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) (5 pts) What is the centripetal acceleration of the car? (b) (5 pts) 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) (5 pts) Determine the coefficient of friction required to keep the car from slipping. Is this a kinetic or static coefficient? Name (last name only) _______________ Section Number____________ Problem 2, continued d) (5pts) 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) (5pts) At what angle must the road be banked to prevent the car from slipping?

Explanation / Answer

In order for a body (the car) of mass m, to move at constant speed v, in a circle of radius r, the centripetal acceleration will be a = v²/r, and so the centripetal force, F[c], required to keep it on that trajectory is F[c] = ma The maximum possible frictional force, F[f], is related to the downward gravitational force (the body's weight), W, by F[f] = µW = µmg because W is equal to the normal force of the pavement upward on the body, since it is on a level surface. In order to keep from sliding away from the desired trajectory, then, it must be the case that F[f] = F[c] µmg = ma µ = a/g = v²/gr = 40² / (9.8 * 200) = 8 / 9.8 = 0.82 f

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