A car of mass M = 1000 kg traveling at 45.0 km/hourenters a banked turn covered

Question

A car of mass M = 1000 kg traveling at 45.0 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 as shown in (Figure 1) . Use g = 9.80 m/s2 throughout this problem

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

Express your answer in meters.

43.8

  m

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 as shown in (Figure 2) . What is min, 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 45.0 km/hour and that the radius of the curve is 43.8 m

43.8

  m

Explanation / Answer

v= 45 km/h = 12.5 m/s , g =9.8 m/s^2 , = 20

v^2 = rg*tan( )

12.5*12.5 = r*9.8*tan(20)

r = 43.8 m

u = v^2/rg = 12.5*12.5/(43.8*9.8)

u = 0.36

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