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A mixing beater consists of three thin rods, each 10.9 cm long. The rods diverge from a central hub, separated from each other by 120, and all turn in the same plane. A ball is attached to the end of each rod. Each ball has cross-sectional area 3.80 cm² and is so shaped that it has a drag coefficient of 0.680. The drag force on each ball is R = 1/2 D? A ✓ where D is the drag coefficient, ? the density of the fluid, A the cross-sectional area, and the speed of the object moving through the fluid. (a) Calculate the power input required to spin the beater at 1000 rev/min in water. (b) The beater is taken out of the water and held in air. If the input power remains the same (it wouldn't, but if it did), what would be the new rotation speed?

A mixing beater consists of three thin rods, each 10.9 cm long. The rods diverge from a central hub, separated from each other by 120, and all turn in the same plane. A ball is attached to the end of each rod. Each ball has cross-sectional area 3.80 cm² and is so shaped that it has a drag coefficient of 0.680. The drag force on each ball is R = 1/2 D? A ✓ where D is the drag coefficient, ? the density of the fluid, A the cross-sectional area, and the speed of the object moving through the fluid. (a) Calculate the power input required to spin the beater at 1000 rev/min in water. (b) The beater is taken out of the water and held in air. If the input power remains the same (it wouldn't, but if it did), what would be the new rotation speed?

Glencoe Physics: Principles and Problems, Student Edition
Glencoe Physics: Principles and Problems, Student Edition
1st Edition
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Paul W. Zitzewitz
Chapter8: Rotational Motion
Section8.2: Rotational Dynamics
Problem 27PP
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A mixing beater consists of three thin rods, each 10.9 cm long. The rods diverge from a central hub, separated from each other by 120, and all turn in the same plane. A ball is attached to the end of each rod. Each ball has cross-sectional area 3.80 cm² and is so shaped that it has a drag coefficient of 0.680. The drag force on each ball is R = 1/2 D? A ✓ where D is the drag coefficient, ? the density of the fluid, A the cross-sectional area, and the speed of the object moving through the fluid. (a) Calculate the power input required to spin the beater at 1000 rev/min in water. (b) The beater is taken out of the water and held in air. If the input power remains the same (it wouldn't, but if it did), what would be the new rotation speed?
Transcribed Image Text:A mixing beater consists of three thin rods, each 10.9 cm long. The rods diverge from a central hub, separated from each other by 120, and all turn in the same plane. A ball is attached to the end of each rod. Each ball has cross-sectional area 3.80 cm² and is so shaped that it has a drag coefficient of 0.680. The drag force on each ball is R = 1/2 D? A ✓ where D is the drag coefficient, ? the density of the fluid, A the cross-sectional area, and the speed of the object moving through the fluid. (a) Calculate the power input required to spin the beater at 1000 rev/min in water. (b) The beater is taken out of the water and held in air. If the input power remains the same (it wouldn't, but if it did), what would be the new rotation speed?
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