A racing car travels at a speed of 180km/h on a track banked at 30° to to the horizontal.the limiting coefficient of friction between the tyres and the track is 0.7.calculate the minimum radius of curvature of the track if the car is not to send outwards.

A crate of eggs is located in the middle of the flatbed of a pickup truck as the truck negotiates a curve in the flat road. The curve may be regarded as an arc of a circle of radius 35.0 m. If the coefficient of static friction between crate and truck is 0.600, how fast can the truck be moving without the crate sliding?

Railroad tracks follow a circular curve of radius 500.0 m and are banked at an angle of 5.0 . For trains of what speed are these tracks designed?

Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen below. To be stable, the force exerted by the ground must be on a line going through the center of gravity. The force on the bicycle wheel can be resolved into two perpendicular components—friction parallel to the road (this must supply the centripetal force) and the vertical normal force (which must equal the system’s weight). (a) Show that (as defined as shown) is related to the speed vand radius of curvature rof the turn in the same way as for an ideally banked roadway—that is, =tan1(v2/rg) . (b) Calculate for a 12.0-m/s turn of radius 30.0 m (as in a race).