How Efficient Is the Spring in Stopping a Rat on a Ski Slope?

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SUMMARY

The discussion focuses on calculating the efficiency of a spring when a 5.0 kg rat collides with it after sliding down a ski slope. The rat's velocity after sliding across a rough patch is 54 m/s, and the spring compresses by 2.42 m. The efficiency formula discussed is e = eout/ein (100%), where Ein is the kinetic energy (Ek = 0.5mv²) and Eout is the elastic potential energy (Eelastic = 0.5k(Δx)²). The user struggles with determining Eout correctly, leading to an incorrect efficiency calculation of around 400%.

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  • Understanding of kinetic energy (Ek = 0.5mv²)
  • Knowledge of elastic potential energy (Eelastic = 0.5k(Δx)²)
  • Familiarity with the concept of energy efficiency (e = eout/ein)
  • Basic principles of mechanics and motion
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LoveandHate
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Homework Statement


So, I have a 5.0 kg rat that goes down a ski slope, slides along a rough patch, and then smashes into a vertical board with a spring attached. I need to find out the efficiency of the spring with this information:
m=5.0 kg
v (after sliding across rough patch)=108 m/s ; it also says that because of internal friction, the velocity is 50% than above, so it's 54 m/s (after hitting the board and spring)
[tex]\Delta[/tex]x=2.42 m (the magnitude of the spring's compression)


Homework Equations


e=eout/ein(100%)
Possibly Ek=.5mv2 and Eelastic=.5k([tex]\Delta[/tex]x)2


The Attempt at a Solution


Well, I think that Ein is equal to Ek, as this is the energy required for the spring to compress, but I'm not completely sure of Eout. Is it possibly Eelastic (I know this value from a previous question)? If I use these two though, I get an answer around 400%, which is obviously wrong.
 
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Are you saying that it hits the spring with a velocity of 104m/s, then exits the spring with a velocity of 54m/s? It might be best to state the problem as exactly worded (both parts).
 

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