A student asks, "The explanation shows that the Gravitational Potential Energy is calculated, but don't you also need to calculate the Elastic Potential Energy too? The explanation never explains why elastic potential energy is completely ignored. Shouldn't you calculate the total potential energy like so: Total PE = Grav. PE + Elast. PE If Elast. PE is 1/2 k X^2 ; where k is elastic constant and X is magnitude of displacement of the spring, then why don't we calculate Elast. PE if the question stem gives you X?"
To answer this question, we must use gravitational potential energy to calculate total energy at the beginning. Then, we take that total energy (GPE) and convert it to elastic potential energy when the rabbit lands and compresses its legs (which we are treating as springs in this question). In other words, the rabbit starts at a height of x=0.5 m (meaning its total energy is 3kg * .5m * 10m/s^2 = 15J. When it falls, this GPE is converted to KE and then when it lands it is converted again, this time to EPE. We are told that the spring is imperfect, so we should assume that a few joules are lost as heat, making 13J the best answer. There is no elastic potential energy at first, because the rabbit is falling and has not yet compressed its legs (which it does upon landing).
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