Waste less time on Facebook — follow Brilliant.

Conservative Forces and Potential Energy

The Horizontal component of a conservative force and its relation to Potential Energy, \(U\), of the system is \(F_x = -\frac{\newcommand*\diff{\mathop{}\!\mathrm{d}} U}{\newcommand*\diff{\mathop{}\!\mathrm{d}} x}\). My physics book went further on to say that in 3 dimensions the equation becomes

\(\vec{F} = -\frac{\partial U}{\partial x}\hat{i} - \frac{\partial U}{\partial y}\hat{j} - \frac{\partial U}{\partial z}\hat{k}\)

Firstly why isn't it this instead

\(\vec{F} = -\frac{\newcommand*\diff{\mathop{}\!\mathrm{d}} U}{\newcommand*\diff{\mathop{}\!\mathrm{d}} x}\hat{i} - \frac{\newcommand*\diff{\mathop{}\!\mathrm{d}} U}{\newcommand*\diff{\mathop{}\!\mathrm{d}} y}\hat{j} - \frac{\newcommand*\diff{\mathop{}\!\mathrm{d}} U}{\newcommand*\diff{\mathop{}\!\mathrm{d}} z}\hat{k}\)

I'm quite new with partial derivates so a brief explanation of them would be helpful

Note by Saad Haider
4 years, 3 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)


Sort by:

Top Newest

Not sure about this, understand that the U here as 3 components, and so therefore it is impossible to use the d in the second equation because there are 3 dependent variables. As far as i know of, normal differentiation doesn't work when you have more than 1 dependent variable.

Tan Gian Yion - 4 years, 2 months ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...