Download MATH 2414 - Calculus II Units of Measurement and Some Applications

MATH 2414 - Calculus II
Units of Measurement and Some Applications
distance
mass
time
velocity
acceleration
force
work
length density
density
weight density
pressure
centimeter/gram/second
(cgs) System
meter/kilogram/second
(mks) System
centimeter (c)
gram (g)
second (s)
centimeters/second (c/s)
centimeters/second2 (c/s2)
dyne (dyn)
erg
g/cm
gram/cm3
dyne/cm3
dyn/cm2 or barye (bar)
meter (m)
kilogram (kg)
second (s)
meters/second (m/s)
meters/second2 (m/s2)
newton (N)
joule (J)
kg/m
kg/m3
N/m3
N/m2 or pascal (Pa)
foot/pound/second
(fps) System
(U.S. Customary System)
foot
slug
second
feet/second (ft/s)
feet/second2 (ft/s2)
pound (lb)
foot-pound (ft-lb)
slug/ft
slug/ft3
lb/ft3
lb/ft2
acceleration due to gravity: 980 cm/sec2 , 9.8 m/sec2 , 32 ft/sec2
weight = mass × acceleration due to gravity w = mg
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Hooke’s Law: The force F applied to a spring is proportional to the distance x the spring is stretched. In
other€words, F = kx , where the constant of proportionality k is called the spring constant.
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Density, usually denoted by the Greek letter rho ( ρ ), is mass per volume, such as kg/m3 or slug/ft 3 .
The€density of water is 1000 kg/m3.
€ as N/m3 or lb/ft 3 and is obtained
€ by multiplying
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Weight density is weight per volume, such
the density
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by the acceleration
due to gravity, so ρg . The weight density of water is 9800 N/m3 or approximately
62.5 lb/ft 3 .
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The pressure P at a depth of€d in a liquid is obtained by multiplying
€ the weight density times the depth,
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so P = ρgd . Pressure units will be weight per area, such as N/m2 or lb/ft 2 .
The force F on a surface with area A at a depth d in a liquid with density ρ is given by F = PA = ρgdA.
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