A spring with spring constant k is extended from x = 0 to x = {x₁} . work done will be

English

Gujarati

Hindi

5.Work, Energy, Power and Collision

easy

A spring with spring constant $k $ is extended from $x = 0$to$x = {x_1}$. The work done will be

A

$kx_1^2$

B

$\frac{1}{2}kx_1^2$

C

$2kx_1^2$

D

$2k{x_1}$

Solution

(b) $F=-k x$

$d w=F \cdot d x$

$\int d x=\int_{0}^{x_1}-k x d x$

$w=-k \int_{0}^{x_1}xdx$

$=-k\left[\frac{x^{2}}{2}\right]_{0}^{x_{1}}$

$=-K\left[\frac{x_{1}^{2}}{2}\right]$

$w=-\frac{-k x_{1}^{2}}{2}$

$w=\frac{-1}{2} k x_{1}^{2}$

work done $=-(w)$

$=-\left[\frac{-1}{2} k x_{1}^{2}\right]$

$=\frac{1}{2} k x_{1}^{2}$

Standard 11

Physics

Share

Similar Questions

Two blocks of mass $2\ kg$ and $1\ kg$ are connected by an ideal spring on a rough surface. The spring in unstreched. Spring constant is $8\ N/m$ . Coefficient of friction is $μ = 0.8$ . Now block $2\ kg$ is imparted a velocity $u$ towards $1\ kg$ block. Find the maximum value of velocity $'u'$ of block $2\ kg$ such that block of $1\ kg$ mass never move is

hard

Initially spring is in natural length and both blocks are in rest condition. Then determine Maximum extension is spring. $k=20 N / M$

hard

(AIIMS-2019)

A block of mass $\sqrt{2}\,kg$ is released from the top of an inclined smooth surface as shown in figure. If spring constant of spring is $100\,N / m$ and block comes to rest after compressing the spring by $1 \,m$, then the distance travelled by block before it comes to rest is ……… $m$

medium

The energy stored in wound watch spring is

easy

This question has Statement $-1$ and Statement $-2$. Of the four choices given after the statements, choose the one that best describes the two statements.

If two springs $S_1$ and $S_2$ of force constants $k_1$ and $k_2$, respectively, are stretched by the same force, it is found that more work is done on spring $S_1$ than on spring $S_2$.

Statement $-1$: If stretched by the same amount, work done on $S_1$, will be more than that on $S_2$

Statement $-2$ : $k_1 < k_2$.

medium