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RAJ RANJAN SINGH 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

6 years ago

Answers : (2)

vikas askiitian expert
510 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

6 years ago
vikas askiitian expert
510 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


 

6 years ago
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