Problem with power and potential energy

  • Thread starter costas
  • Start date
  • #1
3
0

Homework Statement


Particle mass m is moving along the x-axis.
The particle is attracted to the principle axis O to measure power mk/x^2 when x>a
and repels the O with measure power mka/x^3 when 0<x<a, where a,k>0

i) Find the potential energy of the particle
ii)The particle is released from rest at 2a from O. Describe the movement to perform the particle and show that the particle will stand briefly when x=a/sqrt2


The Attempt at a Solution


i) I tried to find the potential energy by integrating the function of power:

.............mk / x ^ 2 , x> a
F (x) =
.............mka / x ^ 3 , 0 <x <a

using the relation F (x) = - dU / dx, but the integral constant C if assume that U (O) = 0, goes infinity (oo).

I still can not design the function of potential energy which found that likely have the form:

..............-mk / x , x> a
U (x) =
...............mka / x ^ 2 , 0 <x <a

ii) For the second question I can not think of anything.
 
Last edited:

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,836
255
Hi costas! :smile:

(try using the X2 tag just above the Reply box :wink:)
using the relation F (x) = - dU / dx, but the integral constant C if assume that U (O) = 0, goes infinity (oo).

Then don't assume U(0) = 0 :wink:

assume U(a) = 0, or U(∞) = 0. :smile:
 

Related Threads on Problem with power and potential energy

  • Last Post
Replies
4
Views
2K
Replies
3
Views
3K
  • Last Post
Replies
12
Views
2K
Replies
13
Views
6K
Replies
1
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
667
  • Last Post
Replies
12
Views
1K
Replies
2
Views
12K
  • Last Post
Replies
10
Views
4K
Top