It was stated in class that the energy stored in an energy-storing element canno

Question

It was stated in class that the energy stored in an energy-storing element cannot change instantaneously or abruptly. If it could, the time-rate of change of the stored energy would be infinite (why?). Now, consider the kinetic energy stored in a point mass, m. Show by mathematics and physics (for example f = ma, etc) that it is physically impossible to get an infinite time-rate of change of the stored energy. This provides a proof that the energy stored in an element cannot be changed instantaneously. Make sure your presentation is simple and yet physically and logically clear to receive credit.

Explanation / Answer

Rate of change of stored energy would be (change in energy)/(time of change). If the stored energy was changed instantaneously, t = 0. Dividing anything by 0 gives you a nonreal answer, but if we use limits we can see that as t approaches 0, the rate of change of stored energy approaches infinity. Example: change in energy is 1J. Start with t = 1 second...rate of change would be 1. Now try t =.1 second. Rate of change would be 10 J/sec. t=.01, rate of change = 100 J/sec, and on and on... Using f=ma we can see that the force required to increase the kinetic energy is dependent on the acceleration on the body. If the acceleration were infinity (time of change is instantaneous), the force would also be infinity. So as an infinite force would produce an infinite acceleration (impossible), a 0 time of change would result in an instantaneous rate of change (impossible).

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