Understanding Potential Energy of Hanging Mass on Spring

In summary, the conversation discusses the concept of energy for a hanging spring and determining the equation for potential energy. The individual is trying to understand if they should integrate from -y to y0 or from y0 to y, but it is concluded that as long as they are consistent, it does not matter.
  • #1
atarr3
76
0
I'm having a little trouble understanding the concept of energy for a hanging spring. Suppose I have a system with a mass that is attached to a hanging spring and then is released, causing the mass to oscillate. I'm trying to determine the equation for potential energy, but I'm thrown off by signs.

I'm using the concept that potential is the negative integral of force.

I set my initial position of the spring to be be y0 = 0, so when the mass is attached, we're moving in the negative y direction. This leads me to believe that my bounds for integration should be from -y to y0.

[tex]\int (kx + mg)dy[/tex] from -y to y0 would give me [tex]- \frac{1}{2}ky^{2}+mgy[/tex] if I substitute in y0 = 0.

I guess my question is if I would be correct in integrating from -y to y0 in order to find potential as a function of position, or if I should integrate from y0 to y like I'm traditionally used to.
 
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  • #2
it's never been a problem from which to which you'll integrate as long as you are consistent with the symbols and convention that you are using.
 
  • #3
Ok that's what I thought thank you so much!
 

Related to Understanding Potential Energy of Hanging Mass on Spring

1. What is potential energy in the context of a hanging mass on a spring?

Potential energy is the energy that an object possesses due to its position or state. In the case of a hanging mass on a spring, potential energy refers to the energy stored in the spring due to its stretched or compressed position.

2. How is the potential energy of a hanging mass on a spring calculated?

The potential energy of a hanging mass on a spring can be calculated using the formula PE = 1/2kx², where k is the spring constant and x is the displacement of the spring from its equilibrium position. This formula assumes that the mass is not moving and there is no friction present.

3. What factors affect the potential energy of a hanging mass on a spring?

The potential energy of a hanging mass on a spring is affected by the spring constant, the displacement of the spring, and the mass of the object. A higher spring constant or greater displacement will result in a higher potential energy, while a heavier mass will result in a lower potential energy.

4. How does changing the height of the hanging mass affect its potential energy on a spring?

The height of the hanging mass does not directly affect its potential energy on a spring. The potential energy is determined by the displacement of the spring, not the height of the mass. However, raising or lowering the mass will change the displacement of the spring and therefore affect the potential energy.

5. Can the potential energy of a hanging mass on a spring be converted into other forms of energy?

Yes, the potential energy of a hanging mass on a spring can be converted into other forms of energy, such as kinetic energy. When the hanging mass is released, the potential energy stored in the spring is converted into kinetic energy as the mass moves up and down. Energy cannot be created or destroyed, only converted from one form to another.

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