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 dataThe mass of the bucket is ${m}_{b}=50kg.$The depth of the water source is $d=100m$.mass of the rope is $1kg/meter.$Step 2: Work doneWork done is the total amount of kinetic energy to bring a body from one place to another. Work done is a scalar quantity.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.Here, $F=mg$, the gravitational force.Step 3: Finding the work doneMass of the rope is, ${m}_{a}=100×1kg=100kg\phantom{\rule{0ex}{0ex}}or{m}_{a}=100kg$The total mass of the bucket-rope system is,$M={m}_{a}+{m}_{b}=\left(50+100\right)kg\phantom{\rule{0ex}{0ex}}orM=150kg.$Now, the work done by the system is,$W=F.S=Mg.S\phantom{\rule{0ex}{0ex}}orW=\left(150×9.8\right)×100\phantom{\rule{0ex}{0ex}}orW=147000joule.$Therefore, the work done by the bucket is $147KJ$.

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