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As stone of mass .m. is projected from a...

As stone of mass .m. is projected from a rubber catpult of of length .`l`. and cross-sectional area A stretched by an amount .e.. If Y be the young.s modulus of rubber then find the velocity of projection of stone?

Text Solution

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Strain energy `=(1)/(2)F.e=(1)/(2) ((YA e)/(l))e=(1)/(2) (Yae^(2))/(l)`
As the stone is released, the strain energy in the capult appears in the form o kinetic energy of the stone.
`therefore (1)/(2) (YA e^(2))/(l)=(1)/(2) mv^(2)`
`v^(2)=(YAe^(2))/(lm), v=sqrt((YA e^(2))/(lm))`
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