Unformatted text preview: PHYS2001 Physics 1
1.1 The Nature of Physics From the very big to the very small, Physics covers it all! y g y , y This semester we will focus on Classical Mechanics big things moving slowly (wrt the speed of light). Next semester you will study Electricity and Magnetism and Quantum Mechanics. Physics is the most fundamental of all the natural sciences. In science, there is only physics. All the rest is stamp collecting. Earnest Rutherford The strength of Physics as a science is that all of the physical laws are based on experimental results. So why should you be required to take Physics??? Physics is like sex. It has practical applications, but that is not the main reason you do it. Richard Feynman Our goal is to describe and explain how and why the world works the way it does. Through this process you will become analytical thinkers and effective problem solvers. Physics is the perfect vehicle for doing this. These are the skills you should take with you when you leave this course. take with you when you leave this course What do we get with this knowledge??? Lasers Rockets Transistors Telecommunications Etc. Et All technology has its roots in Physics! 1.2 Units Accurate measurements require precisely defined quantitative units. Accurate measurements require precisely defined quantitative units We are going to want to measure things like length, mass, and time. There are several different systems of units used for measurement: SI System International or MKS units (meter, kilogram, second) SI System International or MKS units (meter kilogram second) CGS (centimeter, gram, second) BE British Engineering units (ft, slug, second) BE British Engineering units (ft slug second) In this course we will use SI (MKS) units. Length = Meter (m) = Distance light travels in a vacuum in 3.3 ns (3.3 109 s) Mass = Kilogram (kg) (1 kg 2.2 lbs. on the Earth's surface) Length = Second (s) = The time it takes for 9,192,631,770 vibrations of a Cs133 atom to occur 1.3 Converting Between Different Units and Base Units 1 km = 1000 m = 1 103 m 5.2 cm = 0.052 m = 5.2 102 m If you need to brush up on powers of 10 or scientific notation, see Appendix A. To Do Unit Conversions: T t th Treat the units as algebraic quantities it l b i titi Multiply by factors of "1" Example Use the "mol method" My cat, Socola, is fat. He has a 17 in. waist. What is Socola's waist size in m? 17 in. 2.54 cm 1 in. 1 m 100 cm = (17)(2.54) 100 = 0.43 m All of your answers must have appropriate units!!! Mars Climate Orbiter (1999)!!! Factors of 1 Significant Digits Every quantity (number) has a certain number of significant digits. These are digits in the number whose values are known with certainty. For example, Socola is 27.25 cm tall, with the measurement uncertainty occurring in the 3rd decimal place. Thus, all of these digits are significant (known with certainty), and 27.25 cm has 4 significant digits. If a zero is given as the last digit to the right of the decimal point, it is also significant. Example: 7.290 m has 4 significant digits. Example: 7 290 m has 4 significant digits However, zeros immediately to the left of an unexpressed decimal point are not significant. Example: 1500 m only has 2 significant digits. Finally, zeros located between significant digits are significant. Example: 1502 m has 4 significant digits. Example: How many significant digits are there in 150,200.0? There are 7! Why do significant digits matter??? Let s say Socola s top speed is 7.0 mi/h, and I want to calculate his speed in m/s. Thus, I Let's say Socola's top speed is 7 0 mi/h and I want to calculate his speed in m/s Thus I need to convert mi to m and h to s. 7.0 mi. 5280 ft. 12 in. 2.54 cm 1 m 1 h 1 min. 7 0 mi 5280 ft 12 in 2 54 cm 1 m 1h 1 min 1 h 1 mi. 1 ft. 1 in. 100 cm 60 min. 60 s (7.0)(5280)(12)(2.54) (100)(60)(60) = = 3.12928 m/s No!!! Does it make sense to represent his speed with this accuracy??? We only know his speed, 7.0 mi/h, to an accuracy of 2 significant digits. Thus, 3.12928 m/s 3.1 m/s In general, when numbers are multiplied or divided, the number of significant digits in the answer should be equal to the smallest number of significant digits in any of the original factors. Example: Convert 3.141592 m to in. 3.141592 m 100 cm 1 in. 3 141592 100 1i 1 m 2.54 cm (3.141592)(100) (3 141592)(100) = 2.54 = 123.684724409 in. How many significant digits should this final answer have?? 1? 3? 7? It should have 7! 123.6847 in. The 100 cm and the 2.54 cm, etc. are conversion factors. They are known precisely! See Appendix B of your text for more on Significant Digits. 1.4 Trigonometry Take a look at a right triangle. Take a look at a right triangle. We can label the sides relative to the angle . opp. a hyp. yp c b adj. sin = cos = tan = opposite hypotenuse adjacent hypotenuse opposite adjacent a = c b = c a = b These Trigonometric Functions are unitless, since they represent the ratio of two lengths (sides of the triangle). Example: Michael Jordan casts a shadow of length 1.39 m. If the angle between the sun's rays and the ground is 55o, what is Michael's height, h? h 55o 1.39 m 1 39 m h 55o 1.39 m 1.39 m tan = opposite adjacent = h
1.39 m 1.39 m h = (1.39 m)(tan 55o) = 1.98 m (6' 6") Other Trig. Stuff Also for right triangles, we will use the Pythagorean Theorem: a2 + b2 = c2 a c b For all triangles, we can use the following: Law of Sines a b c = = sin sin sin a c Law of Cosines c2 = a2 + b2 2abcos b ...
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