On a banked race track, the smallest circular path on which cars can move has a

Question

On a banked race track, the smallest circular path on which cars can move has a radius of 120 m, while the largest has a radius 169 m, as the drawing illustrates. The height of the outer wall is 18 m. (a) Find the smallest speed at which cars can move on this track without relying on friction. m/s (b) Find the largest speed at which cars can move on this track without relying on friction.

(a) Find the smallest speed at which cars can move on this track without relying on friction.
____m/s

(b) Find the largest speed at which cars can move on this track without relying on friction.
____ m/s

Explanation / Answer

Consider the force equilibrium.

Ptan? = mv^2/r => v=?(g*r*tan?)

tan? = 18/(169- 120) = 18/49
1) The smallest speed when the radius is smallest

=> Vmin =?(9.8*120*18/49) = 20.78 m/s

2)the largeast speed :
Vmax =?(9.8*169*18/49) = 24.66 m/s

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