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

Osvaldo Apodaca 2021-12-19 Answered

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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Expert Answer

Charles Benedict
Answered 2021-12-20 Author has 32 answers
Given data:
r=80 m
θ=15
a) the ideal speed of car v1
The velocity v1 is given by
tanθ=v12rg
v1=rgtanθ
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=μkN=μkmg
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=|F1F2|
on substituting the respective values
μkmg=2.02 m
μk=2.029.8=0.206
μk=0.206

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