CENTRIPETAL FORCEWhen a particle moves over a curved path which is known, the equation of motion for the particle maybe written in the tangential and normal directions.Tangential Force:Normal Force (Centripetal Force)Recall that tangential acceleration, at = dv/dt represents the time rate of change in the magnitude ofvelocity. Consequently, if ΣFt acts in the direction of motion, the particle’s speed will increase, whereas ifit acts in the opposite direction, the particle will slow down.Likewise, normal acceleration, an = v2r represents the time rate of change in the velocity’s direction.Since this vector always acts positive towards the path’s center of curvature, the ΣFn, which causes an,also acts in this direct. Since this force is always directed toward the center of the path, it is oftenreferred to as the centripetal force.Magnitude of Centripetal ForceFrom the second law of motion, we can see that the centripetal force Fn on an object mass m in uniformcircular motion is Fn = m an which has a magnitude
Example: a. Find the centripetal force needed by a 1,200 kg car to make a turn of radius 40m at a speed of 25 km/h (16mi/h). b. Assuming the road is level, find the minimum coefficient of static friction between the car’s tires and the road that will permit the turn to be made. High speed turn on a level road can be dangerous. In this example, increasing the speed to 60 km/h (37mi/h) increases the needed µS to 0.72, which is too much for wet road, and the car would skid.
Banking AngleUsually the friction between the tires and the road is not enough to provide a car with the centripetalforce it needs to make a turn. If the car’s speed is high or the road surface is slippery, however, theavailable force may not be enough and the car will skid. To reduce skids, the highway curves are oftenbanked so that the roadbed tilts inward.The tangent of the proper banking angle θ varies directly with the square of the car’s speed andinversely with the radius of the curve. The mass of the car does not matter. When a car goes around acurve at precisely the design speed, the reaction force of the road provides the centripetal force. If thecar goes more slowly than this, friction tends to keep it from sliding down the inclined roadway; if thecar goes faster, friction tend to keep it from skidding outward.