Springs and Potential Energy

Click For Summary
The discussion focuses on the relationship between gravitational potential energy and elastic potential energy in a spring-wombat system. When the wombat is lowered, the gravitational potential energy lost is equal to twice the elastic potential energy gained. This discrepancy arises because the process involves a non-conservative force, as the wombat is lowered slowly. The key point is that the energy transformation is not equal due to the work done by the person lowering the wombat. Understanding this concept is crucial for solving related physics problems.
BlueEight
Messages
18
Reaction score
0

Homework Statement


An ideal spring is suspended from a ceiling with a wombat attached to the end. The wombat is slowly lowered until the upward force exerted by the spring on the wombat balances the weight of the wombat. Show that the loss of gravitational potential energy equals twice the gain in the elastic potential energy of the spring-wombat-Earth system. WHY are these two quantities NOT equal?

Homework Equations


Change in gravitational potential = -mg(Xf - Xi)
Change in elastic potential = .5k(Xf2 - Xi2)

The Attempt at a Solution


I realize that it is due to the fact that a person slowly lowers the wombat, thus acting as a non-conservative force, but do not know how to derive the solution.
 
Last edited:
Physics news on Phys.org
I realize that the gravitational potential energy must be greater, but why is is exactly twice, no matter the mass of the object?
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
View full post »

Similar threads

Calculating the spring force constant K
  • · Replies 14 ·
Replies
14
Views
2K
Why can we move the spring with constant speed when we apply a force?
  • · Replies 29 ·
Replies
29
Views
3K
Initial velocity of bird landing on horizontal wire modeled as spring
  • · Replies 7 ·
Replies
7
Views
1K
Solving a Spring-Mass-Box System:Energy Conservation
  • · Replies 1 ·
Replies
1
Views
2K
Pan suspended by a spring (Energy + SHM)
  • · Replies 20 ·
Replies
20
Views
4K
Force components for mass attached to two springs
  • · Replies 15 ·
Replies
15
Views
1K
Spring deflection problem using energy equations
  • · Replies 2 ·
Replies
2
Views
2K
Block on slope. Different answers using energy vs forces
  • · Replies 5 ·
Replies
5
Views
953
Energy Conservation of a Vertical Spring
  • · Replies 5 ·
Replies
5
Views
2K
Conservation of Energy of a Spring with Weight Added
  • · Replies 7 ·
Replies
7
Views
2K