$A$ 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 ............. $J$.

$A$ spring of original length $L$ and spring constant $K$ is stretched by a small length $x$. It is further stretched by another small length $y$. Find the work done in the second stretching.

An elastic string of unstretched length $L$ and force constant $k$ is stretched by a small length $x$. It is further stretched by another small length $y$. The work done in the second stretching is

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 the energy of the wagon is lost due to friction,calculate the spring constant.

$A$ block of mass $m$ initially at rest is dropped from a height $h$ onto a spring of force constant $k$. If the maximum compression in the spring is $x$,then:

Statement-$1$ and Statement-$2$ are given. Two springs $S_1$ and $S_2$ have force constants $k_1$ and $k_2$ respectively,where $k_1 < k_2$. They are stretched by the same force $F$. It is found that the work done on spring $S_1$ is greater than the work done on spring $S_2$.
Statement-$1$: If stretched by the same force,the work done on $S_1$ is greater than the work done on $S_2$.
Statement-$2$: $k_1 < k_2$.