PHYSICS 231
INTRODUCTORY PHYSICS I
www.pa.msu.edu/courses/phy231
Course Information
Scott Pratt
http://www.pa.msu.edu/courses/phy231
[email protected]
(517) 355-9200, ext. 2016
Office Hours:
Monday, 9-10:30 AM in 1248 BPS
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Succeeding in Physics 231
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General Physics
1) Do your homework (yourself)!
• First Semester (Phy 231)
2) Use the help room (1248 BPS) !
• Mechanics
3) Make sure you understand both “why” and “why
not”
• Thermodynamics
• Simple harmonic motion
4) Interrupt the lecturer!
• Waves
Second Semester (Phy 232)
•
Electromagnetism
•
Relativity
•
Modern Physics
•
(Quantum Mechanics, …, etc.)
3
Mechanics
4
UNITS (Systéme Internationale)
• Half the course
• Quantified largely by Galileo
• Problems involve:
velocity, acceleration, mass, momentum, energy,
torque, angular momentum, moment of inertia…
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Dimension
SI (mks) Unit
Definition
Length
meters (m)
Distance traveled by light in
1/(299,792,458) s
Mass
kilogram (kg)
Mass of a specific platinumiridium allow cylinder kept by
Intl. Bureau of Weights and
Measures at Sèvres, France
Time
seconds (s)
9,192,631,700 oscillations of
cesium atom
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Dimensional Analysis
Dimensions & units can be treated algebraically.
Variable from Eq.
x
m
t
v=(xf-xi)/t
a=(vf-vi)/t
dimension
L
M
T
L/T
L/T2
Standard Kilogram
at Sèvres
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Dimensional Analysis
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Example 1.1
Checking equations with dimensional analysis:
Check the equation for dimensional consistency:
1
x f ! xi = vi t + at 2
2
(L/T2)T2=L
L
Here, m is a mass, g is an acceleration,
c is a velocity, h is a length
(L/T)T=L
• Each term must have same dimension
• Two variables can not be added if dimensions
are different
• Multiplying variables is always fine
• Numbers (e.g. 1/2 or !) are dimensionless
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Example 1.3
Example 1.2
Given “x” has dimensions of distance, “u” has
dimensions of velocity, “m” has dimensions of
mass and “g” has dimensions of acceleration.
Consider the equation:
m
v2
Mm
=G 2
r
r
Is this equation dimensionally valid?
Where m and M are masses, r is a radius and
v is a velocity.
What are the dimensions of G ?
x=
(4 / 3)ut
1 ! (2gt 2 / x)
Yes
Is this equation dimensionally valid?
L3/(MT2)
x=
11
vt
1 ! mgt 2
No
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Units vs. Dimensions
Example 1.3
• Dimensions: L, T, M, L/T …
• Units: m, mm, cm, kg, g, mg, s, hr, years …
Grandma traveled 27 minutes at 44 m/s.
How many miles did Grandma travel?
• When equation is all algebra: check dimensions
• When numbers are inserted: check units
• Units obey same rules as dimensions:
Never add terms with different units
• Angles are dimensionless but have units
(degrees or radians)
• In physics sin(Y) or cos(Y) never occur unless Y
is dimensionless
44.3 miles
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Prefixes
Example 1.4a
40 m + 11cm = ?
The above expression yields:
In addition to mks units,
standard prefixes can be used,
e.g., cm, mm, µm, nm
a)
b)
c)
d)
40.11 m
4011 cm
A or B
Impossible to evaluate (dimensionally invalid)
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Example 1.4b
Example 1.4b
1.5 m ! 3.0 kg = ?
1.5 m-3.0 kg m/s = ?
The above expression yields:
The above expression yields:
a)
b)
c)
d)
a)
b)
c)
d)
4.5 m kg
4.5 g km
A or B
Impossible to evaluate (dimensionally invalid)
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-1.5 m
-1.5 kg m2
-1.5 kg
Impossible to evaluate (dimensionally invalid)
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