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## Recipe as long as PHY 107 1. Study hard (use the grade of test 1 as a gauge) 2. Come to

Scott, Gail, Food Editor has reference to this Academic Journal, PHwiki organized this Journal Recipe as long as PHY 107 1. Study hard (use the grade of test 1 as a gauge) 2. Come to class 3. Do the homework ( in addition to more) 4. Do not stay behind 5. If you have questions get them answered 6. If you have a problem tell me about it PHY 107 Home page: http://www.physics.buffalo.edu/phy107/ Instructor Coordinates: Name: Surajit Sen Office: 325 Fronczak Telephone: 645-2017 ext.193 E-mail: sen@buffalo.edu Office Hours: Mondays/Tuesdays 9-10 am in addition to By Appointment

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Extra help as long as engineering majors: Begin at the engineering home page: www.eng.buffalo.edu From there click on Freshman Programs: Then on Small Groups Click on submit to sign up If you cannot sign up contact Bill Wild at: wgwild@eng.buffalo.edu Text book: Physics as long as scientists in addition to Engineers Vol.1, 3rd edition, by Fishbane, Gasiorowicz in addition to Thornton (Prentice Hall) Student Solution Manual as long as the textbook above. This contains worked solutions to selected odd-numbered problems. Chapter 1 Tooling Up In this chapter we shall introduce the following concepts which will be used throughout this semester ( in addition to beyond) 1. Units in addition to systems of units 2. Uncertainties in measurements, propagation of errors 3. Vectors (vector addition, subtraction, multiplication of a vector by a scalar, decomposition of a vector into components) (1-1)

Physics Classical (be as long as e 1900) (PHY 107, PHY 108) Modern (after 1900) (PHY 207) In PHY 107 we study mechanics that deals with the motion of physical bodies using Newtons equations. These equations yield accurate results provided that: The bodies in question are macroscopic (roughly speaking large, e.g. a car, a mouse, a fly) 2. The bodies do not move very fast. How fast The yardstick is the speed of light in vacuum. c = 3108 m/s (1-2) The Scientific Method Carry out experiments during which we measure physical parameters such as electric potential V, electric current I, etc Form a hypothesis (assumption) which explains the existing data Check the hypothesis by carrying out more experiments to see if the results agree with the predictions of the hypothesis Example: Ohms law The ratio V/I as long as a conductor is a constant known as the resistance R conductor (1-3) We must measure ! Example: I step on my bathroom scale in addition to it reads 150 150 what 150 lb 150 kg For each measurement we need units. Do we have to define arbitrarily units as long as each in addition to every physical parameter The answer is no. We need only define arbitrarily units as long as the following four parameters: Length, Mass , Time , Electric Current In PHY 107 we will need only units as long as the first three. We will define the units as long as electric current in PHY 108 (1, 4)

In this course we shall use the SI (systeme internationale) system of units as follows: Parameter Unit Symbol Length meter m Mass kilogram kg Time second s Electric Current Ampere A All other units follow from the arbitrarily defined four units listed above Note: SI used to be called the MKSA system of units (1-5) The meter 1 meter AB/107 (1-6) The st in addition to ard meter It is a bar of Platinum-Iridium kept at a constant temperature The meter is defined as the distance between the two scratch marks (1-7)

The kilogram (kg) It is defined as the mass equal to the mass of a cylinder made of platinum-iridium made by the International Bureau of Weights in addition to Measures. All other st in addition to ards are made as copies of this cylinder (1-8) The second (s) The second is defined as the duration of the mean solar day divided by 86400 The mean solar day is the average time it takes the earth to complete one revolution around its axis Where does the 86400 come from 1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 seconds Thus: 1 day 24 60 60 = 86400 s (1-9) 10-12 please correct! Most common Examples: 1 km = 1000 m 1 ms = 10-3 s (1-10)

