A boy's catapult is made of a rubber cord whi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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: $\frac{1}{2} 	imes Y 	imes (9\pi 	imes 10^{-6}) 	imes 0.42 	imes \left( \frac{0.20}{0.42} ight)^2 = \frac{1}{2} 	imes 0.02 	imes (20)^2$.$Y 	imes (9\pi 	imes 10^{-6}) 	imes 0.42 	imes \frac{0.04}{0.1764} = 0.02 	imes 400 = 8$.$Y 	imes (9 	imes 3.14 	imes 10^{-6}) 	imes 0.42 	imes 0.2267 = 8$.$Y \approx 3 	imes 10^6\, N/m^2$.

Similar Questions

When strain is produced in a body within the elastic limit,its internal energy:

$A$ rubber cord catapult has a cross-sectional area of $25\,mm^2$ and an initial length of $10\,cm$. It is stretched by $5\,cm$ and then released to project a missile of mass $5\,g$. Taking $Y_{rubber} = 5 \times 10^8\,N/m^2$,the velocity of the projected missile is ......... $m/s$.

When a block of mass $M$ is suspended by a long wire of length $L$,the length of the wire becomes $(L+l)$. The elastic potential energy stored in the extended wire is:

Two wires of the same material (Young's modulus $Y$) and same length $L$ but radii $R$ and $2R$ respectively are joined end to end and a weight $W$ is suspended from the combination as shown in the figure. The elastic potential energy in the system is

$A$ wire suspended vertically from one end is stretched by attaching a weight $200 \,N$ to the lower end. The weight stretches the wire by $1 \,mm$. The elastic potential energy gained by the wire is ....... $J$

Vedclass Test Series

Exam Paper Generator

Online Exam Module