A rubber cord has a cross -sectional area `1 mm^(2)`and total un-stretched length`10.0cm`. It is stretched to `12.0 cm` and then released to project a missile of mass 5.0 g. Taking young's modulus Y for rubber as `5.0xx10^(8) N//m^(2)`.Calculate the velocity of projection .

Explanation

Equivalent force constant of rubber cord,
`k=(YA)/(l)=((5.0xx10^(8))(1.0xx10^(6)))/((0.1))=5.0xx10^(3)Nm^(-1)`
Now, from conservation of mechanical energy, elastic potential energy of cord=kinetic of missile
`therefore (1)/(2)k(Deltal)^(2)=(1)/(2)mv^(2)`
`therefore v=(sqrt((k)/(m)))Deltal`
`=(sqrt((5.0xx10^(3))/(5.0xx10^(-3))))(12.5-10.0)xx10^(-2)=25 ms^(-1)`
Note following assumptions have been made in this example
(i) k has been assumed constant , even though it depends on the length (l)
(ii) The whole of the elastic potential energy id converted into kinetic energy of missile.