Answer to Question #83299 in Classical Mechanics for Bianca

Question

A car of mass 1000kg travels around a banked track of radius 200m. The angle of banking is 15 degrees and the speed of the car is such that frictional force is zero. By resolving force components into the vertical and horizontal directions:

a) calculate the value of N, the normal contact force
b) calculate the speed at which the car is travelling

The answers are below but i couldn't figure out to get to them.
a) 9.5x10^3 N
b) 22ms-1

Answer 1

The Newton’s second law gives

N=mg/cos⁡θ =(1000×9.8)/cos⁡〖15°〗 =10146 N

tan⁡θ=v^2/gR

v= √(gR tan⁡θ )=√(9.8×200×tan⁡〖15°〗 )=23 m/s