231 PHYSICS INTRODUCTORY PHYSICS I
Section 001
PHYSICS 231 INTRODUCTORY PHYSICS I
Lecturer: Carl Schmidt (Sec. 001) [e-mail] [phone], ext. 2128 Office Hours: To be determined in 1248 BPS or by appointment
Course Information
http://www.pa.msu.edu/courses/phy231 http://www.pa.msu.edu/courses/phy231
Succeeding in Physics 231
1) Do your homework (yourself) ! 2) Use the help room (1248 BPS) ! 3) Make sure you understand both "why" and "why not" 4) Interrupt the lecturer!
General Physics
First Semester (Phy 231) Mechanics Thermodynamics Simple harmonic motion Waves Second Semester (Phy 232) Electromagnetism Relativity Modern Physics (Quantum Mechanics, ..., etc.)
Mechanics
Used by all of physics and other sciences Foundations laid by Galileo and Newton Newton's Principia - 1687
Chapter 1: the Basics
SI Units Unit conversions Dimensional Analysis Significant Figures
UNITS (Systme Internationale)
Dimension SI (mks) Unit Definition Distance traveled by light in 1/(299,792,458) s
Length Mass Time
meters (m)
kilogram (kg) Mass of a specific platinum-
iridium allow cylinder kept by Intl. Bureau of Weights and Measures at Svres, France 9,192,631,700 oscillations of cesium atom
seconds (s)
Standard Kilogram at Svres
Unit conversion Example 1.1
A car goes 50 miles/hour. What is that in m/s?
22 m/s
Dimensional Analysis
Dimensions (like units) can be treated algebraically. Variable from Eq. Dimension x m t v=(xf-xi)/t L/T a=(vf-vi)/t L/T2
L M T
Dimensional Analysis
Checking equations with dimensional analysis:
1 2 x f ! xi = vi t + at 2
(L/T2)T2=L L (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
Example 1.2
Could the following equations be correct?
1) "t = v 0 + 2a"x
No !
2) v = v + 2a"x
2 f
2 0
Yes, It "could" be.
Units vs. Dimensions
Dimensions: L, T, M, L/T ... Units: m, mm, cm, kg, g, mg, s, hr, years ... When equation is all algebra: check dimensions When numbers are inserted: check units Units and dimensions obey same rules: 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
Scientific Notation
Useful for very large... Distance to sun = 150000000000 m = 1.5 x 1011 m or small numbers: radius of iron nucleus = 0.0000000000000044 m = 4.4 x 10-15 m
Prefixes
In addition to mks units, standard prefixes can be used, e.g., km, cm, mm, m
Significant Figures
I measure the table length with my ruler. Which statement is more correct? A. The length is 56.0 in. (or 5.60x101 in) B. The length is 56.00 in. (or 5.600x101 in) Statement A. General Rule: Number of digits used decimal in or scientific notation (including trailing zeros, but not leading zeros) specifies significant figures (i.e, precision) of measurement.
Significant Figures
Other rules: When multiplying or dividing, keep the minimum significant figures of any factors: (5.585)(7.4) = 41. = 41.329 When adding or subtracting, keep the least accurate decimal place of any of the numbers: 113.2 + 2.54 = 115.74 = 115.7
Chapter 2: One-Dimensional Motion
Motion at fixed velocity Definition of average velocity Motion with fixed acceleration Graphical representations
Displacement vs. position
Position: x (relative to origin) Displacement: x = xf-xi
Example: Distance vs. Displacement
Distance between Des Moines, Iowa, and Iowa City, is listed as 113.5 miles or 182.6 km Straight line, to very good approximation
Question:
If we take a round trip Des Moines Iowa City Des Moines, what is the total distance and displacement for this trip? Distance=365.2 km Displacement=0
Average velocity
basic formula !x x f " xi v= = !t t
Average velocity Can be positive or negative Depends only on initial/final positions e.g., if you return to original position, average velocity is zero
Example 2.1
Carol starts at a position x(t=0) = 1.5 m. At t=2.0 s, Carol's position is x(t=2 s)=4.5 m At t=4.0 s, Carol's position is x(t=4 s)=-2.5 m a) What is Carol's average velocity between t=0 and t=2 s? b) What is Carol's average velocity between t=2 and t=4 s? c) What is Carol's average velocity between t=0 and t=4 s? a) 1.5 m/s b) -3.5 m/s c) -1.0 m/s
Graphical Representation of Average Velocity
Between A and D , v is slope of blue line
40m v= = 13.3m/s 3.0s
Instantaneous velocity
basic formula
!x x f " xi ...