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 dtseng96 Feb24-13 04:36 PM

Potential Energy of a Spring Contradiction?

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!

 mfb Feb24-13 05:52 PM

Re: Potential Energy of a Spring Contradiction?

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).

 dtseng96 Feb24-13 06:02 PM

Re: Potential Energy of a Spring Contradiction?

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.

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