Engineers are designing a curved section of a highway. If the radius of curvatur

Question

Engineers are designing a curved section of a highway. If the radius of curvature of the curve is 189 m, at what angle should the curve be banked so that a car traveling at 29.0 m/s will stay on the road without the aid of frictional forces? Engineers are designing a curved section of a highway. If the radius of curvature of the curve is 189 m, at what angle should the curve be banked so that a car traveling at 29.0 m/s will stay on the road without the aid of frictional forces? Engineers are designing a curved section of a highway. If the radius of curvature of the curve is 189 m, at what angle should the curve be banked so that a car traveling at 29.0 m/s will stay on the road without the aid of frictional forces? Engineers are designing a curved section of a highway. If the radius of curvature of the curve is 189 m, at what angle should the curve be banked so that a car traveling at 29.0 m/s will stay on the road without the aid of frictional forces? Engineers are designing a curved section of a highway. If the radius of curvature of the curve is 189 m, at what angle should the curve be banked so that a car traveling at 29.0 m/s will stay on the road without the aid of frictional forces? Engineers are designing a curved section of a highway. If the radius of curvature of the curve is 189 m, at what angle should the curve be banked so that a car traveling at 29.0 m/s will stay on the road without the aid of frictional forces?

Explanation / Answer

There are two forces acting on the car.....A Normal (N) perpendicular to the road (the x component of this force creates the centripetal force to turn the car

and weight (m*g) acting down.

Now summing forces in the vertical we get N*cos(?) - m*g = 0 ..so N = m*g/cos(?)

Now the x component of the normal = N*sin(?) = m*g*sin(?)/cos(?) = m*g*tan(?)

Now this force = m*a = m*v^2/r

So m*g*tan(?) = m*v^2/r ..

So ? = arctan(v^2/(g*r)) = arctan((29.0)^2/(9.8*189)) = 24.42o

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