Physics 114A - Mechanics Lecture 1 (Walker: Ch. 1) Introduction to Physics January 3, 2012 John G. Cramer Professor Emeritus, Department of Physics B451 PAB

January 3, 2012Physics 114A - Lecture 12/21 Physics 114A - Introduction to Mechanics - Winter-2012 Lecture: Professor John G. Cramer Textbook: Physics, (Edition: UW Vol. 1 or Complete 4th), James S. Walker WeekDateL#Lecture TopicPagesSlidesReadingHW DueLab 1 2-Jan-12H1 New Year Holiday No Lab 1st week 3-Jan-121Introduction to Physics1221Chapter 1 5-Jan-122Position & Velocity to 2-3No HW 6-Jan-123Velocity & Acceleration to Jan-124Equations of Motion to D Kinematics 10-Jan-125Vectors to Jan-126r, v & a Vectors to 3-5HW1 13-Jan-127Relative Motion Jan-12H2 MLK Birthhday Holiday Free Fall & Projectiles 17-Jan-1282D Motion Basics to Jan-1292D Examples to 4-5HW2 20-Jan-12E1 EXAM 1 - Chapters 1-4 Lecture Schedule (Part 1) We are here.

January 3, 2012Physics 114A - Lecture 13/21January 3, 2011Physics 114A - Lecture 13/21 Physics and the Laws of Nature Physics: the study of the fundamental laws of nature. ● These laws can be expressed as mathematical equations. (e.g., F = m a) ● Most physical quantities have units, which must match on both sides of an equation. ● Much complexity can arise from even relatively simple physical laws.

January 3, 2012Physics 114A - Lecture 14/21 Units With a few exceptions, all physical quantities have units. Examples: Mass-kilograms (kg) Speed-meters per second (m/s) Pressure-pascals (P) Energy-joules (J) Electric Potential-volts (V) Rather surprisingly, the units of almost all physical quantities can be expressed as combinations of only the units for mass, length, and time, i.e., kilograms, meters, and seconds. A few physical quantities (e.g., index of refraction) are pure numbers that have no associated units.

January 3, 2012Physics 114A - Lecture 15/21 Standard International Units Standard International (SI) Units (also known as MKS) Length:meterm Mass:kilogramkg Time: seconds Unit Conversions 1 in = 2.54 cm1 cm = in 1 mi = km1 km = mi 1 mph = m/s1 m/s = 2.24 mph Note: The English pound unit is a measure of force or weight, not mass. A kilogram of mass has a weight of pounds at standard gravity, but will have slightly different weights at different locations on the Earth (poles, equator). } English Units (Used only in USA, Liberia, and Myanmar) Units for almost all other physical quantities can be constructed from mass, length, and time, so these are the fundamental units.

January 3, 2012Physics 114A - Lecture 16/21 The SI Time Unit: second (s) The second was originally defined as (1/60)(1/60)(1/24) of a mean solar day. Currently, 1 second is defined as 9,192,631,770 oscillations of the radio waves absorbed by a vapor of cesium-133 atoms. This is a definition that can be used and checked in any laboratory to great precision. 13 th Century Water Clock Cesium Fountain Clock

January 3, 2012Physics 114A - Lecture 17/21 The SI Length Unit: meter (m) The meter was originally defined as 1/10,000,000 of the distance from the Earth’s equator to its North pole on the line of longitude that passes through Paris. For some time, it was defined as the distance between two scratches on a particular platinum- iridium bar located in Paris. Currently, 1 meter is defined as the distance traveled by light in 1/299,792,458 of a second

January 3, 2012Physics 114A - Lecture 18/21 The SI Mass Unit: kilogram (kg) The kilogram was originally defined as the mass of 1 liter of water at 4 o C. Currently, 1 kilogram is the mass of the international standard kilogram, a polished platinum-iridium cylinder stored in S è veres, France. (It is currently the only SI unit defined by a manufactured object.) Question: In a “telephone” conversation, could you accurately describe to a member of a alien civilization how big a kilogram was? Answer: More or less. Avagadro’s number of carbon-12 atoms ( … x ) has a mass of exactly … grams.

January 3, 2012Physics 114A - Lecture 19/21 Scientific Notation How many significant figures?

January 3, 2012Physics 114A - Lecture 110/21 Prefixes

January 3, 2012Physics 114A - Lecture 111/21 Dimensions and Units

January 3, 2012Physics 114A - Lecture 112/21 Any valid physical equation must be dimensionally consistent – each side must have the same dimensions. From the Table: Distance = velocity × time Velocity = acceleration × time Energy = mass × (velocity) 2 Dimensional Analysis (1)

January 3, 2012Physics 114A - Lecture 113/21 Dimensional Analysis (2) The period P (T) of a swinging pendulum depends only on the length of the pendulum d (L) and the acceleration of gravity g (L/T 2 ). Which of the following formulas for P could be correct ? (a)(b)(c) P  2  (dg) 2 Example :

January 3, 2012Physics 114A - Lecture 114/21 Dimensional Analysis (3) T Remember that P is in units of time (T), d is length (L) and g is acceleration (L/T 2 ). The both sides must have the same units (a)(b)(c) Try equation (a). Try equation (b). Try equation (c).

January 3, 2012Physics 114A - Lecture 115/21 Some Approximate Magnitudes

January 3, 2012Physics 114A - Lecture 116/21 Order of Magnitude Calculations 1. Make a rough estimate of the relevant quantities to one significant figure, preferably some power of Combine the quantities to make the estimate. 3. Think hard about whether the estimate is reasonable. Example: How fast does an Olympic sprinter cross the finish line in the 100 m dash? Analysis: Typical 100 m dash time is ~10 s, so average speed is about 10 m/s. Sprinters “kick” near the finish line, so speed there is faster. 50% faster? Maybe. That would mean the finish-line speed is ~15 m/s. Reasonable? Yes.

January 3, 2012Physics 114A - Lecture 117/21 Example: Burning Rubber Problem: When you drive your car 1 km, estimate the thickness of tire tread that is worn off. Answer: 1.Estimate the distance require to wear down a tire tread to the point where it needs to be replaced: ~60,000 km (or 37,000 miles) 2.Estimate the thickness of a typical tire tread lost on a worn tire: ~ 1 cm. 3. Consider the following ratio: Therefore, a car loses about 2x10 -7 m = 0.2  m of tire tread in driving 1 km.

January 3, 2012Physics 114A - Lecture 118/21 Problem Solving in Physics No recipe or plug-and-chug works all the time, but here are some guidelines: 1. Read the problem carefully. 2. Draw a sketch of the system. 3. Visualize the physical process involved. 4. Devise a strategy for solving the problem. 5. Identify the appropriate equations. 6. Solve the equations. Calculate the answer. 7.Check your answer. Dimensions? Reasonable? 8.Explore the limits and special cases.

January 3, 2012Physics 114A - Lecture 119/21 Scalars and Vectors Temperature = Scalar Quantity is specified by a single number giving its magnitude. Velocity = Vector Quantity is specified by three numbers that give its magnitude and direction (or its components in three perpendicular directions).

January 3, 2012Physics 114A - Lecture 120/21 Properties of Vectors

End of Lecture 1 Before the Thursday lecture, read Walker, Chapter 2.1 through 2.3. Obtain a HiTT clicker from the University Bookstore. We will use soon. Lecture Homework #1 has been posted on the WebAssign system and is due at or before 11:59 PM on Thursday, Jan. 12, i. e., on Thursday of next week.