Concept explainers
Suppose you know the amount of work the brakes of a car must do to stop a car at a given speed. How much work must they do to stop a car that is moving four times as fast? How will the stopping distances compare?
The change in the work done to stop a car if now the car is moving four times as fast, and to compare the stopping distances.
Answer to Problem 9A
The work done and the stopping distance both will be
Explanation of Solution
Introduction:
Work Energy theorem states that the work done on an object is equal to the change in kinetic energy of the object,
Where,
Also, the change in kinetic energy of the object can be written in terms of applied force
Let the initial work done in stopping be
Negative sign denotes that it decelerates, or stops the motion of the car.
Now, if the car was moving four times of its initial velocity, then the work done to stop the car will be,
Hence, the new work done to stop the car will be
Similarly, using the mentioned formula, the initial stopping distance can be written as,
Then, if the car was moving four times of its initial velocity, then the new stopping distance of the car will be,
Conclusion:
Hence, both the work done as well as the stopping distance will be
Chapter 9 Solutions
Conceptual Physics: The High School Physics Program
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