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
$\frac{1}{2} Ky ^2$
$\frac{1}{2}Ky(2x+y)$
$\frac{1}{2}K(x^2+y^2)$
$\frac{1}{2} k(x+y)^2$
A spring of force constant $k$ is cut into three equal pieces. If these three pieces are connected in parallel the force constant of the combination will be
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 ............. $\mathrm{J}$
The $P.E.$ of a certain spring when stretched from natural length through a distance $0.3\, m$ is $10\, J$. The amount of work in joule that must be done on this spring to stretch it through an additional distance $0.15\, m$ will be ................ $\mathrm{J}$
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 diagram shown, no friction at any contact surface. Initially, the spring has no deformation. What will be the maximum deformation in the spring? Consider all the strings to be sufficiency large. Consider the spring constant to be $K$.