Work is done when the arrow is released from the bow. When this work is not done, the bow is damaged.
We know that energy is neither created nor destroyed rather is converted from one form to another. When the string of the bow is pulled back the elastic potential energy does work and the arropow is released. The elastic potential energy is converted to the kinetic energy of the moving arrow.
However, when this work is not done, the whole energy in the string does work on the bow thereby damaging it.
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