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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

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

Grade:11

2 Answers

vikas askiitian expert
509 Points
10 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

vikas askiitian expert
509 Points
10 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

 

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