Elastic Potential Energy in a Stretched Wire

A rod of iron of Young's modulus $Y=2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$ just fits the gap between two rigid supports $1 \mathrm{m}$ apart. If the rod is heated through$100 °\mathrm{C}$the strain energy of the rod is ($a=18\times {10}^{-6} {\mathrm{m}}^2$ area of cross-section)

The elastic potential energy stored in a steel wire of length $20 \mathrm{m}$ stretched through $2 \mathrm{cm}$ is $80 \mathrm{J}.$ The cross sectional area of the wire is _____ ${\mathrm{mm}}^2.$ (Given, $Y=2.0\times {10}^{11} \mathrm{N} {\mathrm{m}}^{–2}$)

An aluminium rod with Young’s modulus $\mathrm{Y}=7.0 \times {10}^{10} \mathrm{N} {\mathrm{m}}^{-2}$ undergoes elastic strain of $0.04\%$. The energy per unit volume stored in the rod in $\mathrm{SI}$ unit

A force of $10 \mathrm{N}$ holds an ideal spring with a $20 \mathrm{N}/\mathrm{m}$ spring constant in compression. The potential energy stored in the spring is 

A wire loaded by a load $\mathrm{Mg}$ extends by $l$, mechanical energy stored in the wire is,

The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of $5\times {10}^{-4}$ is _____  $\mathrm{kJ} {\mathrm{m}}^{-3}$. Assume that material is elastic upto the linear strain of $5\times {10}^{-4}$.

Write down the expression for the elastic potential energy of a stretched wire.

Define energy density.

A uniform metal rope of length $L$ and area of cross-section $A$ is suspended from ceiling vertically. $d$ is density and $Y$ is Young's modulus of material of the wire respectively. Due to its own weight rope sags such the strain energy stored is $\frac{7d^2{g}^{2}A{L}^3}{nY}$. Find value of $n$.

If the work done in stretching a wire by $1 \mathrm{mm}$ is $2 \mathrm{J}$. Find the work (in $\mathrm{J}$) required for stretching another wire of same material but with double radius of cross-section and half the length by $1 \mathrm{mm}$.

A wire of length $\text{'}L\text{'}$ suspended vertically from a rigid support is made to suffer extension $\text{'}l\text{'}$ in its length by applying a force $\text{'}F\text{'}.$ Then the work done is $\underline{ }$

When a $8 \mathrm{m}$ long wire is stretched by a load of $10 \mathrm{kg}.\mathrm{wt},$ it is elongated by $1.5 \mathrm{mm}.$ The energy stored in the wire in this process is _____$\left(\mathrm{g}=10 \mathrm{m}·{\mathrm{s}}^{-2}\right)$

A rod elongates by $l$ when a body of mass $\mathrm{M}$ is suspended from it. The work done is

A work of$2\times {10}^{-2} \mathrm{J}$ is done on a wire of length $50 \mathrm{cm}$ and area of cross-section $0.5 {\mathrm{mm}}^2$. If the Young's modulus of the material of the wire is $2\times {10}^{10} \mathrm{N} {\mathrm{m}}^{-2}$, then the wire must be

When an elastic material with Young's modulus $E$ is subjected to a stretching stress $S,$ the elastic energy stored per unit volume of the material is

Show that strain energy per unit volume of a strained wire is $\frac{1}{2}\times stress\times strain$.

Write an expression for strain energy in a strained wire.

The ratio of elastic potential energy per unit volume for two wires made out of same material and having same length but diameter in the ratio $1:2$, when stretched by the same load is:

Lengths $L, 2L \mathrm{and} 3L$ and radii $R, 2R \mathrm{and} 3R$ of three wires of the same material (Young's modulus $Y$), respectively which are joined end to end with weight $\mathrm{w}$ is suspended as shown below. Find the elastic potential energy of the system neglecting the self-weight.

A catapult is made of rubber cord which is 42 cm long, with 6 m m diameter of cross-section and of negligble mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of $20{\mathrm{ms}}^{-1}$. Neglect the change in the area of crose-section of the cord while stretched. The Young's modulus of rubber is approx: