Question

A bucket filled with water weighing 20kg is raised from a depth 20m. If the linear density of the rope is 0.2kg per meter, the amount of work done is

Answer 1

The amount of work done will be zero bcause uplifting any object is not a work done displacing it is work done.

Answer 2

Given: Mass of Bucket = 20kg
Linear density of rope = 0.2kg/m
Depth of Well = 20m
Length of Rope Inside the well initially. = 20m
So Inital Mass of Rope = lenght x linear density = 20 x 0.2 = 4kg
Let us take 2 Sytems i.e., bucket and rope separately.
Case i (for Bucket)
Mass of bucket is constant everywhere
Force exerted by bucket = 20 x 10 = 200N
Work Done = F.S = 200 x 20 = 400N
System II : Force Rope
There is a variable mass for rope
Mass of rope at 20 mt depth = 0.2 x 20 = 4 kg
Mass of rope at 19 mt dept = 0.2 x 19 = 3.8 kg
So mass Changes per meter
Let Us Add All the Workdone per meter for 20 mts
W = W1 + W2 + W3..........................W20 (∵Work at 20mt above initial for rope is 0)
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)
We know The Sn = n/2(a + an)
S₂₀ = 20/2(4 + 0.2) ⇒ 42
W= 10(42)
W = 420Nm
By Adding work done of Rope and Bucket We get total Work Done byt the 2 system
i.e W = 4000 + 420 = 4420Nm
∴Total Work Done = 4420Nm