Differential Equations - Acceleration and velocity models

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Differential Equations - Acceleration and velocity models

12. Nuclear waste disposal It is proposed to dispose of nu-
clear wastes-in drums with weight W
ume 8 ft3-by dropping them into the ocean (vo = 0). The
force equation for a drum falling through water is
= 640 lb and vol-
|3D
dv
m
dt
-W + B + FR,
_
where the buoyant force B is equal to the weight (at 62.5
lb/ft³) of the volume of water displaced by the drum
(Archimedes' principle) and FR is the force of water resis-
tance, found empirically to be 1 lb for each foot
of the velocity of a drum. If the drums are likely to burst
upon an impact of more than 75 ft/s, what is the maximum
depth to which they can be dropped in the ocean without
likelihood of bursting?
per
second
Transcribed Image Text:12. Nuclear waste disposal It is proposed to dispose of nu- clear wastes-in drums with weight W ume 8 ft3-by dropping them into the ocean (vo = 0). The force equation for a drum falling through water is = 640 lb and vol- |3D dv m dt -W + B + FR, _ where the buoyant force B is equal to the weight (at 62.5 lb/ft³) of the volume of water displaced by the drum (Archimedes' principle) and FR is the force of water resis- tance, found empirically to be 1 lb for each foot of the velocity of a drum. If the drums are likely to burst upon an impact of more than 75 ft/s, what is the maximum depth to which they can be dropped in the ocean without likelihood of bursting? per second
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