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

Question

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. Part A: 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 Part 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 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

Part A) Here,    v = sqrt(rgtan)

=>    18.05 = sqrt(r * 9.8 * tan20)

=> r   =   91.34 m                 ---------------> radius r of the turn

Part B)    Here, mv2/r = umin * mg

=>    18.05 * 18.05/91.4 =   umin * 9.8

=>     umin   = 0.3637                ------------------>   the minimum value of the coefficient of static friction

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.