Basic Tools for Classical Mechanics - Principles Physics | PHYS 141, Study notes of Physics

Download Basic Tools for Classical Mechanics - Principles Physics | PHYS 141 and more Study notes Physics in PDF only on Docsity! 1 Phys141 – Lecture 3 – Wed 9/7 Review Chapter 1: Basic tools of classical mechanics: – Basic, standardized quantities for measurements: • Length, Mass, Time – Dimensions of quantities • Conversion of units • Density – an example of derived dimensions • Dimensional Analysis – Common sense checks: • “are results reasonable” • Order of magnitude estimate – Uncertainty in measurement and calculation • Significant figures • Rounding ToDo: Read Chapter 2.6; (Skip Chapter 2.7) Read Chapter 3 Homework DUE FRIDAY (online and printout!) Operations with Significant Figures – Multiplying or Dividing Number of significant figures in the answer: ~ smallest number of significant figures of the quantities that are multiplied/divided. Example: 25.57 m x 2.45 m = 62.6 m2 – The 2.45 m limits your result to 3 significant figures Operations with Significant Figures – Adding or Subtracting Number of decimal places in the result: ~smallest number of decimal places in any term in the sum. Example: 135 cm + 3.258 cm = 138 cm – The 135 cm limits your answer to the units decimal value 932m x 0.5 + 12m = ?? 47 8 m 47 8.0 m 4.8 x 10 2 m 5 x 10 2 m 0% 0%0%0% 1. 478 m 2. 478.0 m 3. 4.8 x 102 m 4. 5 x 102 m 4039383736353433323130292827262524232221 2019181716151413121110987654321 2 Rounding Last retained digit is increased by 1 if the last digit dropped is 5 or above Last retained digit remains as it is if the last digit dropped is less than 5 Do not round before you get to the final result Example: Round the sum of 1001 contributions of $0.40 to the nearest $ • Final result of calculation: $400.40 • Rounded final result: $400 • Round each contribution: $0 –> sum (rounded too early) is $0 Chapter 2: Kinematics • Kinematics: Basic tools to characterize motion DEMO Position • Defined only relative to known reference. • Term: “frame of reference” • need to define 1. origin 2. one, two or three axes 3. Measurement units Movie Frame by Frame Example Frame of reference: Cartesian Coordinate System • rectangular coordinate system • x- and y axes intersect at the origin • Points are labeled (x,y) 5 Acceleration Rate of change of the velocity • Average acceleration: • Dimensions [L/T2] • SI units m/s2 −Δ = = Δ Δ xf xix x v vva t t Instantaneous Acceleration Mathematical definition: Instantaneous acceleration is the limit of the average acceleration as Δt approaches 0 Active Figure 2.10: Active Figure 2.11 (practice yourself) 2 20 lim x xx t v dv d xa t dt dtΔ → Δ = = = Δ Useful equations ( ) iv t v at= + 21( ) 2i i x t x vt at= + + for constant acceleration a: ( )a t a= Need to know: -Initial velocity vi Need to know: -Initial position xi -Initial velocity vi Questionnaire answers – Which physics will you need? Examples: • Whatever physics is on the MCAT • Calculating the movements of cells or chemicals • Pathologist: how forces affect me – how they affected organisms in the past • Quantum mechanics for physical chemistry 6 To Do • Read Chapter 2.6; (Skip Chapter 2.7) Read Chapter 3 • short pre-class quiz • Homework due Fri– online and hand in!