A car of mass M = 900 kg traveling at 45.0 km/hourenters a banked turn covered w

Question

A car of mass M = 900 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.

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

Q: 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.(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 45.0km/hour and that the radius of the curve is given by the value you found for r in Part A.

Explanation / Answer

given data

M = 900 kg

v = 45 km/hour = 45*5/18 = 12.5 m/s

angle of banking, theta = 20 degrees

A) Apply, tan(theta) = v^2/(g*r)

==> r = v^2/(g*tan(theta))

= 12.5^2/(9.8*tan(20))

= 43.8 m

B)

Apply, F_static = N*mue_s

M*a_rad = M*g*mue_s

M*v^2/r = M*g*mue_s

mue_s = v^2/(g*r)

= 12.5^2/(9.8*43.8)

= 0.364

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