Potential Energy of a Spring Contradiction?

In summary: What if the two springs have the same potential energy but the box has a different mass? In summary, it does not matter which way the springs are positioned.
  • #1
dtseng96
13
0
Hi everyone, I'm a bit confused about the concept of the potential energy. Let's say we have the following scenarios here: https://dl.dropbox.com/u/29312856/Springs.jpg

In the first scenario, we have two identical springs with spring constant 5000 N/cm angled at 20 degrees below the horizontal, and a box of 2 kg is compressed against the two springs, causing each spring to be compressed 2 cm. The entire system is in space, with no sources of gravity nearby. If we release the box from the spring, the box have a speed of y m/s.

In the second scenario, we have the same two springs as before, except placed vertically upwards. The box is compressed against the two springs, causing each spring to be compressed 2 cm. The entire system is in space, with no sources of gravity nearby. If we release the box from the spring, the box have a speed of z m/s.

Using the law of conservation of energy, it seems like the speed y and the speed z in the two scenarios are the same (meaning that it does not matter which way you position the two springs) because the potential energy of the two springs in each scenario are the same.

Yet, it seems illogical that it would be that way. In the first scenario, the horizontal components of the force from the springs would cancel out, so only the vertical components of the force from the springs would propel the box forward. In the second scenario, the force from the two springs are completely vertical, so they do not cancel each other out. It seems like the box would have a higher speed in the second scenario because there is more force propelling the box forward in the second scenario.

Can anyone explain my confusion? Any help would be appreciated. Thanks!
 
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  • #2
In the second scenario, you need more energy for compression, as 2cm height corresponds to 2cm of compression (this is different in the first setup).
 
  • #3
Thanks for the reply, mfb! That makes sense, I did not think of that. I realized I made a mistake in my question though, so I just changed my question a bit right now.
 
Last edited:

Related to Potential Energy of a Spring Contradiction?

1. What is potential energy of a spring contradiction?

Potential energy of a spring contradiction refers to the discrepancy between the theoretical potential energy of a compressed or stretched spring and the actual potential energy observed in experiments. This contradiction arises due to various factors such as friction, air resistance, and imperfections in the spring.

2. How is potential energy of a spring contradiction measured?

The potential energy of a spring contradiction can be measured by comparing the theoretical potential energy of a spring (calculated using Hooke's Law) with the actual potential energy observed in experiments. The difference between the two values represents the potential energy of the spring contradiction.

3. What causes potential energy of a spring contradiction?

There are several factors that can cause potential energy of a spring contradiction. Some common causes include friction between the spring and its surroundings, air resistance, and imperfections in the spring such as uneven coils or material defects. Additionally, if the spring is not compressed or stretched in a perfectly vertical or horizontal direction, it can also contribute to the contradiction.

4. How does potential energy of a spring contradiction affect the behavior of a spring?

The potential energy of a spring contradiction can affect the behavior of a spring by decreasing its overall potential energy and therefore reducing its ability to store and release energy. This can result in a decreased amplitude of oscillations and a shorter period of oscillation. In extreme cases, the contradiction can cause the spring to behave in an unpredictable manner.

5. Can potential energy of a spring contradiction be eliminated?

No, it is impossible to completely eliminate the potential energy of a spring contradiction. However, it can be minimized by reducing friction and air resistance, using high-quality materials for the spring, and ensuring that the spring is compressed or stretched in a straight and level direction. Additionally, some of the potential energy can be recovered by using energy-conserving mechanisms such as adding a damper or using an elastic band in conjunction with the spring.

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