The energy stored in a wound watch spring is:

$A$ particle of mass $1 \ kg$ is free to move along the $x$-axis. Its potential energy is given by $U(x) = (\frac{x^2}{2} - x) \ J$. If the total mechanical energy of the particle is $2 \ J$,find the maximum speed of the particle.

While a person climbs stairs,the gravitational potential energy of the person increases. The source of this energy is

$A$ rod of mass $m$ and length $l$ is lying on a table. What is the work done to make it stand vertically?

If an object of mass $20 \ g$ falls from a height of $200 \ m$,and at the point where the object touches the Earth's surface,its total potential energy is converted into kinetic energy,then what is the decrease in the potential energy of the object in $J$?

$A$ chain of mass $m$ and length $l$ is hanging freely from edge $A$ (as shown in diagram $I$). Calculate the work done to fold it as shown in diagram $(II)$.