Concept explainers
A velocity vector has a magnitude of 720 m/s. Two students draw arrows representing this vector. Clarisse chooses a scale such that 1 cm → 100 m/s.
a. What is the length of the arrow that Clarisse draws?
b. Francois’s arrow is half as long as Clarisse’s. What is Francois’s scale?
c. Is one student’s choice better than the other? If so, what makes it a better scale?
(a)
The length of the arrow drawn to represent velocity vector using Clarisse’s scale.
Answer to Problem 1PQ
The length of the arrow is
Explanation of Solution
The magnitude of the velocity vector is
When drawing an arrow to represent a vector, the length of the arrow is given by the magnitude of the vector. Thus, the length of the arrow should be
Represent the length in Clarisse’s scale
Conclusion:
Thus, the length of the arrow is
(b)
The scaling chosen by Francois’s scale.
Answer to Problem 1PQ
In Francois’s scale,
Explanation of Solution
The length of Francois’s arrow is half of the length of Clarisse’s scale i.e.
Divide on both sides by
Thus, in Francois’s scale,
(c)
Explain whether one scale choice is better than the other.
Answer to Problem 1PQ
No, either of the scales can be used.
Explanation of Solution
Scaling is an individual’s preference and it doesn’t change the given values. As long as the scales accommodate the range of given values any scale can be used. The above given scales can be drawn to fit on a page and hence both of them are good choices.
Conclusion:
No, either of the scales can be used.
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Chapter 3 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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