The maximum speed vmax the car can have around the curve is the speed at which it is on the verge of skidding outward. At thiss, max =point, the friction force has its maximum value .Apply the equation F = mac = m from the particle in uniform circular motion model in the radial direction for the maximumspeed condition (Use the following as necessary: vmax and r. Do not substitute numerical values; use variables only.)'s, max = Hn = m(1) )Apply the particle in equilibrium model to the car in the vertical direction:Efy = 0 →n - mg = 0 → n = mgSolve Equation (1) for the maximum speed and substitute for n (Use the following as necessary: g, r, and H. Do not substitutenumerical values; use variables only.):HnrHgmgrVmax =m(2)Substitute numerical values:Vmax =m/sFinalize If the speed limit on this roadway is higher than vmax this roadway could benefit greatly from some banking, as in the nextexample! Notice that the maximum speed does not depend on the ---Select---need multiple speed limits to cover the various masses of vehicles using the road.], which is why curved highways do notEXERCISEOn a wet day, the car described in the example begins to skid on the curve when its speed reaches 14.3 m/s. What is the coefficientof static friction in this case?Hint curve as shown in figure (a). If the radius of the curve is 45.0 m andA 1,475 kg car moving on a flat, horizontal road negotiatesthe coefficient of static friction between the tires and dry pavement is 0.570, find the maximum speed (in m/s) the car can have andstill make the turn successfully.aThe force of static friction directed toward thecenter of the curve keeps the car moving in acircular path.mgThe forces acting on the car.SOLUTIONConceptualize Imagine that the curved roadway is part of a large circle so that the car is moving in a circular path.Categorize Based on the Conceptualize step of the problem, we model the car as a particle in ---Select---v inthe horizontal direction. The car is not accelerating vertically, so it is modeled as a particle in ---Select---v inthe vertical direction.Analyze(Use the following as necessary: H, and n for the magnitude of n. Do not substitute numerical values; use variables only.)Figure (b) shows the forces on the car. The force that enables the car to remain in its circular path is the force of static friction. (It isstatic because ---Select--- v slipping occurs at the point of contact between road and tires. If this force of static friction were---Select--- v -for example, if the car were on an icy road-the car would continue in a straight line and slide off the curved road.)

Question

Accepted Answer

Mass of the car,
m=1475 kg
 
The radius of the curve,
r=45 m
 
The coefficient of static friction…

A 1,475 kg car moving on a flat, horizontal road negotiates a curve as shown in figure (a). If the radius of the curve is 45.0 m and the coefficient of static friction between the tires and dry pavement is 0.570, find the maximum speed (in m/s) the car can have and still make the turn successfully.