Please I want some to do answer it clearly and step by step A basket of ripe tom

Question

Please I want some to do answer it clearly and step by step

A basket of ripe tomatoes of mass 20 kg is being hoisted using a pulley. The rope (of negligible mass) is wound around the pulley which consists of a solid cylinder having a radius of 0.1 m and a mass of 10 kg. The mass of the crank handle is negligible. The operator accidentally lets go of the handle when the basket is 6 m above the ground, and the rope unwinds. Use conservation of energy to find the linear speed of the basket when it strikes the ground? (You may assume the basket starts to fall from rest.)

Explanation / Answer

mass of tomato basket = m = 20kg

radius of cylinder in the pulley = r

mass of cylinder in the pulley = M = 10kg

initial height of the basket from the ground h = 6m

Intital energy of the pulley+basket system = potential energy, PE = mgh

Finally when the basket touches the ground, the potential energy becomes zero but the pulley and basket acquire kinetic energy,KE.

Let us suppose the angular velocity of the cylinder in the pulley be and let the linear velocity of the basket be v when the basket strikes the ground.

then = vr

Now KE of the basket = (1/2)mv2  when the basket strikes the ground.

Similarly KE of the pulley when the basket strikes the ground = (1/2)I2 = (1/2)I(v/r)2

where I = moment of Inertia of the cylinder about its axis = (Mr2)/2

So net KE when the basket strikes the ground = (1/2)I(v/r)2 + (1/2)mv2 = (1/2)[(Mr2)/2](v/r)2 + (1/2)mv2

or, net KE = (1/4)Mv2 +(1/2)mv2

Now applying conservaion of enery, we get:

mgh = (1/4)Mv2 +(1/2)mv2 = (M/4 + m/2)v2

or, (20kg)(10m/s2)(6m) = (10kg/4 + 20kg/2)v2 (taking g =10m/s2 )

or, 1200J = 12.5v2

or, v = 9.79m/s

This concludes the answer. If you need any more clarification you are welcome!!!

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