Energy Conservation of a Vertical Spring

In summary: The stone is at rest in the equilibrium position, so all that energy which would have been KE at that position has somehow been dissipated.
  • #1
Physicsboi123
3
0
Homework Statement
A 9-kg stone is at rest on top of a spring, which causes it to compress 15cm.
What is the spring constant of the spring?
Relevant Equations
Ei=Ef, F=kx, W=mg, Ek=0.5kx^2
Using conservation of energy,

0.5kx^2=mgh=mgx

0.5kx=mg

0.5kx=mg, x=0.15, m=9, g= 9.8

So isn't it k= 1176N/m?

For this problem, I understand that you can't use conservation of energy, but why? There is gravitational potential energy at the top and spring elastic energy at the bottom, and no kinetic energy at both points since it is at rest on top of the spring?

Any help would be much appreciated!

Thanks!
 
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  • #2
Physicsboi123 said:
Homework Statement:: A 9-kg stone is at rest on top of a spring, which causes it to compress 15cm.
What is the spring constant of the spring?
Homework Equations:: Ei=Ef, F=kx, W=mg, Ek=0.5kx^2

you can't use conservation of energy, but why?
If you were to place the stone carefully on top of the relaxed spring and let go, what would happen?
 
  • #3
haruspex said:
If you were to place the stone carefully on top of the relaxed spring and let go, what would happen?
I suppose it would slowly descend to resting place and stop? I know you have to use Fnet=0 to calculate k, but wouldn't that just be where acceleration is 0, not velocity?
 
  • #4
Physicsboi123 said:
I suppose it would slowly descend to resting place and stop?
That's not what springs do usually.
Physicsboi123 said:
wouldn't that just be where acceleration is 0, not velocity?
Exactly! All the while the stone is above the equilibrium position the net force is downward, so the speed is increasing. When it reaches the equilibrium position it is at maximum speed, so a lot of KE.
In the question you were given, the stone is at rest in the equilibrium position, so all that energy which would have been KE at that position has somehow been dissipated.
 
  • #5
haruspex said:
That's not what springs do usually.

Exactly! All the while the stone is above the equilibrium position the net force is downward, so the speed is increasing. When it reaches the equilibrium position it is at maximum speed, so a lot of KE.
In the question you were given, the stone is at rest in the equilibrium position, so all that energy which would have been KE at that position has somehow been dissipated.
Oh, I understand, so the spring oscillates for a while before coming to rest.

I understand that KE is greatest at equilibrium and that energy, but the question didn't mention that the stone is at rest in equilibrium position, which is mg=kx. How would you deduce that v=0 when x=mg/k, an energy isn't conserved?
 
  • #6
Physicsboi123 said:
the question didn't mention that the stone is at rest in equilibrium position
It says "A 9-kg stone is at rest on top of a spring". How can it be at rest if not at the equilibrium position?
 

1. What is energy conservation in a vertical spring?

Energy conservation in a vertical spring refers to the principle that the total mechanical energy (potential energy + kinetic energy) of a spring remains constant as it oscillates up and down vertically. This means that the energy is neither created nor destroyed, but rather transferred between potential and kinetic forms.

2. How is potential energy conserved in a vertical spring?

Potential energy is conserved in a vertical spring because the spring's displacement from its equilibrium position determines the amount of potential energy it has. As the spring is compressed or stretched, its potential energy increases or decreases accordingly. This potential energy is then converted into kinetic energy as the spring moves up and down.

3. What factors affect the conservation of energy in a vertical spring?

The conservation of energy in a vertical spring is affected by several factors, including the spring constant (k), the mass of the object attached to the spring, and the amplitude of the oscillations. A higher spring constant and a larger mass will result in a higher amount of potential energy, while a larger amplitude will result in a higher amount of kinetic energy.

4. Can energy be lost in a vertical spring?

In an ideal system, energy cannot be lost in a vertical spring. This means that the total mechanical energy of the spring will remain constant, and there will be no energy dissipation due to factors such as friction or air resistance. However, in real-world systems, some energy may be lost due to these factors, resulting in a decrease in the amplitude of the oscillations over time.

5. How does energy conservation in a vertical spring relate to the law of conservation of energy?

Energy conservation in a vertical spring is a specific application of the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted between different forms. The principle of energy conservation in a vertical spring demonstrates this law by showing that the total energy of the system remains constant despite the conversion between potential and kinetic forms.

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