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Physics for Dentistry and Medicine students PHYS 145 Text book Physics; John D. Cutnell and Kenneth W. Johnson; 7th edition; Wiley; 2007. Chapter 1 Introduction and Mathematical concepts The animation techniques used in the film Star Wars: Episode III—Revenge of the Sith rely on computers and mathematical concepts such as trigonometry and vectors. These mathematical tools will also be useful throughout this book in dealing with the laws of physics. (Lucasfilm/20th Century Fox/The Kobal Collection, Ltd.) Units of Measurement System SI (International system) CGS BE (British Engineering system) Meter (m) Centimeter (cm) Foot (ft) Mass Kilogram (kg) Gram (g) Slug (sl) Time Second (s) Second (s) Second (s) Length Meter • Originally, the distance measured along the earth’s surface between the north pole and the equator. • Eventually, the meter became the distance between two marks on a bar of platinum–iridium alloy (Figure) kept at a temperature of 0 °C. • Today, the meter is defined as the distance that light travels in a vacuum in a time of 1/299 792 458 second. (The speed of light is a universal constant that is defined to be 299 792 458 m/s) The standard platinum–iridium meter bar. (Courtesy Bureau International des Poids et Mesures, France) kilogram • Originally, the kilogram was expressed in terms of a specific amount of water. • Today, one kilogram is defined to be the mass of a standard cylinder of platinum– iridium alloy, (Figure 2). The standard platinum–iridium kilogram is kept at the International Bureau of Weights and Measures in Sévres, France. This copy of the standard kilogram is housed at the National Institute of Standards and Technology. (Sissy Riley, Information Services Division/National Inst of Standards and Technology) Second • Originally, the second was defined according to the average time for the earth to rotate once about its axis, one day being set equal to 86 400 seconds. The earth’s rotational motion was chosen because it is naturally repetitive, occurring over and over again. • Today, we use the electromagnetic waves emitted by cesium-133 atoms in an atomic clock like that in (Figure 3). One second is defined as the time needed for 9 192 631 770 wave cycles to occur. This atomic clock, the NIST-F1, is considered one of the world’s most accurate clocks. It keeps time with an uncertainty of about one second in twenty million years. (© Geoffrey Wheeler) Standard Prefixes Used to Denote Multiples of Ten Prefix Symbol Factor Prefix Symbol Factor Prefix Symbol Factor tera T 1012 Giga *G 109 Mega M 106 Kilo k 103 Hecto h 102 Deka da 101 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 pico p 10-12 femto f 10-15 The Conversion of Units • Example: Body Mass Index (BMI) The body mass index (BMI) takes into account your mass in kilograms (kg) and your height in meters (m) and is defined as follows: Massin kg BMI = Heightin m Determine the expression for the BMI of a person who has a mass of 180 lb. and a height of 71 in. (1 kg corresponds to 2.205 lb, and 1 ft = 12 in., 1 m = 3.281 ft.; 1 in. = 2.54 cm) 2 1 kg X kg 1m 2.205 lb 180 Ib X = 81.6 kg 3.281 ft 39.372 in. Xm 71 in. X = 1.8 m MBI 81.6 25.1 kg / m 2 2 1.8 BMI (Kg/m2) Evaluation Below 18.5 Underweight 18.5–24.9 Normal 25.0–29.9 Overweight 30.0–39.9 Obese 40 and above Morbidly obese Scalars and Vectors • A scalar quantity is one that can be described with a single number (including any units) giving its size or magnitude. Examples: temperature, mass, volume, energy and time. • A vector quantity is a quantity that deals inherently with both magnitude and direction. • displacement vector, velocity, force, weight and acceleration. A vector quantity has a magnitude and a direction. The colored arrow in this drawing represents a displacement vector. Vectors Addition and Subtraction R A B R 275m, dueeast 125m, dueeast 400m, dueeast R A B R A2 B 2 B A t an1 R 275m, dueeast 125m, duenorth R 275m 2 125m 2 302m 125m o 24 . 4 north of east 275m t an1 (a) The displacement vector for a woman climbing 1.2 m up a ladder is D . (b) The displacement vector for a woman climbing 1.2 m down a ladder is D The Components of a Vector Ax A cos Ay A sin Example: Finding the Components of a Vector • A displacement vector has a magnitude of r = 175 m and points at an angle of 50.0° relative to the x - axis in the figure. Find the x and y components of this vector. 112m y r sin 175m sin 50.0 134m x r cos 175m cos50.0 o o Example: Using Components to Add Vectors • The figure shows three displacement vectors A, B, and C. These vectors are arranged in tail-to-head fashion, because they add together to give a resultant displacement R, which lies along the x axis. Note that the vector B is parallel to the x axis. What is the magnitude of the vector C? A B C R Ax Bx C x Rx Ay B y C y R y A 20 m sin 60.0 17.3 m B 10 m cos 0 10.0 m B 10 m sin 0 0 m R 35.0 m cos 0 35.0 m R 35.0 m sin 0 0 m Ax 20 m cos60.0 o 10.0 m o y o x o y o x o y C x Rx Ax Bx 15.0 m C y Ry Ay By 17.3 m C 15 17.3 22.9 m 2 tan1 2 17.3 49.07o south of east 15 Questions • Are two vectors with the same magnitude necessarily equal? Give your reasoning. • (a) Is it possible for one component of a vector to be zero, while the vector itself is not zero? (b) Is it possible for a vector to be zero, while one component of the vector is not zero? Explain. • Can two nonzero perpendicular vectors be added together so their sum is zero? Explain. Problems • Azelastine hydrochloride is an antihistamine nasal spray. A standard size container holds one fluid ounce (oz) of the liquid. You are searching for this medication in a European drugstore and are asked how many milliliters (mL) there are in 1 oz. Using the following conversion factors, determine the number of milliliters in a volume of one fluid ounce: 1 gallon (gal) = 128 oz.; 3.785 x 10-3 m3 = 1 gal; 1 mL = 10-6 m3. Problem • At a picnic, there is a contest in which hoses are used to shoot water at a beach ball from three directions. As a result, three forces act on the ball, F1, F2, and F3. Where F1 = 50.0 N and F2 = 90.0 N. Determine (a) the magnitude of F3 and (b) the angle θ such that the resultant force acting on the ball is zero. Problem • Vector A points along the +y-axis and has a magnitude of 100.0 units. Vector B points at an angle of 60.0° above the + xaxis and has a magnitude of 200.0 units. Vector C points along the + x-axis and has a magnitude of 150.0 units. Which vector has (a) the largest x component and (b) the largest y component? Problem • Soccer player #1 is 8.6 m from the goal. If she kicks the ball directly into the net, the ball has a displacement labeled A. If, on the other hand, she first kicks it to player #2, who then kicks it into the net, the ball undergoes two successive displacements, Ay and Ax. What are the magnitudes and directions of Ax and Ay?