 # 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 agent3     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

11 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

11 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