Conservation of energy springs.

[computer_geek]

Hello, I have a question regarding the conservation of energy.

So you have a long spring (the kind that wants to stay closed, as in when you pull on it, it reacts in the opposite direction) situated in a vertical position. You attach the weight to the bottom of the spring, and let it bounce up and down several times.

Now, using distance sensors and what not, you can calculate kinetic, potential (gravitational), and potential (elastic) energy. Would it be correct to assume that when the 3 are added together, a somewhat constant value is achieved?

Well, that's what my teacher claims. I think otherwise because although (potential) gravitational energy decreases when (potential) elastic energy increases, they change at different rates, therefore not resulting in a straight line when added.

Any comments would be greatly appreciated!
Thanks

 

[physicsfox]

Why do you think the PEspring and PEgrav change at different rates? Think about this question: If an object falls from rest, from a height of h, the object has PE defined by mgh, and KE defined by 1/2mv^2. These also appear to change at different rates... yet you would probably agree that as the PE decreases, the KE increases by the exact same amount. The spring system is, in a way, very similar. Back to the freefall example - try sketching graphs of PE vs. time, and on the same axis, KE vs. time. (As a start, also think about your Vel. vs. time graph for an object in freefall - your KE graph would be the square of the Vel. vs. time)

 

[quicknote]

for your question about the conservation of energy. In this scenario, it is important to consider the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred from one form to another. In this case, the energy is being transferred between kinetic, potential (gravitational), and potential (elastic) forms as the spring bounces up and down.

When you add all three forms of energy together, you should indeed get a constant value. This is because, as you mentioned, as potential (gravitational) energy decreases, potential (elastic) energy increases in equal amounts. This is known as the principle of energy conservation.

It is important to note that the rate at which the energy is being transferred between forms may not be constant, but the total amount of energy should remain constant. This can be seen in the oscillation of the spring, where the energy continually transfers back and forth between kinetic and potential forms, but the total amount of energy remains the same.

I would suggest discussing this further with your teacher to better understand their explanation and to see if they can provide any additional clarification. It is also always a good idea to question and critically think about scientific concepts, so keep up the good work!