Why don't they use springs as an energy source for cell phones? I know they used springs for clocks way back in the day and now it's all lithium ion batteries.
For reference, consider the Iphone that has a battery with a capacity of 5 Watt hours (18,000 joules).
For portable energy sources, fuel cells have been investigated, but they have a lot of down falls (mainly they're dangerous and not particularly efficient). Super capacitors are great, but they cannot handle large voltages because the electrolyte in them will break down; sadly it will still be a long time before we can replace chemical batteries with capacitors. So, what about springs? Of course, it's a lot more work to convert the mechanical energy into electrical, but look at how sophisticated some mechanical watches are. I don't think there is a lack of ingenuity to make a gear reduction and a miniature generator. Though I'm not sure about getting 18 kJ of energy into a spring of a convenient size for a cell phone, but it was noted by a manufacturer as being "... one of the most efficient energy storage devices available"
Would it be feasible/practical to do so?
 A: We tend to think that our modern electronic devices are very energy-efficient so mechanical mainsprings etc. must be enough but they're not. After all, the (Intel i7) microprocessors have over 1 billion transistors per chip and each transistor has to consume some nonzero (and not "totally" negligible) energy, after all, to do an operation and they do billions of operations per second.
The mainsprings are an extremely lousy storage of energy. The total mechanical energy of such a mainspring may be calculated as $E=\int F\cdot d\ell$. This integral is comparable to the longitudinal force of the mainspring multiplied by the change of its length after it unwinds.
When the numbers are substituted, the mainspring 2824-2 in a wristwatch only contains 0.3 joules. One may basically view the energy as extensive and fill a volume with mainsprings. The energy stored in these mechanical devices will be 1530 joules per liter. It is just 1.5 kilojoules per liter.
This is tiny compared to the energy stored in gasoline – 35 megajoules per liter which is 20,000 times more concentrated energy than the energy in mainsprings. The energy stored in the same volume of batteries will be comparable to gasoline (because both of them are based on the chemical energy of electronic orbitals), just a little bit lower. Lithium-ion batteries have about 4 megajoules per liter, about 9 times lower than gasoline, see the table here

https://en.wikipedia.org/wiki/Energy_density#Energy_densities_of_common_energy_storage_materials

Lithium-ion batteries still store 3,000 times more energy than the mainspring of the same volume. It shouldn't be surprising microscopically. The mainspring only rearranges macroscopic pieces of the metal which only uses relatively small forces we may afford not to make the spring too dangerous when it cracks. On the other hand, the chemical energy (gasoline, lithium-ion) uses the much larger forces that keep the atoms together or apart etc. They store the near-maximum chemical energy in every atom or every pair of adjacent atoms, so to say.
The nuclear energy stored per kilogram is over 1 million times greater than the gasoline; and it is almost 1 billion times more concentrated energy than gasoline on the per-volume basis (because the uranium etc. is denser). An even more shocking comparison is the uranium-vs-mainspring comparison on the per-volume basis: uranium (nuclear) is about 1 trillion times more concentrated form of useful energy than the mainsprings. (If we could get lots of antimatter and annihilate it against matter, we would gain another factor of nearly 1,000 in the energy content per liter – almost 1 quadrillion times denser useful energy than in mainsprings – and no further improvement would be possible.)
For those reasons, the mainsprings are a romantic old-fashioned solution but it is not practical for the modern devices which consume much more energy than what a mainspring may give.
Ordinary people know quite something about how much energy batteries can carry. They have batteries e.g. in portable small vacuum cleaners (not to mention Tesla cars) and they may easily see that the amount of mechanical work that the vacuum cleaner (let alone car) may perform with new batteries would be enough to wind a mainspring many times.
Because this question is literally about the approximate calculation of energy, qualitative physical mechanisms behind different types of storages, and the same order-of-magnitude estimates (in atomic physics etc.) that a part of our physics PhD qualifying exams at Rutgers were full of, I strongly disagree with the users who classified this question as an "off-topic question on engineering" before they closed it.
