During a TV report about ground water contamination, a reporter stands next to a

Question

During a TV report about ground water contamination, a reporter stands next to an old style well which works by lowering a bucket at the end of a rope into a deep hole inthe ground to get water. At the top of the well, a single vertical pulley, which is essentially a heavy stell ring supported by light spokes, is mounted to help raise and lower the bucket. To demonstate the depth of the well, the reporter completely wraps the thin rope around the pulley, then releases the bucket, which starts at rest near the pulley then falls to the bottom of the well, unwinding the rope from the pulley as it falls. The fall takes t=3.5 s . Although the depth of the well is never mentioned, you decide to calculate it. You estimate that the pulley has the same mass of the bucket and is well-oiled, since you didn't hear any squeaking.

Explanation / Answer

Lets assume mass of pully and bucket be M each and radius of pully be R

Moment of inertia = 0.5MR^2

Tenson in rope T = Mg - Ma.....equation 1

because it is circular motion of pully

a = alpha R = TR*R/(0.5MR^2) = 2T/M

T= Ma/2

putting T in equation 1

Ma/2 = Mg - Ma

3a/2 = g

a = 2g/3 = 9.8*0.667 = 6.533 m/s

h = 0.5at^2

= 0.5*6.533*3.5*3.5

= 40 m Answer

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