(B) According to the work-energy theorem,the work done by all forces acting on a body is equal to the change in its kinetic energy.For observer $A$ (g

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(B) According to the work-energy theorem,the work done by all forces acting on a body is equal to the change in its kinetic energy.For observer $A$ (ground frame),the initial kinetic energy of the block is $K_i = \frac{1}{2}mv_0^2$ and the final kinetic energy is $K_f = 0$ (since the block comes to rest).The only force doing work on the block in the horizontal direction is the spring force $(F_s)$.Therefore,$W_{spring} = K_f - K_i = 0 - \frac{1}{2}mv_0^2 = -\frac{1}{2}mv_0^2$.Thus,the work done by the spring force as observed by $A$ is $-\frac{1}{2}mv_0^2$.

Class 11 Physics Work, Energy, Power and Collision Work Done by Spring and Potential Energy of Spring

Medium

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ until the mass comes to rest,as shown in the figure. This phenomenon is observed by two observers:
$A$: standing on the horizontal surface
$B$: standing on the block
To an observer $A$,the work done by the spring force is

A
negative but nothing can be said about its magnitude
B
$ - \frac{1}{2}mv_0^2$
C
positive but nothing can be said about its magnitude
D
$ + \frac{1}{2}mv_0^2$

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Class 11 Questions

Class 11

Physics Questions

Chapter

Work, Energy, Power and Collision

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Work Done by Spring and Potential Energy of Spring

If the potential energy of a spring is $V$ on stretching it by $2 \, cm$,then its potential energy when it is stretched by $10 \, cm$ will be

Medium

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$A$ block of mass $m$ moving at a speed $v$ compresses a spring through a distance $x$ before its speed becomes one fourth. Find the spring constant of the spring.

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$A$ light spring of length $10 \ cm$ is stretched by $2 \ cm$ when a mass of $20 \ g$ is attached to its end. The mass is pulled until the total length of the spring becomes $14 \ cm$. What is the elastic potential energy stored in the spring (in Joules)?

Medium

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Two similar springs $P$ and $Q$ have spring constants $K_P$ and $K_Q$,such that $K_P > K_Q$. They are stretched first by the same amount (case $a$),then by the same force (case $b$). The work done by the springs $W_P$ and $W_Q$ are related as,in case $(a)$ and case $(b)$ respectively:

MediumAIPMT 2015

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When a spring is stretched by a distance $x$,its potential energy is $10 \ J$. The work done to stretch this spring by an additional distance $x$ is ........ $J$.

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If the potential energy of a spring is $V$ on stretching it by $2 \, cm$,then its potential energy when it is stretched by $10 \, cm$ will be

$A$ block of mass $m$ moving at a speed $v$ compresses a spring through a distance $x$ before its speed becomes one fourth. Find the spring constant of the spring.

$A$ light spring of length $10 \ cm$ is stretched by $2 \ cm$ when a mass of $20 \ g$ is attached to its end. The mass is pulled until the total length of the spring becomes $14 \ cm$. What is the elastic potential energy stored in the spring (in Joules)?

Two similar springs $P$ and $Q$ have spring constants $K_P$ and $K_Q$,such that $K_P > K_Q$. They are stretched first by the same amount (case $a$),then by the same force (case $b$). The work done by the springs $W_P$ and $W_Q$ are related as,in case $(a)$ and case $(b)$ respectively:

When a spring is stretched by a distance $x$,its potential energy is $10 \ J$. The work done to stretch this spring by an additional distance $x$ is ........ $J$.

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