4) Curves on some race courses are very steeply banked. This banking, with the a

Question

4) Curves on some race courses are very steeply banked. This banking, with the aid of tire friction and very stable car configurations, allows the curves to be taken at very high speed. the curve has 200 meter in diameter and the curve is banked at 45.0", mass of car is 800 kg. assuming the road is frictionless, calculate a) centripetal force of the car; b) centripetal acceleration of the car; c) the linear velocity of the car, d) angular velocity of the car, and e) how long (the time) for the car to travel one complete circle of the race course.

Explanation / Answer

4. given

diameter, 2r = 200 m

r = 100 m

theta = 45 deg

m = 800 kg

fricitonless road

a. centripital force = mv^2/r = Fc

normal reaction = N

from force balnce

Ncos(theta) = mg

Nsin(theta) = Fc

hence

tan(theta) = Fc/mg

hence

Fc = mg*tan(theta) = 7848 N

b. centripital accelration = Fc/m = 9.81 m/s/s

c. mv^2/r = Fc

v = 31.32091 m/s

d. angular velocity = v/r = 0.3132091 rad/s

e. time taken to complete one complete revolution = T

2*pi*r/T = v

hence

T = 20.0606729 s

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