f a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads). (a) Calculate the ideal speed to take a 80 m radius curve banked at 15.0⋅. (b) What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 25.0 km/h?

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Charles Benedict · Accepted Answer

Given data:  r=80 m  θ=15∘  a) the ideal speed of car v1  The velocity v1 is given by  tan⁡θ=v12r⋅g  v1=r⋅g⋅tan⁡θ  v1=80×9.8×tan⁡(15)  v1=14.49 ms  b) where the coefficient of friction μ  We know force of friction of given by  f=μk⋅N=μk⋅m⋅g  the centripetal force acting on the car for speed v1  F1=ma1=m(v1)2r=m(14.49)280=2.62 m  the centripetal force acting on the car for speed v2=25 kmh=6.94 ms  F2=ma2=m(v2)2r=m(6.94)280=0.6 m  the frictional force acting due to the centripetal force  f=|F1−F2|  on substituting the respective values  μk⋅m⋅g=2.02 m  μk=2.029.8=0.206  μk=0.206

f a car takes a banked curve at less than the ideal speed, friction is

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