Question

A woman does 760J of work in lifting a 30kg bucket of water from a well. Calculate the depth up to which the bucket is raised by her in the well.{Take g=10m/s2 }

Answer 1

Answer:

Work done by the person is the change in potential energy of the bucket and the rope.

Given, the rope has a uniform mass m. So the center of mass for the rope is at half of the length of the rope.

So, it will be at a distance h/2 from the bottom.

Work done = Change in PE of bucket+Change in PE of rope

W=Mgh+mg

2

h

=(M+

2

m

)gh

Answer 2

Work done by the person is the change in potential energy of the bucket and the rope.

Given, the rope has a uniform mass m. So the center of mass for the rope is at half of the length of the rope.

So, it will be at a distance h/2 from the bottom.

Work done = Change in PE of bucket+Change in PE of rope

$\tt \ \: {w = mgh + \: mg \times \frac{h}{2} } \\ \\ \tt \ \: \implies { (m + \frac{m}{2})}gh$

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