Use energy considerations to determine the drum\'s rotation rate when the anchor

Question

Use energy considerations to determine the drum's rotation rate when the anchor hits the water. Neglect the mass of the cable.

A ship^'s anchor weighs 5000 mto the water. Use energy considerations to determine the drum's rotation rate when the anchor hits the water. Neglect the mass of the cable. m. The drum is mounted on a frictionless axle. The anchor is released and drops 16kgand radius 1.1N. Its cable passes over a roller of negligible mass and is wound around a hollow cylindrical drum of mass 380

Explanation / Answer

using conservation of energy

(1/2) m V^2 + (1/2) I w^2 = m g h

m is the mass of anchor, h is the height of fall. here I = MR^2 , V = R w so

(1/2) m R^2 w^2+ (1/2) M R^2 w^2 = m g h

w = sqrt [ 2m g h / (m+M) R^2]

= 12.19 rad /s

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