Two block of masses $m_1$ and $m_2$ connected with the help of a spring of spring constant $k$ initially to natural length as shown. A sharp impulse is given to mass $m_2$ so that it acquires a velocity $v_0$ towards right. If the system is kept an smooth floor then find the maximum elongation that the spring will suffer
${v_0}\sqrt {\frac{{{m_1}{m_2}}}{{k({m_1} + {m_2})}}} $
${v_0}\sqrt {\frac{{({m_1} + {m_2})}}{{k{m_1}{m_2}}}} $
${v_0}\sqrt {\frac{{2{m_1}{m_2}}}{{k({m_1} + {m_2})}}} $
$2{v_0}\sqrt {\frac{{{m_1}{m_2}}}{{k({m_1} + {m_2})}}} $
spring block system is placed on a rough horizontal floor. The block is pulled towards right to give spring some elongation and released. the block will have maximum velocity when
$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ till 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 $B$, when the block is compressing the spring
An engine is attached to a wagon through a shock absorber of length $1.5\,m$. The system with a total mass of $50,000 \,kg$ is moving with a speed of $36\, km\,h^{-1}$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by $1.0\,m$.
If $90\%$ of energy of the wagon is lost due to friction, calculate the spring constant.
A ball of mass $100 \,g$ is dropped from a height $h =$ $10\, cm$ on a platform fixed at the top of vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $\frac{ h }{2}$. The spring constant is.......... $Nm^{-1}$ . (Use $g=10\, ms ^{-2}$ )
The potential energy of a long spring when stretched by $2\,cm$ is $U$. If the spring is stretched by $8\,cm$, potential energy stored in it will be $.......\,U$