Physics Homework Help With System Of Variable Mass

System Of Variable Mass

Till now, we have considered a system where the mass is constant. Now consider the system where the mass is varying.

For example (i) A chain is moving in vertical direction, and it comes to rest after striking the floor. (ii) A fluid stream moving in horizontal direction and it comes to rest after striking the vertical wall.

Consider a fluid stream moving horizontally with uniform velocity (v).

The momentum associated with an element of length (Dx) located close to wall is


As it comes to rest after striking the wall, its final momentum

\ Change in momentum towards left.

Now



F =
(
Mass per unit length, Þ )

=

Þ

If r ® density of fluid, A ® Area of cross section;

Then F =

F =

Note: If the fluid stream rebound back with a velocity v’ then force

F = r Av (v + v’)

Till now, we have considered a system where the mass is constant. Now consider the system where the mass is varying.

For example (i) A chain is moving in vertical direction, and it comes to rest after striking the floor. (ii) A fluid stream moving in horizontal direction and it comes to rest after striking the vertical wall.

Consider a fluid stream moving horizontally with uniform velocity (v).

The momentum associated with an element of length (Dx) located close to wall is

As it comes to rest after striking the wall, its final momentum

\ Change in momentum towards left.

Now



F = ( Mass per unit length, Þ )

=

Þ

If r ® density of fluid, A ® Area of cross section;

Then F =

F =

Note: If the fluid stream rebound back with a velocity v’ then force

F = r Av (v + v’)

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