GREPhysics.NET
GR | # Login | Register
   
  GR9677 #44
Problem
GREPhysics.NET Official Solution    Alternate Solutions
This problem is still being typed.
Mechanics}Chain Rule

Recall that a=\frac{dv}{dt}=\frac{dv}{dx}\frac{dx}{dt}=v\frac{dv}{dx}. \frac{dv}{dx}=-n\beta x^{-n-1}\Rightarrow v\frac{dv}{dx}=-n\beta^2 x^{-2n-1}, as in choice (A).

See below for user comments and alternate solutions! See below for user comments and alternate solutions!
Alternate Solutions
There are no Alternate Solutions for this problem. Be the first to post one!
Comments
JasonHupp
2018-07-30 11:09:59
Before the energy conversion is a hectic task to me but when i have seen here this simple tutorial on how to solve i was surprised. As i have been looking for a help and thinking is assignmenthelps.com.au legit good to help me out in this problem solving. Mean while got yours.NEC
RayGSD
2006-11-03 15:38:36
You can also do this through energy conservation.

\frac{1}{2} m v(x)^2 + U(x) = E_0

\Rightarrow U(x) = E_0 - \frac{1}{2} m \beta^2 x^{-2n}

and

-\frac{\partial U(x)}{\partial x} = F = m a

So

a = 1/2 \beta^2 \frac{\partial}{\partial x}\left( x^{-2n} \right)

a = -n \beta^2 x^{-2n-1}
FutureDrSteve
2011-11-02 14:36:35
I don't think this is faster or easier than the posted solution, but it's very elegant. Nice job!
NEC
StudyTime
2005-11-11 09:16:50
You can also do it through dimensional analysis.NEC

Post A Comment!
You are replying to:
You can also do this through energy conservation.
\frac{1}{2} m v(x)^2 + U(x) = E_0
\Rightarrow U(x) = E_0 - \frac{1}{2} m \beta^2 x^{-2n}
and
-\frac{\partial U(x)}{\partial x} = F = m a
So
a = 1/2 \beta^2 \frac{\partial}{\partial x}\left( x^{-2n} \right)
a = -n \beta^2 x^{-2n-1}

Username:
Password:
Click here to register.
This comment is best classified as a: (mouseover)
 
Mouseover the respective type above for an explanation of each type.

Bare Basic LaTeX Rosetta Stone

LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces .
type this... to get...
$\int_0^\infty$
$\partial$
$\Rightarrow$
$\ddot{x},\dot{x}$
$\sqrt{z}$
$\langle my \rangle$
$\left( abacadabra \right)_{me}$
$\vec{E}$
$\frac{a}{b}$
 
The Sidebar Chatbox...
Scroll to see it, or resize your browser to ignore it...