# Conceptual Problem with Springs and Energy

• Dorothy Weglend
In summary, the problem is that there is no kinetic energy in the system, so the potential energy of the spring must come from somewhere.
Dorothy Weglend
Here is the problem, it is simple:

An air glider is attached to a massless spring, which is compressed 0.18 m from it's relaxed position. Find the velocity of the glider at its original position, and at 0.25 m. Spring constant is 10 N/m, mass of glider is 0.15 kg.

I have solved this problem, but I am having trouble understanding the potential energy issues for the distance of 0.25 m. The first is easy:

kx^2/2 = mv^2/2

The second is also not difficult:

kx^2/2 = mv^2/2 + k(0.25-0.18)^2/2

But I do not really "get" this second equation. I understand that the massless spring can't have any kinetic energy, since k = mv^2/2, and it is massless, then k-0 when the spring is at its original position, and I think that would be the highest speed.

But as it continues past that point, it must build up a potential energy. But I don't know how to think about this. There must be some energy somewhere that is being converted into potential energy, but if there is truly no kinetic energy, where is the potential energy of the spring coming from? I can't believe it is coming from the glider, that makes no sense, but there is nothing else that is doing anything here.

If someone could help me understand this, I would be so grateful.

Thanks,
Dorothy

Just a thought: Is it that the intial potential energy gets converted into potential energy in the opposite direction? But doesn't it have to go through an intermediate stage first, Us -> Ks -> -Us ?

Thanks again,
Dorothy

Dorothy Weglend said:
Just a thought: Is it that the intial potential energy gets converted into potential energy in the opposite direction?
The spring stores PE when compressed a distance X as well as when stretched a distance X. But spring PE is always >= 0 (the zero point is the unstretched position). (Energy doesn't have direction--it's a scalar.)

But doesn't it have to go through an intermediate stage first, Us -> Ks -> -Us ?
Yes, PE gets converted first to KE, then back to PE. (But not negative PE!)

Is the spring attached so that the glider is not free past the uncompressed point of the spring? Normally a spring-launched glider would just fly off past that point, so the velocity would be the same as at the x=0 point (neglecting air resistance). But if the spring is fully attached to the (un-)glider, then it will start to rob KE from the glider and convert it back to PE. Just calculate how much PE is in the spring at 0.25m, and adjust the glider's KE accordingly.

Thank you both. Yes, energy is a scalar. That must be my mantra for now.

And thank you, Berkeman. That must be what is happening. Yes, the glider is attached to the spring, and that makes perfect sense.

Thank you both so much.
Dorothy

## 1. What is the concept of potential energy in a spring?

Potential energy in a spring refers to the energy stored in a spring when it is stretched or compressed. This energy is stored in the form of elastic potential energy and is directly proportional to the displacement of the spring from its equilibrium position.

## 2. How does the spring constant affect potential energy?

The spring constant, also known as the stiffness of a spring, directly affects the potential energy in a spring. A higher spring constant means that the spring is stiffer and will require more force to stretch or compress, resulting in a higher potential energy stored in the spring.

## 3. What is the relationship between the force applied and the displacement of a spring?

According to Hooke's Law, the force applied to a spring is directly proportional to the displacement of the spring from its equilibrium position. This means that as the displacement increases, the force required to stretch or compress the spring also increases.

## 4. Can potential energy be converted into kinetic energy in a spring?

Yes, potential energy can be converted into kinetic energy in a spring. When a spring is released from its stretched or compressed position, the potential energy stored in the spring is converted into kinetic energy as the spring returns to its equilibrium position.

## 5. How does the mass of an object attached to a spring affect its potential energy?

The mass of an object attached to a spring does not directly affect the potential energy in the spring. However, a heavier object will require more force to stretch or compress the spring, resulting in a higher potential energy stored. Additionally, the displacement of the object will also affect the potential energy, as a larger displacement will result in a higher potential energy.

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