A car of mass M = 1300 kg traveling at 65.0 km/hour enters a banked turn covered

Question

A car of mass M = 1300 kg traveling at 65.0 km/hour enters 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.

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 65.0 km/hour and that the radius of the curve is 91.4 m .

Explanation / Answer

v = 65 km/h = 65 x 1000 m / 3600 s

v = 18.06 m/s

perpendicular to the incline,

In vertical,

Ncos@ = mg

in horizontal,

Nsin@ = m aC = m v^2 / R

Nsin@ / Ncos@ = tan@ = v^2 / gR

tan@ = 18.06^2 / (9.81 x 91.4) = 0.36

@ = 19.98 deg OR 20 deg

--------------------

when car is at flate surface then

N = mg

and friction = umg

so umg = mv^2/R

u x 9.81 = 18.06^2 / 91.4

u = 0.36

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