A block B is attached to two unstretched spri | vedclass

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Question

(C) When the block $B$ is displaced by a distance $x$ towards wall $1$,spring $S1$ is compressed by $x$,while spring $S2$ remains unstretched because

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(C) When the block $B$ is displaced by a distance $x$ towards wall $1$,spring $S1$ is compressed by $x$,while spring $S2$ remains unstretched because support $M2$ is not fixed to the wall and moves with the block. The potential energy stored in the system is $U_i = \frac{1}{2} k x^2$.When the block is released,it moves towards the equilibrium position and then towards wall $2$. When it moves towards wall $2$ by a distance $y$,spring $S2$ is compressed by $y$,while spring $S1$ remains unstretched. The potential energy stored in the system is $U_f = \frac{1}{2} (4k) y^2$.Since there is no friction and the supports have negligible mass,the total mechanical energy is conserved.Equating the initial and final potential energies: $\frac{1}{2} k x^2 = \frac{1}{2} (4k) y^2$.Simplifying this,we get $x^2 = 4y^2$,which implies $y^2 = \frac{x^2}{4}$.Taking the square root,we find $y = \frac{x}{2}$.Therefore,the ratio $\frac{y}{x} = \frac{1}{2}$.

Similar Questions

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:

$A$ $1\, kg$ block moves towards a light spring with a velocity of $8\, m/s$. When the spring is compressed by $3\, m$,its momentum becomes half of the original momentum. The spring constant of the spring is:

$A$ body of mass $0.1 \ kg$ moving with a velocity of $10 \ m/s$ hits a spring (fixed at the other end) of force constant $1000 \ N/m$ and comes to rest after compressing the spring. The compression of the spring is .............. $m$.

$A$ spring $40 \, mm$ long is stretched by the application of a force. If $10 \, N$ force is required to stretch the spring by $1 \, mm$,then the work done in stretching the spring by $40 \, mm$ is ............. $J$.

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