Chapter 19: Q35P (page 579)

Ten particles are moving with the following speeds: four at $200 m / s$ , two at $500 m / s$ , and four at $600 m / s$ . Calculate their
a) Average speed
b) Rms speed
c) Is $v_{r m s} > v_{a v g}$ ?

Short Answer

Expert verified

Step by step solution

Given data

Four particles have speed $200 m / s$
Two particles have speed $500 m / s$
Four particles have speed $600 m / s$

Understanding the concept

Average speed is calculated by adding the speed of each molecules and then by dividing the total number of molecules.

The RMS speed of molecules is given by,

$v_{r m s} = \sqrt{\frac{\sum_{}^{} v^{2}}{N}}$

(a) Calculate the average speed

Average speed is given by

$V_{a v g} = \frac{1}{N}_{i = 1}^{N} V_{i}$

We have total of $10$ particles, so $N = 10$

Four particles have speed of $200 m / s .$

So, $V_{1} = 4 \times 200 = 800$

Two particles have speed of . $400 m / s$

So, $V_{2} = 2 \times 500 = 1000$

Four particles have speed of. $600 m / s$

So, $V_{3} = 4 \times 600 = 2400$

$V_{a v g} = \frac{1}{N} (V_{1} + V_{2} + V_{3})$

$\begin{matrix} V_{a v g} = \frac{1}{10} (800 + 1000 + 2400) \\ = 420 m / s \end{matrix}$

Therefore the average speed is . $420 m / s$

(b) Calculate the RMS speed Vrms

The rms speed is given by

$V_{r m s} = \sqrt{\frac{1}{N}_{i = 1}^{N} V_{i}^{2}}$

$\begin{matrix} V_{r m s} = \sqrt{\frac{1}{10} [4 {(200 \frac{m}{s})}^{2} + 2 {(500 \frac{m}{s})}^{2} + 4 {(600 \frac{m}{s})}^{2}} \\ = 458 m / s \end{matrix}$

Therefore the RMS speed is $458 m / s$ .

(c) Figure out if Vrms>Vavg

Yes; $V_{r m s} > V_{a v g}$

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Ten particles are moving with the following speeds: four at $200 m / s$ , two at $500 m / s$ , and four at $600 m / s$ . Calculate their
a) Average speed
b) Rms speed
c) Is $v_{r m s} > v_{a v g}$ ?

Short Answer

Step by step solution

Given data

Understanding the concept

(a) Calculate the average speed

(b) Calculate the RMS speed Vrms

(c) Figure out if Vrms>Vavg

One App. One Place for Learning.

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Ten particles are moving with the following speeds: four at200 m/s, two at500 m/s, and four at600 m/s. Calculate theira) Average speedb) Rms speedc) Isvrms>vavg?

Short Answer

Step by step solution

Given data

Understanding the concept

(a) Calculate the average speed

(b) Calculate the RMS speed Vrms

(c) Figure out if Vrms>Vavg

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Classical Mechanics

Translational Dynamics

Engineering Physics

Fluids

Linear Momentum

Waves Physics

Study anywhere. Anytime. Across all devices.

Ten particles are moving with the following speeds: four at $200 m / s$ , two at $500 m / s$ , and four at $600 m / s$ . Calculate their
a) Average speed
b) Rms speed
c) Is $v_{r m s} > v_{a v g}$ ?