Answer:
Total Work Done = 39600 N
Step-by-step explanation:
This problem involves a tool box and a rope used to pull the tool box.
So the work done will be calculated in two parts:
1) Work done on Tool Box
2) Work done on Rope
1)Work done on Tool Box:
mass of tool box = m= 200 kg
Force = F = mass x gravity = mg = 200 x 9.8
F= 1960 N
distance = d = 20m
Now,We will use formula of work done:
Work done = Force x Distance = F x d
Work Done = W = 1960 x 20
Work done on Box= 39200 N ----------------------- Eq. 1
2) Work done on rope:
Here we will consider that the rope has infinitesimally small parts namely Δx and after pulling the rope at a certain random length , we call it [tex]x_{i}[/tex]
We can represent it using the work done formula in limits :
Work Done = [tex]\lim_{n \to \infty}[/tex] ∑ ρ Δx [tex]x_{i}[/tex]
(Note : For ∑, its is from 1 to Infinity)
(Note : ρ is the density of rope)
ρ = density of rope = 2 kg/m
We can further write it in integral form as :
Work done on rope = W = [tex]\int\limits^d_0 {2 x} \, dx[/tex]
After integration :
W= [tex]\frac{2}{2}[/tex][tex]x^{2}[/tex] [tex]\left \| {{20} \atop {0}} \right.[/tex]
W = [tex]20^{2} - 0[/tex]
W= 400N ----------------------------------------(Eq .2)
Which is the work done on rope
Total Work done = Work done on rope + Work done on tool box
Total Work Done = 400 + 39200
Total Work Done = 39600 N
