A block of mass $m = 0.1\,kg$ is connected to a spring of unknown spring constant $k.$ It is compressed to a distance $x$ from its equilibrium. position and released from rest . After approaching half the distance $(\frac {x}{2})$ from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity $3\,ms^{-1}.$ The total initial energy of the spring is ................ $\mathrm{J}$
$0.3$
$0.6$
$0.8$
$1.5$
$A$ ball of mass $m = 60gm$ is shot with speed $v_0 = 22m/s$ into the barrel of spring gun of mass $M = 240g$ initially at rest on $a$ frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. What fraction of initial kinetic energy of the ball is now stored in the spring?
A bullet of mass $m$ strikes a block of mass $M$ connected to a light spring of stiffness $k,$ with a speed $v_0.$ If the bullet gets embedded in the block then, the maximum compression in the spring is
Two blocks $A(5kg)$ and $B(2kg)$ attached to the ends of a spring constant $1120N/m$ are placed on a smooth horizontal plane with the spring undeformed. Simultaneously velocities of $3m/s$ and $10m/s$ along the line of the spring in the same direction are imparted to $A$ and $B$ then
A spring of force constant $10\, N/m$ has an initial stretch $0.20\, m.$ In changing the stretch to $0.25\, m$, the increase in potential energy is about.....$joule$
Explain the elastic potential energy of spring and obtain an expression for this energy.