Please answer all questions and show all work. 8. A 2000 kg car rounds a curve o

Question

Please answer all questions and show all work.

8. A 2000 kg car rounds a curve of radius 86.0 m banked at an angle of 13°. What is the maximum speed that the car can reach without skidding if the coefficient of static friction between the tires and the road is 0.60? m's 9. A coin is placed 18.0 cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 44.0 rpm is reached, at which point the coin slides off. What is the coefficient of static friction between the coin and the turntable?

Explanation / Answer

Here ,

8) m = 2000 Kg

u = 0.60

theta = 13 degree

for the maximum speed

v = sqrt(rg * (tan(theta) + u)/(1 - u * tan(theta)))

v = sqrt(86 * 9.8 * (tan(13 degree) + 0.60)/(1 - 0.60 * tan(13 degree)))

v = 28.51 m/s

the maximum speed is 28.51 m/s

9)

final angular speed , w = 44 rpm

w = 44 * 2pi/60

w = 4.61 rad/s

let the coefficient of friction is u

r = 18 cm = 0.18 m

u * g = w^2 * r

u * 9.8 = 4.61^2 * 0.18

solving for u

u = 0.40

the coefficient of friction is 0.40

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