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.

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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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 this
s, 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 maximum
speed 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 = mg
Solve Equation (1) for the maximum speed and substitute for n (Use the following as necessary: g, r, and H. Do not substitute
numerical values; use variables only.):
Hnr
Hgmgr
Vmax =
m
(2)
Substitute numerical values:
Vmax =
m/s
Finalize If the speed limit on this roadway is higher than vmax this roadway could benefit greatly from some banking, as in the next
example! 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 not
EXERCISE
On 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 coefficient
of static friction in this case?
Hint
Transcribed Image Text: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 this s, 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 maximum speed 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 = mg Solve Equation (1) for the maximum speed and substitute for n (Use the following as necessary: g, r, and H. Do not substitute numerical values; use variables only.): Hnr Hgmgr Vmax = m (2) Substitute numerical values: Vmax = m/s Finalize If the speed limit on this roadway is higher than vmax this roadway could benefit greatly from some banking, as in the next example! 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 not EXERCISE On 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 coefficient of static friction in this case? Hint
curve as shown in figure (a). If the radius of the curve is 45.0 m and
A 1,475 kg car moving on a flat, horizontal road negotiates
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.
a
The force of static friction directed toward the
center of the curve keeps the car moving in a
circular path.
mg
The forces acting on the car.
SOLUTION
Conceptualize 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 in
the horizontal direction. The car is not accelerating vertically, so it is modeled as a particle in ---Select---
v in
the 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 is
static 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.)
Transcribed Image Text:curve as shown in figure (a). If the radius of the curve is 45.0 m and A 1,475 kg car moving on a flat, horizontal road negotiates 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. a The force of static friction directed toward the center of the curve keeps the car moving in a circular path. mg The forces acting on the car. SOLUTION Conceptualize 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 in the horizontal direction. The car is not accelerating vertically, so it is modeled as a particle in ---Select--- v in the 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 is static 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.)
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