Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781337026345
Author: Katz
Publisher: Cengage
bartleby

Concept explainers

Question
Book Icon
Chapter 20, Problem 6PQ

(a)

To determine

The average velocity of the particles.

(a)

Expert Solution
Check Mark

Answer to Problem 6PQ

The average velocity of the particles is (3.1i^1.1j^0.02k^)m/s.

Explanation of Solution

Write the equation for the average velocity in the x direction for the particles.

    (vx)av=v1x+v2x+v3x+v4x+v5x5                                                                     (I)

Here, (vx)av is the average velocity in the x direction for the particles, v1x is the x component of the first particle, v2x is the x component of the second particle, v3x is the x component of the third particle, v4x is the x component of the fourth particle and v5x is the x component of the fifth particle.

Write the equation for the average velocity in the y direction for the particles.

    (vy)av=v1y+v2y+v3y+v4y+v5y5                                                                    (II)

Here, (vy)av is the average velocity in the y direction for the particles, v1y is the y component of the first particle, v2y is the y component of the second particle, v3y is the y component of the third particle, v4y is the y component of the fourth particle and v5y is the y component of the fifth particle.

Write the equation for the average velocity in the z direction for the particles.

    (vz)av=v1z+v2z+v3z+v4z+v5z5                                                                     (III)

Here, (vx)av is the average velocity in the z direction for the particles, v1z is the z component of the first particle, v2z is the z component of the second particle, v3z is the z component of the third particle, v4z is the z component of the fourth particle and v5z is the z component of the fifth particle.

Write the equation for the average velocity of the particles.

    vav=(vx)avi^+(vy)avj^+(vz)avk^                                                                  (IV)

Conclusion:

Substitute 3.4m/s for v1x, 2.4m/s for v2x, 0.4m/s for v3y, 9.2m/s for v4y and 0.9m/s for v5y in equation (I) to find (vx)av.

  (vx)av=3.4m/s+2.4m/s0.4m/s+9.2m/s+0.9m/s5=3.1m/s

Substitute 5.6m/s for v1y, 6.6m/s for v2y, 1.6m/s for v3y, 9.8m/s for v4y and 3.6m/s for v5y in equation (II) to find (vy)av.

  (vy)av=5.6m/s6.6m/s+1.6m/s9.8m/s+3.6m/s5=1.1m/s

Substitute 6.7m/s for v1z, 3.7m/s for v2z, 10.7m/s for v3z, 3.6m/s for v4z and 4.0m/s for v5z in equation (III) to find (vz)av.

  (vz)av=6.7m/s3.7m/s10.7m/s+3.6m/s+4.0m/s5=0.02m/s

Substitute 3.1m/s for (vx)av, 1.1m/s for (vy)av and 0.02m/s for (vz)av in equation (IV) to find vav.

    vav=3.1m/si^1.1m/sj^0.02m/sk^=(3.1i^1.1j^0.02k^)m/s

Thus, the average velocity of the particles is (3.1i^1.1j^0.02k^)m/s.

(b)

To determine

The average speed of the particles.

(b)

Expert Solution
Check Mark

Answer to Problem 6PQ

The average speed of the particles is 9.5m/s.

Explanation of Solution

Write the equation for the speedof the first particle.

    v1=(v1x)2+(v1y)2+(v1z)2                                                                  (V)

Write the equation for the average speed.

    vav=v1+v2+v3+v4+v55                                                                                (VI)

Conclusion:

Substitute 3.4m/s for v1x, 5.6m/s for v1y, 6.7m/s for v1z in equation (V) to find v1.

  v1=(3.4m/s)2+(5.6m/s)2+(6.7m/s)2=9.4m/s

Similarly, calculate the speed of the second particle.

    v2=7.9m/s

Calculate the speed of the third particle.

    v3=10.8m/s

Calculate the speed of the fourth particle.

    v4=13.9m/s

Calculate the speed of the fifth particle.

    v4=5.5m/s

Substitute 9.4m/s for v1, 7.9m/s for v2, 10.8m/s for v3, 13.9m/s for v4 and 5.5m/s for v5 in equation (VI) to find vav.

    vav=9.4m/s+7.9m/s+10.8m/s+13.9m/s+5.5m/s5=9.5m/s

Thus, the average speed of the particles is 9.5m/s.

(c)

To determine

The rms speed of the particles.

(c)

Expert Solution
Check Mark

Answer to Problem 6PQ

The rms speed of the particles is 9.9m/s.

