Energy storage devices that use spinning flywheels to store en- ergy are becoming available. To maximize energy storage, the flywheel must spin as fast as possible. Unfortunately, if it spins too fast, internal stresses in the flywheel cause it to come apart catastrophically. Therefore, it is important to keep the speed at the periphery of the flywheel below about 1000 m/s. It is also critical that the flywheel be well balanced to avoid the damaging vibrations that would otherwise result. With this in mind, let the flywheel D with diameter 0.3 m rotate at o = 60,000 rpm. In ad- top view dition, assume that the cart B is constrained to move rectilinearly along the guide tracks. Given that the flywheel is not perfectly balanced, that the unbalanced weight A has mass ma, and that the total mass of the flywheel D, cart B, and electronics package E is mg, determine the constraint force between the wheels of guide tracks the cart and the guide tracks as a function of 0, the masses, the diameter, and the angular speed of the flywheel. What is the maximum constraint force between the wheels of the cart and the guide tracks? Finally, evaluate your answers for mA = 1g (about the mass of a paper clip) and mg = 70 kg. Assume that
Energy storage devices that use spinning flywheels to store en- ergy are becoming available. To maximize energy storage, the flywheel must spin as fast as possible. Unfortunately, if it spins too fast, internal stresses in the flywheel cause it to come apart catastrophically. Therefore, it is important to keep the speed at the periphery of the flywheel below about 1000 m/s. It is also critical that the flywheel be well balanced to avoid the damaging vibrations that would otherwise result. With this in mind, let the flywheel D with diameter 0.3 m rotate at o = 60,000 rpm. In ad- top view dition, assume that the cart B is constrained to move rectilinearly along the guide tracks. Given that the flywheel is not perfectly balanced, that the unbalanced weight A has mass ma, and that the total mass of the flywheel D, cart B, and electronics package E is mg, determine the constraint force between the wheels of guide tracks the cart and the guide tracks as a function of 0, the masses, the diameter, and the angular speed of the flywheel. What is the maximum constraint force between the wheels of the cart and the guide tracks? Finally, evaluate your answers for mA = 1g (about the mass of a paper clip) and mg = 70 kg. Assume that
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:Problem 3.126 !
Energy storage devices that use spinning flywheels to store en-
ergy are becoming available. To maximize energy storage, the
flywheel must spin as fast as possible. Unfortunately, if it spins
too fast, internal stresses in the flywheel cause it to come apart
catastrophically. Therefore, it is important to keep the speed at
the periphery of the flywheel below about 1000 m/s. It is also
critical that the flywheel be well balanced to avoid the damaging
vibrations that would otherwise result. With this in mind, let the
flywheel D with diameter 0.3 m rotate at = 60,000 rpm. In ad- top view
dition, assume that the cart B is constrained to move rectilinearly
along the guide tracks. Given that the flywheel is not perfectly
balanced, that the unbalanced weight A has mass mд, and that
the total mass of the flywheel D, cart B, and electronics package
E is mg, determine the constraint force between the wheels of
the cart and the guide tracks as a function of 9, the masses, the
diameter, and the angular speed of the flywheel. What is the
maximum constraint force between the wheels of the cart and
the guide tracks? Finally, evaluate your answers for m₁ = 1 g
(about the mass of a paper clip) and mg = 70 kg. Assume that
the unbalanced mass is at the periphery of the flywheel.
guide
tracks
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