Show that the work done by a constant force field F = ai + bj + ck in moving a particle along any path from A to B is W = F · AB
Added by Sarah N.
Step 1
** Show more…
Show all steps
Close
Your feedback will help us improve your experience
Israel Hernandez and 81 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Work by a constant force Show that the work done by a constant force field $\mathbf{F}=a \mathbf{i}+b \mathbf{j}+c \mathbf{k}$ in moving a particle along any path from $A$ to $B$ is $W=\mathbf{F} \cdot \overrightarrow{A B} .$
Integrals and Vector Fields
Path Independence Conservative Fields and Potential
If $\mathbf{F}(x, y, z)=a_{1} \mathbf{i}+a_{2} \mathbf{j}+a_{3} \mathbf{k}$ is a constant force vector field, show that the work done in moving a particle along any path from $P$ to $Q$ is $W=\mathbf{F} \cdot \overrightarrow{P Q}$.
Vector Analysis
Conservative Vector Fields and Independence of Path
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD