A weight of mass 3.7 kg is attached to a rope that is wrapped around a freely ro

Question

A weight of mass 3.7 kg is attached to a rope that is wrapped around a freely rotating drum of radius 0.3 m. The drum has a mass moment of inertia of 0.22 kg.m2. (g = 9.81m.s-2) Answer all questions to at least 3 sf. If necessary, you may enter answers in standard form (e.g. answer = 7.12e7, for an answer of 71.2 million). Enter your answers in SI units but do not enter the units. How many radians will the drum have travelled through when the weight drops to 10m? [rad] How fast will the weight be dropping when it has fallen 1.1m from rest? [m.s-1] How fast will the weight be dropping when it has fallen through 1.1m from rest if 7 Joules of energy is extrated from the system? [m.s-1]

Explanation / Answer

Energy extracted = 7 Joules mgh = 7 + 1/2 mv^2 + 1/2 I w^2 3.7 * 9.81*1.1 = 7 + 0.5*3.7 *v^2 + 0.5 * 0.22 * v^2/0.3^2 32.92 = (1.85+1.22)v^2 v = 3.275 m/s

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