PHYSICS 231 INTRODUCTORY PHYSICS I Section 001 PHYSICS 231 INTRODUCTORY PHYSICS I Lecturer Carl Schmidt Sec 001 schmidt pa msu edu 517 355 9200 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 Syst me Internationale Dimension SI mks Unit Definition Length meters m Distance traveled by light in 1 299 792 458 s Mass Time kilogram kg Mass of a specific platinum iridium allow cylinder kept by Intl Bureau of Weights and Measures at S vres France seconds s 9 192 631 700 oscillations of cesium atom Standard Kilogram at S vres 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 L M T v xf xi t a vf vi t L T L T2 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 2 f 2 0 2 v v 2a x No 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 in decimal 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 v t t Let time interval approach zero Defined for every instance in time Equals average velocity if v constant SPEED is absolute value of velocity Graphical Representation of Average Velocity Between A and D v is slope of blue line Graphical Representation of Instantaneous Velocity x t x v lim t 0 t Slope of tangent at that point Graphical Representation of Instantaneous Velocity v t 3 0 is slope of tangent green line Example 2 2a The instantaneous velocity is zero at A a B b d C c e Example 2 2b The instantaneous velocity is negative at A B C D E a b c d e Example 2 2c The average velocity is zero in the interval A B C D E a c b d c d c e d e Example 2 2d The average velocity is negative in the interval s A B C D a b a c c e d e SPEED Speed is v and is always positive Average speed is sum over x elements divided by elapsed time Example 2 3 x m a What is the average velocity between B and E 8 b What is the average speed between B and E 4 6 E B 2 A 0 a 0 2 m s b 1 2 m s D C 0 2 4 6 8 10 12 t s
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