$A$ block of mass $m$ moving with speed $v$ compresses a spring through distance $x$ before its speed is halved. What is the value of the spring constant $k$?

When a long spring of $4 \ cm$ is stretched by $1 \ cm$,the potential energy stored in the spring is $U$. If it is stretched by $4 \ cm$,the potential energy stored in it is (in $U$)

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.

Two springs have their force constants as $k_1$ and $k_2$ $(k_1 > k_2)$. When they are stretched by the same force $F$,which of the following statements is true regarding the work done?

$A$ mass of $1 \ kg$ falls from a height of $1 \ m$ and lands on a massless platform supported by a spring having spring constant $15 \ N \ m^{-1}$ as shown in the figure. The maximum compression of the spring is. (acceleration due to gravity $= 10 \ m \ s^{-2}$)

When a spring is stretched by $2 \, cm$,it stores $100 \, J$ of energy. If it is stretched further by $2 \, cm$,the stored energy will be increased by ............. $J$.