Item 6 A car of mass M = 1100kg traveling at 40.0km/hour enters a banked turn co

Question

Item 6 A car of mass M = 1100kg traveling at 40.0km/hour enters a banked turn covered with ice. The road is around the turn)? banked at an angle Theta, and there is no friction between the road and the car's tires. (Figure 1) . Use g = 9.80 m/s^2 throughout this problem. Part A What is the radius r of the turn if Theta= 20.0 degree (assuming the car continues in uniform circular motion around the turn) ? Express your answer in meters. r= 34.6 m Part B Now, suppose that the curve is level (Theta= 0) and that the ice has melted, so that there is a coefficient of static friction Mu between the road and the car's tires.(Figure 2) What is Mumin , 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 40.0km/hour and that the radius of the curve is given by the value you found for r in Part A. Express your answer numerically. Mumin=

Explanation / Answer

A. Ncos@ = mg

Nsin@ = mv^2 / r

tan@ = v^2 /rg

v^2 = rgtan@

(40 x 1000 /3600 m/sec)^2 = r x 9.8 x tan20

r = 34.61 m

B) now friction = mv^2 / r = u.mg

v^2 / rg = u

u = (40 x 1000 /3600 m/sec)^2 / 9.8x 34.61 = 0.36

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