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 $$P=\overline{F} \cdot \overline{v} = \overline{v} \cdot (\overline{v} \dfrac{dm}{dt}) = v^2 \dfrac{dm}{dt}$$.