Calculus question:
Let x=length remaining below winch.
and
ρ=mass density
Work done winding up a length of dx
is equivalent to bringing the length dx up by a distance of x, i.e.
dW=ρg xdx
Integrate
W=ρg∫xdx from 0 to L
=ρg L²/2
Physics question:
Centroid of chain, X = -L/2
mass of chain, M = ρL
Total work done
=MgX
=ρgL(0-L/2)
=ρgL²/2
a 50 m long chain hangs vertically from a cylinder attached to a winch. assume there is no friction in the system and that the chain has a density of 5 kg/m. how much work is required to wind the entire chain onto the cylinder using the winch
1 answer