Concept explainers
(a)
The average velocity of the particles.
(a)
Answer to Problem 6PQ
The average velocity of the particles is
Explanation of Solution
Write the equation for the average velocity in the x direction for the particles.
Here,
Write the equation for the average velocity in the y direction for the particles.
Here,
Write the equation for the average velocity in the z direction for the particles.
Here,
Write the equation for the average velocity of the particles.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Thus, the average velocity of the particles is
(b)
The average speed of the particles.
(b)
Answer to Problem 6PQ
The average speed of the particles is
Explanation of Solution
Write the equation for the speedof the first particle.
Write the equation for the average speed.
Conclusion:
Substitute
Similarly, calculate the speed of the second particle.
Calculate the speed of the third particle.
Calculate the speed of the fourth particle.
Calculate the speed of the fifth particle.
Substitute
Thus, the average speed of the particles is
(c)
The rms speed of the particles.
(c)
Answer to Problem 6PQ
The rms speed of the particles is
Explanation of Solution
Write the equation for the rms speed of the particles.
Conclusion:
Substitute the values for the speeds of the particles in equation (VII) to find
Thus, the rms speed of the particles is
(d)
Compare the speeds of the particles.
(d)
Answer to Problem 6PQ
The rms speed is greater than the average speed.
Explanation of Solution
Write the equation for the magntide of the average velocity.
Here,
Conclusion:
Susbtitute
The value of rms speed is greater than the mahnitude of the average velocity. This is becauses, in calculationg the average velocity, the particles moving in the opposite direction is also considered.
Thus, the rms speed is greater than the average speed.
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Chapter 20 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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