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Grade: 11

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

Answers : (2)

vikas askiitian expert
509 Points

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
vikas askiitian expert
509 Points

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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