of car less than optimum speed < v v0 If the speed of the car is less than the optimum speed for the curve then the v vO horizontal component of the normal force will be greater than the required centripetal force and the car will "want to" slide down the incline toward the centre of the curve. If there is a frictional force present between the car's tyres and the road it will oppose this relative motion and pull the car up the incline. Fig. 6. Free-body diagram for the forces acting on car on banked circular track: weight, normal force and frictional force. We can Newton’s Second Law to the X and Y components of the forces: We can use the approximation for the frictional to relate it to the normal force We can now eliminate and from our equations FN Ff If we take the case for we get the same result again for the optimum speed Example (Syllabus) A car travels at speed around a circular curved track of radius v1 R. (a) Find the banked angle (inclination of the track to the horizontal), if there is to be no tendency for the car to slip sideways up or down the track. (b) If the speed of a second car of mass then show that the sideways frictional v2 m force exerted by the surface of the track on the wheels of the car is
of car less than optimum speed v < v0 If the speed of the car v is less than the optimum speed vO for the curve then the horizontal component of the normal force will be greater than the required centripetal force and the car will "want to" slide down the incline toward the centre of the curve. If there is a frictional force present between the car's tyres and the road it will oppose this relative motion and pull the car up the incline. Fig. 6. Free-body diagram for the forces acting on car on banked circular track: weight, normal force and frictional force. We can Newton’s Second Law to the X and Y components of the forces: We can use the approximation for the frictional to relate it to the normal force We can now eliminate FN and Ff from our equations If we take the case for we get the same result again for the optimum speed Example (Syllabus) A car travels at speed v1 around a circular curved track of radius R. (a) Find the banked angle (inclination of the track to the horizontal), if there is to be no tendency for the car to slip sideways up or down the track. (b) If the speed v2 of a second car of mass m then show that the sideways frictional force exerted by the surface of the track on the wheels of the car is