Energy Challenge!

Energy Challenge

Predict where to compress two different springs so that the carts of equal mass come off with the same velocity.

We began by determining the spring constants for each spring.

Red: 84 n/m

Blue: 112 n/m

From there, we made an LOL chart to find the mathematical equation to use in order to find the amount of energy in the system. 

Then, we determined that Eel = Ek would, in relationship to the formula, be equal to 

1/2kv^2 = 1/2mv^s

The Eel and mass for each spring was:

Eel = 1/2kv^2

Eel = 1/2(84)^2 = 3528J

Mass = 550g = .55kg

Eel = 1/2kv^2

Eel = 1/2(112)^2 = 6272J

Mass = 539.4g = .5394kg

With this new information, we were able to plug everything into the Ek formula. We gave the system a predicted velocity of .55. 

Ek = 1/2mv^2

Ek = 1/2(.55)(.55)^2 = .0831875J

Ek = 1/2mv^2
Ek = 1/2(.5394)(.55)^2 = .08158425J

Now, to predict the amount each spring must be compressed, we re-tried the Eel formula and plugged in the new numbers we found in the previous formulas.

Eel = 1/2kx^2
3528 = 1/2(.0831875)x^2 
X = 69.42935806 = 69.4m


Eel = 1/2kx^2
6272 = 1/2(.08158425)x^2
X = 79.19570195 = 79.2m


From this information, I can say that the red spring should be compressed 69.4m while the blue spring should be compressed 79.2m. Unfortunately, I was unable to test the springs on the track but the calculations seem a bit too high.