Finding Power Ratio of Two Pulley Systems

AI Thread Summary
The discussion focuses on calculating the power ratio of two pulley systems using the equation P1/P2 = τ1ω1/τ2ω2. The relationship T1/T2 is derived from part B as r1/r2, while the angular velocities ω1 and ω2 are related to the radii of the pulleys. It is noted that (ω1/ω2) should not be equated to vr1/vr2, as the velocities are not the same. The conclusion drawn is that the power ratio simplifies to (r1/r2)², leading to an answer of 1. The participants emphasize the importance of correctly applying the relationships between torque, angular velocity, and radius in pulley systems.
henry3369
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Homework Statement


Part C:
http://imgur.com/mFlXGZs

Homework Equations


Power = τω

The Attempt at a Solution


P1/P2 = τ1ω1/τ2ω2 = (T1/T2) * (ω1/ω2)
T1/T2 is found in part B: r1/r2
(ω1/ω2) = vr1/vr2 (velocities are the same) = (r1/r2)
(r1/r2)*(r1/r2) = (r1)^2/(r2)^2

The answer is 1.
 
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henry3369 said:
(ω1/ω2) = vr1/vr2 (velocities are the same) = (r1/r2)

Check this. See part (A). (ω1/ω2) ≠ vr1/vr2
 
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