Answer to Question #152469 in Physics for Trix Wu

Question

1.     Find the central force acting on a 1,100 kg car traveling at 27 m/s around a high way curve of radius 150 m.

1.     A car speeds around an 80-m radius curve of a freeway. A 60 kg passenger holds the armrest of the car door with a force of 220 N so as not to slide or thrown away. Disregarding friction, determine the cars speed in km/h.

Answer 1

The centripetal force in the first problem is

$$F_c=mv^2/R=1100\cdot27^2/150=5346\text{ N}.$$

Second problem: use the same equation but express speed. The force required to overcome inertia is equal to the centripetal force:

$$v=\sqrt{\frac{F_cR}{m}}=17.1\text{ m/s},\\\space\\ v=17.1\cdot3600/1000=61.6\text{ km/h}.$$