Question

A long spring is stretched by X cm its PE is U . if the spring is stretched by Nx cm the PE stored in it will be
plz ans me guys​

Answer 1

Answer:

Given :

Potential Energy of a spring is U , when it is stretched by X cm.

To find:

The potential energy when the spring is stretched by nX cm.

Concept:

Spring force is a conservation force . That's because the work done to stretch the ends of the string actually gets stored as the Potential energy within the string.

That energy never gets lost or dissipated , hence Spring force is a Conservative force.

Calculation:

In 1st case :

$\red{ \sf{ \huge{U = \dfrac{1}{2} k {X}^{2} }}}$

In the 2nd case : New length = nX

Let me potential energy be U2

$\blue{ \sf{ \huge{U2 = \dfrac{1}{2} k {(nX)}^{2} }}}$

$\blue{ \sf{ \huge{ = > U2 = {n}^{2} \bigg( \dfrac{1}{2} k {X}^{2} \bigg)}}}$

$\blue{ \sf{ \huge{ = > U2 = {n}^{2} U}}}$

So final answer :

$\red{\boxed{\boxed{ \bold{ \green{ \sf{ \huge{ U2 = {n}^{2} U}}}}}}}$

Answer 2

Solution :

➡ Given:

✏ A long spring is stretched by x cm

✏ Potential energy stored in spring = U

➡ To Find:

✏ PE stored in the spring by stretching it nx cm

➡ Formula:

✏ Formula of magnitude of Potential energy stored in the spring is given by

$\star \: \underline{ \boxed{ \bold{ \rm{ \pink{U = \frac{1}{2} k {x}^{2} }}}}} \: \star$

➡ Terms indication:

✏ U denotes potential energy which is stored in the string by external force.

✏ k denotes spring constant.

✏ x denotes change in length of spring by stretching.

➡ Calculation:

• First case:

$\implies \rm \: U= \frac{1}{2} k {x}^{2} .........(1)$

• Second case:

$\implies \rm \: U'= \frac{1}{2} k {(nx)}^{2} \\ \\ \implies\rm \: U' = {n }^{2} \times (\frac{1}{2} k {x}^{2} ) \: .........(2)$

✏ Putting value of second equation in first equation.

$\implies \rm \: \underline{ \boxed{ \bold{ \rm{ \orange{U' = {n}^{2}U}}}}} \: \star$

➡ Additional information:

✏ Spring force is Conservative type of force.

✏ Therefore, whatever work done on it will be stored in it as Potential energy.