### Work, Energy and Power

goals
A boy takes $3$ minutes to lift  $20$ litres of water from a $20 m$ deep well, while his father does the same in $2$ minutes
Conservative forces are those forces for which
A body of mass $m$ starts moving with velocity ${ V }_{ 0 }$ at point $A$ on a frictionless path as shown in the figure.
A system consists of two identical cubes, each of mass $m$, linked together by the compressed weightless spring of stiffness $\kappa$ (figure shown above). The cubes are also connected by a thread which is burned through at a certain moment.
Sand drop from a stationary hopper at a rate $\dfrac{dm}{dt}$ on to a conveyer belt moving with a velocity $v$ in the reference frame of the laboratiry. Since $\dfrac{dv}{dt} = 0$, Therefore, it is an example of variable mass. To an observer at rest on the belt the falling sand would appear to have a horizontal motion with speed $v$ in a direction opposite to that shown for the belt in the laboratory. Therefore $v_{rel} = -v.$ In this example $\dfrac{dm}{dt}$ is positive as the system is gaining mass. Note that in the absence of friction mass of the belt does not enter the problem. power supplied by the external force is $P=\overline{F} \cdot \overline{v} = \overline{v} \cdot (\overline{v} \dfrac{dm}{dt}) = v^2 \dfrac{dm}{dt}$.