Explanation of Solution

Write the equation for the rms speed of the particles.

    vrms=1Nj=1Nvj2                                                                               (VII)

Conclusion:

Substitute the values for the speeds of the particles in equation (VII) to find vrms.

  vrms=15[(9.4m/s)2+(7.9m/s)2+(10.8m/s)2+(13.9m/s)2+(5.5m/s)2]=9.9m/s

Thus, the rms speed of the particles is 9.9m/s.

(d)

To determine

Compare the speeds of the particles.

(d)

Expert Solution
Check Mark

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.

    |vavg|=(vav)x2+(vav)y2+(vav)z2                                                             (VIII)

Here, |vavg| is the magntide of the average velocity

Conclusion:

Susbtitute 3.1m/s for (vav)x, 1.1m/s for (vav)y and 0.20m/s for (vav)y to find |vavg|.

  |vavg|=(3.1m/s)2+(1.1m/s)2+(0.20m/s)2=3.3m/s

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
19:39 · C Chegg 1 69% ✓ The compound beam is fixed at Ę and supported by rollers at A and B. There are pins at C and D. Take F=1700 lb. (Figure 1) Figure 800 lb ||-5- F 600 lb بتا D E C BO 10 ft 5 ft 4 ft-—— 6 ft — 5 ft- Solved Part A The compound beam is fixed at E and... Hình ảnh có thể có bản quyền. Tìm hiểu thêm Problem A-12 % Chia sẻ kip 800 lb Truy cập ) D Lưu of C 600 lb |-sa+ 10ft 5ft 4ft6ft D E 5 ft- Trying Cheaa Những kết quả này có hữu ích không? There are pins at C and D To F-1200 Egue!) Chegg Solved The compound b... Có Không ☑ ||| Chegg 10 וח
No chatgpt pls will upvote
No chatgpt pls will upvote

Chapter 20 Solutions

Physics for Scientists and Engineers: Foundations and Connections

Ch. 20 - Prob. 5PQCh. 20 - Prob. 6PQCh. 20 - Prob. 7PQCh. 20 - Prob. 8PQCh. 20 - Particles in an ideal gas of molecular oxygen (O2)...Ch. 20 - Prob. 10PQCh. 20 - Prob. 11PQCh. 20 - Prob. 12PQCh. 20 - Prob. 13PQCh. 20 - Prob. 14PQCh. 20 - The mass of a single hydrogen molecule is...Ch. 20 - Prob. 16PQCh. 20 - The noble gases neon (atomic mass 20.1797 u) and...Ch. 20 - Prob. 18PQCh. 20 - Prob. 19PQCh. 20 - Prob. 20PQCh. 20 - Prob. 22PQCh. 20 - Prob. 23PQCh. 20 - Prob. 24PQCh. 20 - Prob. 25PQCh. 20 - Prob. 26PQCh. 20 - Prob. 27PQCh. 20 - Prob. 28PQCh. 20 - Consider the Maxwell-Boltzmann distribution...Ch. 20 - Prob. 30PQCh. 20 - Prob. 31PQCh. 20 - Prob. 32PQCh. 20 - Prob. 33PQCh. 20 - Prob. 34PQCh. 20 - Prob. 35PQCh. 20 - Prob. 36PQCh. 20 - Prob. 37PQCh. 20 - Prob. 38PQCh. 20 - Prob. 39PQCh. 20 - Prob. 40PQCh. 20 - Prob. 41PQCh. 20 - Prob. 42PQCh. 20 - Prob. 43PQCh. 20 - Prob. 44PQCh. 20 - Figure P20.45 shows a phase diagram of carbon...Ch. 20 - Prob. 46PQCh. 20 - Prob. 47PQCh. 20 - Consider water at 0C and initially at some...Ch. 20 - Prob. 49PQCh. 20 - Prob. 50PQCh. 20 - Prob. 51PQCh. 20 - Prob. 52PQCh. 20 - Prob. 53PQCh. 20 - Prob. 54PQCh. 20 - Prob. 55PQCh. 20 - Prob. 56PQCh. 20 - Consider again the box and particles with the...Ch. 20 - Prob. 58PQCh. 20 - The average kinetic energy of an argon atom in a...Ch. 20 - For the exam scores given in Table P20.60, find...Ch. 20 - Prob. 61PQCh. 20 - Prob. 62PQCh. 20 - Prob. 63PQCh. 20 - Prob. 64PQCh. 20 - Prob. 65PQCh. 20 - Prob. 66PQCh. 20 - Determine the rms speed of an atom in a helium...Ch. 20 - Consider a gas filling two connected chambers that...Ch. 20 - Prob. 69PQCh. 20 - Prob. 70PQCh. 20 - A 0.500-m3 container holding 3.00 mol of ozone...Ch. 20 - Prob. 72PQCh. 20 - Prob. 73PQ
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning