Concept explainers
A 9.00-kg object starting from rest falls through a viscous medium and experiences a resistive force given by Equation 6.2. The object reaches one half its terminal speed in 5.54 s. (a) Determine the terminal speed. (b) At what time is the speed of the object three-fourths the terminal speed? (c) How far has the object traveled in the first 5.54 s of motion?
(a)
The terminal speed of the object.
Answer to Problem 6.65CP
The terminal speed of the object is
Explanation of Solution
The mass of the object is
Write the expression for the terminal speed of the object
Here,
Write the expression for the speed of the object at an instant of time
Here,
From the given condition, it is clear that the speed of the object is one half of its terminal speed at
Substitute
Further solve the above expression.
Substitute
Conclusion:
Substitute
Therefore, the terminal speed of the object is
(b)
The time at which the speed of the object is three-fourth of the terminal speed.
Answer to Problem 6.65CP
The time at which the speed of the object is three-fourth of the terminal speed is
Explanation of Solution
From the given condition, it is clear that the speed of the object is three-fourth of its terminal speed.
Substitute
Rearrange the above expression for
Conclusion:
Substitute
Therefore, the time at which the speed of the object is three-fourth of the terminal speed is
(c)
The distance travelled by the object in first
Answer to Problem 6.65CP
The distance travelled by the object in first
Explanation of Solution
Write the expression for the speed of an object
Here,
Rearrange the above expression for
Recall equation (II)
Substitute
Conclusion:
Substitute
Therefore, the distance travelled by the object in first
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Chapter 6 Solutions
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