Physics Homework Help With System Of Variable Mass

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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 system of variable mass image

system of variable mass image1

As it comes to rest after striking the wall, its final momentum system of variable mass image2

\ Change in momentum system of variable mass image3 towards left.

Nowsystem-of-variable-mass-image4system of variable mass image5

system of variable mass image6
system-of-variable-mass-image7
F= system of variable mass image8
( system of variable mass image9
Mass per unit length, system of variable mass image10Þ system of variable mass image11 )

= system of variable mass image12

system of variable mass image13 Þ system of variable mass image14

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

Then F = system of variable mass image15

F = system of variable mass image16

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 system of variable mass image17
system of variable mass image18

As it comes to rest after striking the wall, its final momentum system of variable mass image19

\ Change in momentum system of variable mass image20 towards left.

Now system of variable mass image22

system of variable mass image22
system of variable mass image23

F= system of variable mass image24 ( system of variable mass image25 Mass per unit length, system of variable mass image26 Þ system of variable mass image27 )

= system of variable mass image28

system of variable mass image26 Þ system of variable mass image27

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

Then F = system of variable mass image29

F = system of variable mass image30

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

F = r Av (v + v’)

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