Question

Calculate the work done by the field F when the object moves along the given path from the initial point to the final point.\ F (x, y, z) = (x, y, z), r (t) = (cos (t), sin (t), t) for $\pi \le t \le 4\pi$\ (Express numbers in exact form. Use symbolic notation and fractions where needed.)\ W =

          Calculate the work done by the field F when the object moves along the given path from the initial point to the final point.\
F (x, y, z) = (x, y, z), r (t) = (cos (t), sin (t), t) for $\pi \le t \le 4\pi$\
(Express numbers in exact form. Use symbolic notation and fractions where needed.)\
W =
        
Show more…
Calculate the work done by the field F when the object moves along the given path from the initial point to the final point.F (x, y, z) = (x, y, z), r (t) = (cos (t), sin (t), t) for π≤ t ≤ 4π(Express numbers in exact form. Use symbolic notation and fractions where needed.)W =

Added by Adam L.

Close

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
Calculate the work done by the field F when the object moves along the given path from the initial point to the final point. Fxy,z=xyz),rt=costsint,tfort4 Express numbers in exact form.Use symbolic notation and fractions where needed. W=
Close icon
Play audio
Feedback
Powered by NumerAI
Kathleen Carty David Collins
Danielle Fairburn verified

Harshita Goel and 88 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.

*

Recommended Videos

-
find-the-work-done-by-the-force-field-f-on-a-particle-moving-along-the-given-path-mathbffx-y-zy-z-ma

Find the work done by the force field $F$ on a particle moving along the given path. $\mathbf{F}(x, y, z)=y z \mathbf{i}+x z \mathbf{j}+x y \mathbf{k}$ C: line from (0,0,0) to (5,3,2) (FIGURE CAN'T COPY)

Calculus Early Transcendental Functions

Vector Analysis

Line Integrals

determine-and-state-the-work-done-by-the-vector-field-over-the-given-path-in-each-situation_-f-x-2y3x-moving-from-a00-to-b44-to-c62-16-pts-each-19853

Adi S.

find-the-work-done-by-the-force-field-mathbff-on-a-particle-moving-along-the-given-path-mathbffx-y-2

Find the work done by the force field $\mathbf{F}$ on a particle moving along the given path. $\mathbf{F}(x, y, z)=y z \mathbf{i}+x z \mathbf{j}+x y \mathbf{k}$ $C:$ line from (0,0,0) to (5,3,2)

Essential Calculus

Vector Analysis

Line Integrals


*

Recommended Textbooks

-
Calculus: Early Transcendentals

Calculus: Early Transcendentals

James Stewart 8th Edition
achievement 1,563 solutions
Calculus: Early Transcendentals

Calculus: Early Transcendentals

William Briggs, Lyle Cochran, Bernard Gillet 3rd Edition
achievement 1,546 solutions
Thomas Calculus

Thomas Calculus

George B. Thomas Jr. 14th Edition
achievement 1,944 solutions

*

Transcript

-
00:01 In this problem of line integrals, we have to find the work run y, a force field given here, which is f of x, y and z is equals to yzi plus x z j plus x, y, k, and along the line, i'm showing you the figure.
00:25 So this is the required figure and curve c is such that c is a line from 0 ,000 to, and 2 this is 5 3 and 2 so this point is 5 3 and 2 now we have to parameterize so c is just line straight line from 0 0 to 5 3 2 so we can say that rt would be equals to 5 t so this is 5 t plus 3 t plus 2 t this is i j and k respectively so this this is i j and k 2 tk this is 2 tk and the value of t is varying from 0 to 1 so this is value of t is varying from 0 to 1 now we have to find the value of d r so d r is equal to when we differentiate it so this is 5 i plus 3 j plus 2 k and this is d t now we have to calculate f f so, f of t, f of t would be here.
01:42 From here we say that x is equals to 5 t, y is equals to 3 t and z is equal to 2 t.
01:49 Putting the value y z, so this is 3 t multiplied with 2 t which is equals to 6 t square i, x that is 5 t multiplied with 2 t that is 10 t squared j plus x y that is 5 multiplied by 3 that is 15 t square k now we have to take the dot product for finding the work so work is f dot d r along the path c taking the dot product so this is equal to 60 square is multiplied with 5 so which is equal to 30 t square 10 t squared is multiplied with 3 so which is again 30 t square and 15 t square is multiplied with 2 t so this is only 2 so this value would be again 30 t square and d t now integration from 0 to 1.
02:38 So when we add all the terms, so this is equal to 90 t squared d t, integration from 0 to 1...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade


Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever