Why does Work Done Appear to be More than 100% Energy in a System? [closed]

Question

Energy is equivalent to the work done on a motor. The work done on the motor is multiplied by more than 100% by recycling the energy the motor uses. Why then does the energy in the system appear to be more than one hundred percent?

For instance if a motor is powered from a capacitor with 1 joule of energy in it then the motor has done 1 joule's worth of work.

Yet when the energy is recycled, by pulsing and recovering the energy through the utilization of a collapsing magnetic field, then the motor can now do more work than what it originally could have done if the energy was used only once.

If the work done in the motor is directly related, proportional and equal to the energy that was in the capacitor, then would this mean that the energy has now gone above 100% as well? That is the question.

Any answers would be greatly appreciated. I will remain neutral to any and all answers as I don't consider them right or wrong.

More information and clarification can be found here. I actually figured out the answer for myself and hopefully for others as well here.

Answer 1

For the most part, you can ignore the difference between energy and work. They're not quite the same, but they're similar enough that, in my experience, I haven't seen anyone get a wrong answer because they got them confused.

Work specifically is what a force does when there is a displacement in the point of application of that work. In laymans terms, work is what happens when a force moves something. By the Work-Energy principle, the amount of kinetic energy gained by a rigid body is exactly equal to the amount of work done on it.

So by that technical definition, using a capacitor to power a motor which moves an object is doing work, while using a capacitor to power a lightbulb is not because no kinetic energy was added to any object. Instead, that electrical potential energy was converted to thermal energy, which was then radiated as light. In practice, this distinction is not emphasized. In all situations I am aware of (except perhaps exam questions), I could say "the capacitor is doing work, lighting the light bulb," and people would properly interpret what I meant.

The big difference is really that energy is a property of a "thing" while work is a property of a force. This is funny since forces aren't "things," but rather abstract mathematical constructs to make sense of how the world works. Philosophers may squabble over this, but I've never found any practical issue caused by the misuse of work vs. energy. People generally use the correct word in the correct places.

So, to answer your final question, the only reason 1W of work done over 1 second is not quite equivalent to 1J of energy is simply because work is associated with a force, while energy is associated with a thing. However, practically speaking, I've never seen any reason why you would get in trouble thinking of them as equivalent.

Answer 2

The short answer is yes. The long answer is somewhat more subtle. It is true that work is dimensionally equivalent to energy (their units are the same). Therefore, you could always say that work represents energy.

The subtility lies in the fact that there are different forms of energy. If I lift a stone of $0.1$ g $1$ m above the ground, it will have gained approximately $1$ Joule of energy (the gravitational potential energy is $mgh$, with $m$ the mass, $g$ the earth's gravity field ($9.81 m /s^2$), and $h$ the height). However, due to air friction, I will have performed slightly more work than that (although the difference would be negligible). Also, my body will have used more energy than the amount of work I did, because the human body definitely does not have a $100 \%$ efficency when converting energy into this kind of work. Where, then, did the excess energy go?

The answer is heat. Heat is also a form of energy. Whenever something moves in a non-ideal environment, it will undergo friction, and that friction will cause some energy to dissipate as heat.

To summarize, in an ideal situation, you can generally say that work done equals change in energy. In a non-ideal situation, this is also true, but some of the energy will be dissipated as heat.