Concept explainers
In the braking test of a sports car, its velocity is reduced from 70 mi/h to zero in a distance of 170 ft with slipping impending. Knowing that the coefficient of kinetic friction is 80 percent of the coefficient of static friction, determine (a) the coefficient of static friction, (b) the stopping distance for the same initial velocity if the car skids. Ignore air resistance and rolling resistance.
(a)
Find the coefficient of static friction.
Answer to Problem 12.122RP
The coefficient of static friction is
Explanation of Solution
Given information:
The initial velocity
The final velocity (v) of the sports car is 0.
The distance
Calculation:
Write the general equation of weight of the car (W).
Here, m is the mass of the car and g is the acceleration due to gravity.
Sketch the free body diagram and kinetic diagram of the sports car as shown in Figure (1).
Refer Figure (1).
Consider the vertical equilibrium.
Here, N is the normal force on the car.
Substitute mg for W.
Substitute
Find the deceleration of the car using the equation:
Substitute 0 for v, 70 mi/h for
Apply coefficient of static friction for braking without skidding.
Refer Figure 1.
Find the coefficient of static friction.
Substitute 32.2m for N and
Thus, the coefficient of static friction is
(b)
Find the stopping distance for the same initial velocity if the car skids.
Answer to Problem 12.122RP
The stopping distance for the same initial velocity if the car skids is
Explanation of Solution
Given information:
The coefficient of kinetic friction is 80 percent of the coefficient of static friction.
Calculation:
Find the coefficient of kinetic friction using the equation:
Substitute 0.963 for
Apply coefficient of kinetic friction for braking with skidding.
Refer Figure (1).
Find the deceleration of the sports car
Substitute 0.7704 for
The deceleration is constant.
Find the stopping distance for the same initial velocity if the car skids using the equation:
Substitute 0 for v, 70 mi/h for
Thus, the stopping distance for the same initial velocity if the car skids is
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