
Concept explainers
How fast can a racecar travel through a circular tum without skidding and hitting the wall? The answer could depend on several factors:
- The weight of the car;
- The friction between the tires and the road;
- The radius of the circle;
- The “steepness” of the turn.
In this project we investigate this question for NASCAR racecars at the Bristol Motor Speedway in Tennessee. Before considering this track in particular, we use
A car of mass m moves with constant angular speed to around a circular curve of radius R (Figure 3.20). The curve is banked at an angle
Figure 3.20 Views of a lace ear moving around a track.
As the car moves around the curve, three forces act on it: gravity, the force exerted by the road (this force is perpendicular to the ground), and the friction force (Figure 3.21). Because describing the frictional force generated by the tires and the road is complex, we use a standard approximation for the frictional force. Assume that
Figure 3.21 The car has three forces acting on it: gravity (denoted by mg), the friction force f, and the force exerted by the road N.
Let
The next three questions deal with developing a formula that relates the speed
7. Show that
Now that we have a formula
The Bristol Motor Speedway is a NASCAR short track in Bristol, Tennessee. The track has the approximate shape shown in Figure 3.22. Each end of the track is approximately semicircular, so when cars make turns they are traveling along an approximately circular curve. If a car takes the inside track and speeds along the bottom of turn 1, the car travels along a semicircle of radius approximately
Figure 3.22 At the Bristol Motor Speedway, Bristol, Tennessee (a), the turns have an inner radius of about
The coefficient of friction for a normal fire in Elly conditions is approximately

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Chapter 3 Solutions
Calculus Volume 3
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University Calculus: Early Transcendentals (4th Edition)
Elementary Statistics (13th Edition)
A First Course in Probability (10th Edition)
Elementary Statistics: Picturing the World (7th Edition)
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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