Concept explainers
A curve in a speed track has a radius of 1000 ft and a rated speed of 120 mi/h. (See Sample Prob. 12.7 for the definition of rated speed.) Knowing that a racing car starts skidding on the curve when traveling at a speed of 180 mi/h, determine (a) the banking angle θ, (b) the coefficient of static friction between the tires and the track under the prevailing conditions, (c) the minimum speed at which the same car could negotiate the curve.
Fig. P12.52
(a)
Find the banking angle
Answer to Problem 12.52P
The banking angle
Explanation of Solution
Given information:
The radius
The rated speed
The frictional force
The speed (v) at prevailing condition is 180 mi/h.
Calculation:
Write the general equation weight (W).
Here, m is the mass and g is the acceleration due to gravity.
Write the general equation of acceleration (a) in curved path.
Here, v is the speed and
Sketch the free body diagram and kinetic diagram of the racing car as shown in Figure (1).
Refer Figure (1):
Consider the racing car moves at rated speed.
Find the banking angle
Apply Newton’s law of equation along x-axis.
Substitute 0 for
Substitute 120 mi/h for
Thus, the banking angle
(b)
Find the coefficient of static friction between the tires and the track under the prevailing conditions.
Answer to Problem 12.52P
The coefficient of static friction between the tires and the track under the prevailing conditions is
Explanation of Solution
Calculation:
Refer Figure (1):
Consider the racing car moves in prevailing condition.
Apply Newton’s law of equation along y-axis.
Substitute
Apply Newton’s law of equation along y-axis.
Substitute
Find the coefficient of static friction
Write the general equation of normal force(N).
Substitute Equation (1) and (2) in Equation (3).
Substitute 180 mi/h for v,
Thus, the coefficient of static friction between the tires and the track under the prevailing conditions is
(c)
Find the minimum speed at which the same car could negotiate that curve.
Answer to Problem 12.52P
The minimum speed at which the same car could negotiate that curve is
Explanation of Solution
Calculation:
Write the general equation of normal force (N) in minimum speed.
Substitute Equation (1) and (2) in Equation (3).
Substitute 0.390 for
Thus, the minimum speed at which the same car could negotiate that curve is
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Chapter 12 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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