"If a 3kg rabbit's leg muscles act as imperfectly elastic springs, how much energy will they hold if the rabbit lands from a height of 0.5 m and its legs are compressed by 0.2 m?"
Why are we able to disregard the compression distance when solving this question? When given a compression situation, I automatically think (PEelastic = ½kx2), but this question was solved simply using (PE = mgh)
Thank you!
FL 3 C/P Q52

 Posts: 766
 Joined: Fri May 25, 2018 9:15 am
Re: FL 3 C/P Q52
Thanks for the question!
We can basically do this because of the options that are present in the answer choices. If there were values like 9 J, 10 J, and 11 J, then we'd need to know exactly how much energy would be lost due to the imperfect elastic springs of the rabbit's legs. Since the answers are far apart, we can basically just solve this as a conservation of energy problem. Initially, there are approximately mgh = 15 J of energy. After falling, we know the springs should theoretically take all that energy as it's converted to KE and then elastic PE. BUT, we were told they are imperfect, so we assume some amount of energy must be lost due to heat. 10 J is our only logical answer. Note that 14.7 may be tempting, but because 10 m/s^2 is already rounded up, 14.7 is actually just closer to the true value of the initial gravitational PE.
I hope this makes sense. Good luck with your prep!
We can basically do this because of the options that are present in the answer choices. If there were values like 9 J, 10 J, and 11 J, then we'd need to know exactly how much energy would be lost due to the imperfect elastic springs of the rabbit's legs. Since the answers are far apart, we can basically just solve this as a conservation of energy problem. Initially, there are approximately mgh = 15 J of energy. After falling, we know the springs should theoretically take all that energy as it's converted to KE and then elastic PE. BUT, we were told they are imperfect, so we assume some amount of energy must be lost due to heat. 10 J is our only logical answer. Note that 14.7 may be tempting, but because 10 m/s^2 is already rounded up, 14.7 is actually just closer to the true value of the initial gravitational PE.
I hope this makes sense. Good luck with your prep!