Physics for Dentistry and Medicine students Physics for Dentistry and Medicine students PHYS 145 Text book Physics; John D. Cutnell and Kenneth W. Johnson; 7 th 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) LengthMeter (m)Centimeter (cm)Foot (ft) MassKilogram (kg)Gram (g)Slug (sl) TimeSecond (s)

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.Figure Today, the meter is defined as the distance that light travels in a vacuum in a time of 1/ second. (The speed of light is a universal constant that is defined to be 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).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 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 wave cycles to occur.Figure 3

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 teraT10 12 Giga* G10 9 MegaM10 6 Kilok10 3 Hectoh10 2 Dekada10 1 decid10 -1 centic10 -2 millim10 -3 microμ10 -6 nanon10 -9 picop femtof10 -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: BMI = 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 lb, and 1 ft = 12 in., 1 m = ft.; 1 in. = 2.54 cm)

1 kg2.205 lb X kg180 Ib X = 81.6 kg 1 m3.281 ft in. X m71 in. X = 1.8 m BMI (Kg/m 2 )Evaluation Below 18.5Underweight 18.5–24.9Normal 25.0–29.9Overweight 30.0–39.9Obese 40 and aboveMorbidly 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

(a) The displacement vector for a woman climbing 1.2 m up a ladder is. (b) The displacement vector for a woman climbing 1.2 m down a ladder is

The Components of a Vector

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.

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?

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.; x m 3 = 1 gal; 1 mL = m 3.

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, F 1, F 2, and F 3. Where F 1 = 50.0 N and F 2 = 90.0 N. Determine (a) the magnitude of F 3 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 units. Vector B points at an angle of 60.0° above the + x- axis and has a magnitude of units. Vector C points along the + x-axis and has a magnitude of 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, A y and A x. What are the magnitudes and directions of A x and A y ?