track.