4.1 Find the force for each of the following potential energy functions: (a) \( V=c x y z+C \) (b) \( V=\alpha x^{2}+\beta y^{2}+\gamma z^{2}+C \) (c) \( V=c e^{-(\alpha x+\beta y+\gamma z)} \) (d) \( V=c r^{n} \) in spherical coordinates
Added by Concepci-N M.
Close
Step 1
- The force \(\mathbf{F}\) is related to the potential energy \(V\) by the negative gradient: \(\mathbf{F} = -\nabla V\). Show more…
Show all steps
Your feedback will help us improve your experience
Supreeta N and 63 other Physics 101 Mechanics 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
Determine whether each of the following forces is conservative. Find the potential energy function if it exists. A.) F=(x^2+y^2, y^2+z^2, z^2+x^2) B.) F=(2xyz, 2xyz, 2xyz) C.) F=(8xy+2y^2z, 4x^2+4xyz, 26z+2xy^2) D.) Given the potential energy V(x,y,z) = 14xyz^3 + 2x^2 + y^3, what is the force associated with this potential?
Supreeta N.
Find the force corresponding to the potential energy $U(x)=-a / x+b / x^{2}$
Find the potential function f for the field F. F = 2xe^(x^2+y^2) i + 2ye^(x^2+y^2) j f(x, y, z) = e^(x^2+y^2) + C f(x, y, z) = 2e^(x^2+y^2) + C f(x, y, z) = e^(x^2+y^2) / 2 + C f(x, y, z) = e^(x^2) + e^(y^2) + C
Madhur L.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Watch the video solution with this free unlock.
EMAIL
PASSWORD