Potential energy of spring and mass system

In summary, the conversation discusses a system of 3 equal masses connected by springs with length a and spring constant k, which can only move in the x axis. The question raised is about the potential of the system. The attempted solution is an equation involving the positions of the masses and the spring constant, but it is corrected to consider the rest length of the springs.
  • #1
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Homework Statement



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There are 3 equal masses connected by springs with length a and spring constant k.

The system can only move in the x axis.
x1,x2,x3 is the position of each massWhat is the potential of the system?

The Attempt at a Solution



I came up with this equation:

[itex] U=\frac{1}{2} k [(a-x2-x1)^2 + (a-x3-x2)^2] [/itex]

is it right? thanks
 
Last edited:
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  • #2
Try x_1 = -100, x_2 = -99, a=1 (in meters if you like). Clearly the spring between 1 and 2 is not stretched (it has rest length 1 and the distance between the points is 1). What does your function give for that spring? Can that be right?
 
  • #3
[itex] U=\frac{1}{2} k [(x2-x1-a)^2 + (x3-x2-a)^2] [/itex]

got it
 

Related to Potential energy of spring and mass system

1. What is potential energy of a spring and mass system?

The potential energy of a spring and mass system is the energy stored in the spring when it is stretched or compressed. It is calculated as 1/2*k*x^2, where k is the spring constant and x is the displacement from the equilibrium position.

2. How is the potential energy of a spring and mass system related to its equilibrium position?

The potential energy of a spring and mass system is directly proportional to the displacement from the equilibrium position. As the displacement increases, so does the potential energy, and vice versa.

3. Does the mass of the object affect the potential energy of a spring and mass system?

Yes, the mass of the object does affect the potential energy of a spring and mass system. The greater the mass, the greater the potential energy at a given displacement. This is because a heavier object will require more force to be stretched or compressed to the same displacement as a lighter object.

4. How does the spring constant affect the potential energy of a spring and mass system?

The spring constant, represented by the variable k, is a measure of the stiffness of the spring. A higher spring constant means the spring is stiffer and will require more force to be stretched or compressed to a given displacement. Therefore, a higher spring constant will result in a higher potential energy at a given displacement.

5. Can potential energy in a spring and mass system be converted into other forms of energy?

Yes, potential energy in a spring and mass system can be converted into kinetic energy when the mass is released and the spring returns to its equilibrium position. This conversion of energy follows the principle of conservation of energy, where energy cannot be created or destroyed, only converted from one form to another.

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