To simulate car accidents,auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass $1000 \; kg$ moving with a speed $18.0 \; km/h$ on a smooth road and colliding with a horizontally mounted spring of spring constant $6.25 \times 10^{3} \; N m^{-1}$. What is the maximum compression of the spring in $m$?

In the figure,the ball $A$ is released from rest when the spring is at its natural (unstretched) length. For the block $B$ of mass $M$ to leave contact with the ground at some stage,the minimum mass of $A$ must be

$A$ block $B$ is attached to two unstretched springs $S1$ and $S2$ with spring constants $k$ and $4k$,respectively (see figure $I$). The other ends are attached to identical supports $M1$ and $M2$ which are not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block $B$ is displaced towards wall $1$ by a small distance $x$ (figure $II$) and released. The block returns and moves a maximum distance $y$ towards wall $2$. Displacements $x$ and $y$ are measured with respect to the equilibrium position of the block $B$. The ratio $\frac{y}{x}$ is:

What is the work done by a spring force in a cyclic process?

The work done in stretching a spring of force constant $5 \times 10^3 \ N/m$ from $5 \ cm$ to $10 \ cm$ is ...... $N-m$.

$A$ block of mass $m=25 \ kg$ sliding on a smooth horizontal surface with a velocity $v=3 \ ms^{-1}$ meets a spring of spring constant $k=100 \ N/m$ fixed at one end as shown in the figure. The maximum compression of the spring and the velocity of the block as it returns to the original position are, respectively: