Calculating Potential Energy Stored in Springs

[vysero]

A mass of 10kg hangs from an ideal (massless) spring from the ceiling. The mass and spring are in static equilibrium, so there is no motion. If the spring has a spring constant k=1000N/m and g = 10 m/s/s, what is the (potential) energy stored in the spring?



PE = mgh and KE(of spring)= 1/2kx^2 and maybe hooks law



Kind of stumped.

I am not sure how to go about this problem as I am not sure if it is a trick question. Since PE = mgh and there is no height here would the PE = 0? If I set PE = 1/2kx^2 I have one equation with two unknowns which does not help me. I want to say its a conservation of energy problem but I am not sure. Please help me understand.

 

[haruspex]

Since PE = mgh and there is no height here would the PE = 0?

It asks for the PE stored in the spring, not gravitational PE.
But you do need to work out the spring extension.

 

[vysero]

Ah okay so:

100N = 1000(x), x = .1

and (1/2)(1000)(.1)^2= 5 joules, is that right?

 

[haruspex]

Looks right.

 

[Nickie]

I understand your confusion with this problem. It is important to remember that potential energy is the energy that is stored within a system due to its position or configuration. In this case, the potential energy stored in the spring is due to its compression or elongation from its equilibrium position. This potential energy can be calculated using the equation PE = 1/2kx^2, where k is the spring constant and x is the displacement from the equilibrium position.

In this problem, the mass and spring are in static equilibrium, meaning that the forces acting on them are balanced and there is no motion. This equilibrium is maintained by the force of gravity pulling the mass down and the force of the spring pushing the mass up. Since there is no motion, we can assume that the displacement of the spring from its equilibrium position is also zero.

Therefore, using the equation PE = 1/2kx^2, we can calculate the potential energy stored in the spring as PE = 1/2(1000N/m)(0)^2 = 0 J.

In summary, the potential energy stored in the spring in this scenario is zero since there is no displacement from its equilibrium position. I hope this helps clarify the problem for you.