A car of mass M = 1400 kg traveling at 50.0 km/hourenters a banked turn covered

Question

A car of mass M = 1400 kg traveling at 50.0 km/hourenters a banked turn covered with ice. The road is banked at an angle , and there is no friction between the road and the car's tires. Use g = 9.80 m/s2 throughout this problem.

A. What is the radius r of the turn if = 20.0 (assuming the car continues in uniform circular motion around the turn)?

The answer is 54.1 N

B. Now, suppose that the curve is level (=0) and that the ice has melted, so that there is a coefficient of static friction between the road and the car's tires. What ismin, the minimum value of the coefficient of static friction between the tires and the road required to prevent the car from slipping? Assume that the car's speed is still 50.0 km/hour and that the radius of the curve is 54.1 m .

Explanation / Answer

mass of car , m = 1400 Kg

theta = 20 degree

g = 9.8 m/s^2

speed , v = 50 km/hr

v = 50 * 1000/3600

v = 13.9 m/s

a) let the radius of turn is r

m* g * sin(theta) = m * v^2/r

9.8 * sin(20) = 13.9^2/r

solving for r

r = 57.6 m

the radius of turn r is 57.6 m

part B)

let the coefficient of friction is u

u * m*g = m * v^2/r

u * 9.8 = 13.9^2/(54.1)

solving for u

u = 0.364

the coefficient of friction is 0.364

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