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Question

A bucket of water of 50kg is raised from a depth of 100m to the ground by a rope. The mass of the rope is 1kg per meter what is the work done?


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Solution

Step 1: Given data

  1. The mass of the bucket is mb=50kg.
  2. The depth of the water source is d=100m.
  3. mass of the rope is 1kg/meter.

Step 2: Work done

  1. Work done is the total amount of kinetic energy to bring a body from one place to another. Work done is a scalar quantity.
  2. The work done is defined by the form, W=F.S, where, F and S are the applied force and S is the displacement of the body.
  3. Here, F=mg, the gravitational force.

Step 3: Finding the work done

Mass of the rope is,

ma=100×1kg=100kgorma=100kg

The total mass of the bucket-rope system is,

M=ma+mb=50+100kgorM=150kg.

Now, the work done by the system is,

W=F.S=Mg.SorW=150×9.8×100orW=147000joule.

Therefore, the work done by the bucket is 147KJ.


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