5. A ball of mass m gm and radius 7 cm is released from rest in a liquid of viscosity gm/(cm sec). The ball falls under the influence of gravity but the liquid exerts a drag proportional to its velocity v cm/sec. If y cm measures the vertical distance the ball has fallen, then its equation of motion is m d²y dt² dy + 6πμη = mg. dt Determine y(t). What can you say about the velocity v(t)? Suppose a steel ball of density p = 8 gm/cc is dropped in water (μ = 0.01 gm/(cm sec)). Determine the radius of the ball that will fall steadily at 5.05 mph (the fastest speed of a swimmer). Answer: 0.35 mm.
5. A ball of mass m gm and radius 7 cm is released from rest in a liquid of viscosity gm/(cm sec). The ball falls under the influence of gravity but the liquid exerts a drag proportional to its velocity v cm/sec. If y cm measures the vertical distance the ball has fallen, then its equation of motion is m d²y dt² dy + 6πμη = mg. dt Determine y(t). What can you say about the velocity v(t)? Suppose a steel ball of density p = 8 gm/cc is dropped in water (μ = 0.01 gm/(cm sec)). Determine the radius of the ball that will fall steadily at 5.05 mph (the fastest speed of a swimmer). Answer: 0.35 mm.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:5. A ball of mass m gm and radius 7 cm is released from rest in a liquid
of viscosity gm/(cm sec). The ball falls under the influence of gravity
but the liquid exerts a drag proportional to its velocity v cm/sec. If y
cm measures the vertical distance the ball has fallen, then its equation of
motion is
m
d²y
dt²
dy
+ 6πμη
= mg.
dt
Determine y(t). What can you say about the velocity v(t)?
Suppose a steel ball of density p = 8 gm/cc is dropped in water (μ = 0.01
gm/(cm sec)). Determine the radius of the ball that will fall steadily at
5.05 mph (the fastest speed of a swimmer).
Answer: 0.35 mm.
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