A car travels around a curve of radius R=200m at a constant speed of 40m/s : (a)

Question

A car travels around a curve of radius R=200m at a constant speed of 40m/s :
(a) What is the centripetal acceleration of the car?
(b) If the curve is flat, and we can assume friction, draw the free body diagram for the car (show the coordinate system you choose).
(c) Determine the coefficient of friction required to keep the car from slipping. Is this a kinetic or static coefficient?
d) Now assume the road is covered in a thin sheet of ice, and is effectively frictionless. The curve is now banked. Draw the free body diagram for the car (show the coordinate system you choose).
e) At what angle must the road be banked to prevent the car from slipping?

Explanation / Answer

the centripetal acc v2/r=1600/200=8m/s2

the centripetal force is provided by friction

normal reaction = mg hence frictional force =mg

mg=mv2/r ==>=v2/(rg)=0.816 no units

when there is banking and no friction the normal reaction provides neccesary cenpetal force

nsin=mg ncos=mv2/r ==>cot=v2/(rg) =33.1958128

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