Concept explainers
(a)
To Calculate: The minimum distance to make the car stop.
(a)
Answer to Problem 48P
The minimum distance it takes to stop the car is
Explanation of Solution
Given Information:
An automobile is going up a
The coefficient of static friction between the tires and the road is
Formula Used:
Third equation of motion:
Where symbols have their usual meanings.
Calculation:
Initial velocity of the automobile
Final velocity of the automobile
Let the minimum displacement be
Let the acceleration of the car be
Free body diagram for automobile going up the inclined plane is shown below
Use the third kinematics relation
From the free body diagram, along the x-axis
Along the y-axis:
Substitute
Substitute the value of acceleration in
Conclusion:
Thus, the minimum stopping distance is
(b)
To Calculate: The minimum distance it would take to stop if the car were going down the grade.
(b)
Answer to Problem 48P
Explanation of Solution
Given Information:
An automobile is going up a
The coefficient of static friction between the tires and the road is
FormulaUsed:
Third equation of motion:
Where, symbols have their usual meanings
Calculation:
Initial velocity of the car
Final velocity of the car
Let the minimum displacement be
And let the acceleration of the car be
Use the third kinematic equation
Along the x-axis
And along the y-axis we conclude that,
Substitute
Substitute the value of acceleration in
Here, the negative sign indicates that the displacement of the car is in the opposite direction as in part
Conclusion:
Therefore, the magnitude of displacement is
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Physics for Scientists and Engineers
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- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University