i need some calculus help…this one is tough and i cant figure it out
C)A chain lying on the ground is 10 m long and its mass is 80 kg. How much work (in J) is required to raise one end of the chain to a height of 6 m?
3 Answers

mass density per unit length
ρ = m/x
ρ = 80/10
ρ = 8 kg/m
dW = F dx
dW = ρ g x dx
W = ρ g ∫ x dx
W = ½ ρ g x² + C
W(0) = 0
0 = ½ ρ g (0)² + C
C = 0
W(x) = ½ ρ g x²
W(6) = ½ (8) (9.8) (6)²
W(6) = 1411.2 J

No calculus required:
The weight of the raised portion is (80/10)*6*g = 48*9.8 = 470.4 N
The C/M of the raised portion is moved upward 3 m.
W = F*y = 470.4*3 = 1411.2 J
Source(s): KISS principle 
I’ll make this quick. the mass is equally devided by the length, that means 1m of chain weights 8kg. now by pulling one end up by 6m, the best way of doing this is to lift 6m of chain vertically above the ground. now by having half of that lifted chain equally devided between 36m heights and the other half equally devided between 30m which means the 6m of chain is lifted at an AVERAGE height of 3m (one end at 6m other end at 0m) now 6m of chain weight 48kg. 48kg*3m*9.8m/s²= 1411,2J