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A CHAIN OF MAAS M AND LENGHT L is heaped on a smooth ground 1 find the vertical force required to pull the chain with constant accn A and velocity v as the function of the lenght x pulled up.. 2 find the w.d by the driving force and power delivered by external agent 3 what is the normal reaction offered by the grount also n.r as a function of distance raised 4 find accn of C.M. plz give easy expressions with full explanation calculus is weak xi standard i" approve

```
9 years ago

```							let mass per unit length is k ... k = M/L

now , after some time let x part of chain is above the ground
mass of part above ground = kx

let constant force applied by external source = F then
F - (kx)g = (kx)a            (a is accleration)
F = (kx)g + kx(a)       ....................1

from above eq , a = [F - (kx)g]/kx
a = [F/kx - g]         ................2
now ,  a = dv/dt
multiply both sides by dx
a(dx)= dv(dx/dt)                   {dx/dt = v }
adx = vdv = v2/2           ............3

from eq 2 & 3
[F/kx - g ]dx = v2/2
integrating both sides
[Flnx/k - gx] = v2
v = { [Flnx/k - gx ]}1/2               ...................4
```
9 years ago
```							workdone = F.dx

F =(kxg + kxa)

k = M/L          (mass per unit length)

W= k(g+a)xdx
W = k(g+a)x2/2                  (work performed by external agent)

when x part  is above the ground then L-x part is on ground ,

mass of this (L-x) part = k(L-x)

normal reaction will be only due to this part

N = k(L-x)g

```
9 years ago
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