4) Cu friction and very stable car configurations, allows the curves to be taken

Question

4) Cu 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. rves on some race courses are very steeply banked. This banking, with the aid of tire

Explanation / Answer

here,

radius , r = 200/2 = 100 m

theta = 45 degree

mass of car , m = 800 kg

normal reaction force , N = m * g /cos(theta)

Fnet = Fcentripital = N * sin(theta) = m * g * tan(theta)

a)

centripital force , F = m * g * tan(theta)

F = 800 * 9.81 * tan(45) N

F = 7848 N

b)

centripital accelration , ac = F /m

ac = 9.81 m/s^2

c)

the linear velocity of car , v = sqrt(r * g * tan(theta))

v = sqrt(100 * 9.81 * tan(45))

v = 31.3 m/s

d)

angular speed of the car , w = v/r

w = 0.31 rad/s

e)

the time taken , T = 2 * pi /w

T = 2 * pi/0.31 = 20.3 s

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