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Question

(B) The potential energy stored in the stretched rubber cord is converted into the kinetic energy of the stone.The energy stored in the stretched cord

Vedclass · Accepted Answer

$10^6\, N/m^2$

Vedclass · Answer

(B) The potential energy stored in the stretched rubber cord is converted into the kinetic energy of the stone.The energy stored in the stretched cord is given by $U = \frac{1}{2} 	imes Y 	imes A 	imes \ell 	imes \left( \frac{\Delta \ell}{\ell} ight)^2$,where $Y$ is Young's modulus,$A$ is the cross-sectional area,$\ell$ is the original length,and $\Delta \ell$ is the extension.Given: $\ell = 0.42\, m$,$r = 3\, mm = 3 	imes 10^{-3}\, m$,$\Delta \ell = 0.20\, m$,$m = 0.02\, kg$,$v = 20\, m/s$.Area $A = \pi r^2 = \pi 	imes (3 	imes 10^{-3})^2 = 9\pi 	imes 10^{-6}\, m^2$.Equating energy: $\frac{1}{2} 	imes Y 	imes (9\pi 	imes 10^{-6}) 	imes 0.42 	imes \left( \frac{0.20}{0.42} ight)^2 = \frac{1}{2} 	imes 0.02 	imes (20)^2$.$Y 	imes (9\pi 	imes 10^{-6}) 	imes 0.42 	imes \frac{0.04}{0.1764} = 0.02 	imes 400 = 8$.$Y 	imes (9 	imes 3.14 	imes 10^{-6}) 	imes 0.42 	imes 0.2267 = 8$.$Y \approx 3 	imes 10^6\, N/m^2$.

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