Question

a bucket filled with water weighing 20 kg is raised from a well of depth 20m if the linear density of rope is 0.2kg per metre,the amount of work done is

Answer 1

Mass of Bucket = 20kg
density of rope = 0.2kg/m
Depth of Well = 20m
Length of Rope Inside the well at start = 20m

So Inital Mass of Rope = length x linear density
= 20 x 0.2
= 4kg

Now in Case of Bucket:

as the mass of bucket is same than Force exerted by bucket
= 20 x 10 = 200N

Work = F.S = 200 x 20 = 400N

Now for the Force in rope:

The mass is not same in rope so, 
Mass of rope at 20 m depth
= 0.2 x 20 = 4 kg

Mass of rope at 19 m depth 
= 0.2 x 19 = 3.8 kg
So mass Changes with every meter length

now the Work done per meter for 20 m
W = W1 + W2 + W3.......+W20 
W = m1gs + m2gs + m3gs........+m20gs
W = gs(m1 + m2 +m3.....+m20)
W = 10(1)(4 + 3.8 + 3.6 + .....+ 0.2 + 0)
W = 10(4 +3.8 +....+0.2)

Sn = n/2(a + an)
S₂₀ = 20/2(4 + 0.2)
= 42

W= 10(42)
W = 420Nm

total work done by the rope;
W = 4000 + 420 = 4420 Nm

Answer 2

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