Welcome to Physics 151 James Walker, Physics, 3 rd Ed. Prentice Hall Preliminary list of topics Walker, Chapters 1-18 Description of motion: Kinematics Position (in 1-, 2-, 3- dimensions), Velocity & Acceleration Forces and Motion: Net Force equals mass times acceleration Examples of forces: Contact forces (friction, normal force) Gravity Elastic forces: Springs and waves Kinetic Energy, Potential Energy, Work Momentum, Collisions Torque and Statics Oscillations & Waves Fluids & Thermodynamics Walker, Chapter 1 2
Introduction Physics and Laws of Nature Units of Length, Mass, and Time Dimensional Analysis Significant Figures Converting Units Precision and Significant Figures Problem Solving in Physics Walker, Chapter 1 3 What is Physics? In science in general, and physics in particular, we seek to develop and evaluate theories/concepts/ideas/perceptions... The goal is to gain a deeper understanding of the world in which we live. Physics is the study of the fundamental laws of nature, which are the laws that underlie all physical phenomena in the universe. These laws can be expressed in terms of mathematical equations. We can make quantitative comparisons between the predictions of theory and the observations of experiment. Walker, Chapter 1 4
Why Physics? 19 th century: economy was dominated by harnessing the power of steam. 20 th century economy was dominated by the internal combustion engine and the microelectronics revolution. 21 st century economy may be revolutionized by the manipulation of individual atoms. Walker, Chapter 1 5 Distance It is impossible to talk about distance or motion in any terms other than quantitative. How far is it from CNU to Colonial Williamsburg? How far is it from the Earth to the nearest large galaxy? It is impossible to speak quantitatively without defining a unit of measure. It is meaningless to say that the distance to the Colonial Williamsburg is 20. Physical quantities have both numerical value and units. It is 20 miles from CNU to Colonial Williamsburg. 20 miles equals 32 kilometers. 20 miles also equals 105,600 ft = 32,208 m. Walker, Chapter 1 6
Typical Distances Distance from the Earth to the nearest large galaxy (the Andromeda Galaxy, M31) Diameter of our galaxy (the Milky Way) Distance from the Earth to the nearest star (other than the Sun) One light year Average radius of Pluto s orbit Distance from Earth to the Sun Radius of Earth Length of football field Height of a person Diameter of a CD Diameter of the aorta Diameter of the period in a sentence Diameter of a red blood cell Diameter of the hydrogen atom Diameter of a proton 2 x 10 22 m 8 x 10 20 m 4 x 10 16 m 9.46 x 10 15 m 6 x 10 12 m 1.5 x 10 11 m 6.37 x 10 6 m 10 2 m 2 m 0.12 m 0.018 m 5 x 10 4 m 8 x 10 6 m 10 10 m 2 x 10 15 m Walker, Chapter 1 7 Time The second is defined as the duration of 9,192,631,770 oscillations of a particular atomic transition in Cesium-133 (defined by the spectral color of the light). It is not an accident that the typical human heartbeat is 1 sec. Age of the universe Age of the Earth Existence of human species Human lifetime One year One day 5 x 10 17 s 1.3 x 10 17 s 6 x 10 13 s 2 x 10 9 s 3 x 10 7 s 8.6 x 10 4 s Walker, Chapter 1 8
The Equals Sign At the heart of mathematical notation is the equals sign "=". In algebraic notation, "=" means "has the value of" v = 60 mi/hr, means my speed on the highway, represented by the symbol v has a value of 60 mi/hr F = m a, means The net force acting on an object is numerically equal to the mass m of the object times its acceleration a. In this example the left and right hand sides of the equal refer to totally different concepts, that Newton tells us nonetheless have the same numerical values. Notice that the symbol (e.g. V ) includes both magnitude and units. We do not write V mi/hr, nor V = 60, but V = (60 mi/hr) Walker, Chapter 1 9 Mass In SI units, mass is measured in Kg. We don t define the Kg to be the weight but rather the amount of substance contained in the object, which is an intrinsic and unchanging property. Weight, in contrast, is the measure of the gravitational force acting on an object. W = mg Galaxy (Milky Way) Sun Earth Elephant Human Honey bee Bacterium 4 x 10 41 kg 2 x 10 30 kg 5.95 x 10 24 kg 5400 kg 70 kg 1.5 x 10-4 kg 10-15 kg Walker, Chapter 1 10
Converting Units How do we convert from inches to cm, or miles to km (without crashing into Mars as NASA recently did in 1999!). By international convention 1 in = 2.54 cm Convert 4.75 in to cm 2.54cm in ( 4.75in) = (4.75in) = (4.75 2.54) cm = 12. 065cm 1in in Notice that units divide just like numbers (in/in) =1 Walker, Chapter 1 11 Experimental Uncertainties Physics is quantitative, not exact. Every physical quantity has an associated uncertainty, either in its measurement or in its prediction. Note that error is used sometimes to mean uncertainty and sometimes to mean mistake. Carpenters rulers are marked off in 1/8 inch increments. Given the flexibility of a wooden house it is unnecessary and useless to try to measure dimensions in home construction to better than 1/8 inch Estimating the uncertainty is often the most difficult part of a measurement. In your physics lab, you must make judgments about the precision of the distances, times, weights, etc. that you measure. Walker, Chapter 1 12
Precision and Significant Figures If we say the acceleration due to gravity is 9.80 m/s/s, (three significant figures) we imply an uncertainty of +/ 0.01 Thus: 9.80 m/s/s = (9.80 ±0.01) m/s/s 9.80 m/s/s is not the same as 9.8 m/s/s In the homework and tests, we will assume 3 significant figures unless specified otherwise. To avoid round-off errors, you must carry through all intermediate calculations to at least 4 significant figures. Use of excessive significant figures will result in point deductions on tests. Even though your calculator gives answers to 10 significant figures, it is wrong to write, e.g. the ball stayed in the air for 2.314078504 sec if all the input data are not given with that precision. Walker, Chapter 1 13