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?

Answer 1

Step 1: Given data

1. The mass of the bucket is $m_b=50kg.$
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,

$$\begin{gathered} m_a=100\times 1kg=100kg \\ or{m}_a=100kg \end{gathered}$$

The total mass of the bucket-rope system is,

$$\begin{gathered} M=m_a+m_b=\left(50+100\right)kg \\ orM=150kg. \end{gathered}$$

Now, the work done by the system is,

$$\begin{gathered} W=F.S=Mg.S \\ orW=\left(150\times 9.8\right)\times 100 \\ orW=147000joule. \end{gathered}$$

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