A uniform chain of length l begins to fall with a velocity v on the table. Find the thrust force exerted by the chain on the table.

Explanation

Let us assume that the mass of the chain is m and length l.
We assume that after time t, x length of the chain has fallen on the table. Then the speed of the upper part of the chain is `sqrt(2gx)` as shown in figure.

Now its time t + dt, length of chain has fallen on the table is v dt. Then the mass of chain has fallen on the table is
`dm=m/l.vdt`
Now the rate of increase of mass
`(dm)/(dt)=m/(l)v=m/lsqrt(2gx)`
Here v is downward and mass is increasing so thrust force act in down ward direction and is given by
`f_(t)=v_(r)(dm)/(dt)`

`=sqrt(2gx)m/l(sqrt(2gx))`
`f_(t)=lv^(2)`