It might help to understand WHY a bow needs to “store energy”. (Note that in physics, “energy” and “work” are the same thing).
Shooting an arrow with a bow uses work done by your arms, so why use the bow? Why not just throw the arrow?
It takes about 0.5 seconds to draw a bow, but only 0.01s to shoot. The bow stores up 0.5s worth of output from your arm and releases it all at once (relatively speaking).
The way the bow stores energy is to use work done by your arms to bend wood into a configuration it does not ‘want’ to be in. The wood ‘wants’ to go back to its original shape, and the bow is made so that in order to get back to its original shape, the wood has to pull the bowstring, which pushes the arrow forward.
All forms of energy storage involve putting something into a state it doesn’t normally “want” to be in, which always takes work to do (which is how the work/energy gets stored). E.g. you can store energy in a wheel by spinning the wheel really fast with your hands. You can store energy in water by carrying it up higher off the ground. You can store energy in a spring by stretching/bending it, and that’s what a bow is: a spring.
What makes the wood used in a bow good at storing energy this way is A: the fact that it gives back a decent amount of the energy you put in (nowhere near 100%, but much better than, say, corn stalks, which would make a really terrible spring), and B: the fact that it can release the energy it stores by being a spring fairly quickly.
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