Question: How do we define all other units Answer: Using an equation that connects the parameter whose units we wish to define with other parameters whose units are known. Example 1: Find the units of acceleration h = gt2/2 Solve this equation as long as g g = 2h/t2 Units of left Units of right h in addition to side h in addition to side Units (g) = units (2h/t2) = m/s2 Note: The number 2 has no units (1-11) g = Example 2: Find the units of as long as ce Newtons second law F = ma Units of left Units of right h in addition to side h in addition to side Units(F) = units(m) units(a) = kg.m/s2 Note: We call the SI unit of as long as ce the Newton in honor of Isaac Newton who as long as mulated the three laws of motion in mechanics. Symbol: N (1-12) = Uncertainty in Measurement (1-13) There is no such thing as a perfectly accurate measurement. Each in addition to every measurement has an uncertainty due to: 1. the observer, 2. the instrument, in addition to 3. the procedure used How do we express the uncertainty in a measurement Assume that we are asked to measure the length L of an object with the ruler shown on page (1-14). The smallest division on this ruler is 1 mm. The uncertainty L in L using that particular ruler is 1 mm. (If one is careful one can reduce it to 0.5 mm). If L is found to be 21.6 cm we write this as: L = (21.6 0.1)cm This simply means that the real value is somewhere between 21.5 cm in addition to 21.7 cm. We can give L using three significant figures

(1-14) The smallest division of this ruler is equal to 1 mm millimeters inches We are given the ruler shown on page (1-14) in addition to are asked to measure the width L1 in addition to height L2 of the rectangle shown L1 = (21.6 0.1) cm L2 = (27.9 0.1) cm Area A = L1L2 = 21.627.9 = 602.6 cm2 The uncertainties L1 in addition to L2 in the measurement of L1 in addition to L2 will results in an error A in the calculated value of the rectangle area A. This is known as error propagation. (1-15) A Dimensional Analysis The dimensional analysis of a physical parameter such as velocity v, acceleration a , etc expresses the parameter as an algebraic combination of length [L], mass [M], in addition to time [T]. This is because all measurements in mechanics can be ultimately be reduced to the measurement of length, mass , in addition to time. [L], [M], in addition to [T] are known as primary dimensions How do we derive the dimensions of a parameter We use an equation that involves the particular parameter we are interested in. For example: v = x/t . In every equation [Left H in addition to Side] = [Right H in addition to Side] Thus: [v] = [L]/[T] = [L][T]-1 (1-16)

Note: The dimensions of a parameter such as velocity does not depend on the units. [v] = [L][T]-1 whether v is expressed in m/s, cm/s, or miles/hour Dimensional analysis can be used to detect errors in equations Example: h = gt2/2 [LHS] = [RHS] [LHS] = [h] = [L] [RHS] = [gt2/2] = [g][t2] = [L][T]-2[T]2 = [L] Indeed [LHS] = [RHS] = [L] as might be expected from the equation h = gt2/2 which we know to be true. (1-17) g Note 1: If an equation is found to be dimensionally incorrect then it is incorrect Note 2: If an equation is dimensionally correct it does not necessarily means that the equation is correct. Example: Lets try the (incorrect) equation h = gt2/3 [LHS] = [L] [RHS] = [g][t2] = [L] Even though [LHS] = [RHS] equation h = gt2/3 is wrong! (1-18) g Physical Quantities Scalars Vectors A scalar is completely described by a number. E.g. mass (m), temperature (T), etc A vector is completely described by : Its magnitude Its direction Example: The displacement vector magnitude = 30 paces direction = northeast (1-19)

Vector notation 1. A vector is denoted either by an arrow on top or by bold print. Example: The vector of acceleration a is written either as: or as: a Both methods are used 2. The magnitude of a vector is denoted either by the symbol: or by the symbol of the vector written with regular type. Example: the magnitude of the acceleration vector can be written either as: or as: a 3. A vector is represented by an arrow whose length is proportional to the vectors magnitude. The arrow has the same direction as the vector (1-20) a Vector addition (geometric method) Recipe as long as determining R = A + B (see fig.a) At the tip of the first vector (A) place the tail of the second vector (B) 2. Join the tail of the first vector (A) with the tip of the second (B) Note 1: A + B = B + A (see fig.b) Note 2: the above recipe can be used as long as more than two vectors (1-21) A + B B + A We are given vectors A, B, in addition to C in addition to are asked to determine vector S = A + B + C At the tip of A we place the tail of B At the tip of B we place the tail of C To get S we join the tail of A with the tip of C (1-22)

Negative of a vector We are given vector B in addition to are asked to determine B 1. Vector B has the same magnitude as B 2. Vector B has the opposite direction (1-23) Vector Subtraction (geometric method) We are given vectors A in addition to B are are asked to determine T = A B Determine B from B Add vector (-B) to vector A using the recipe of page (1-21) A B (1-24) Multiplication of a vector B by a scalar b; determine bB The magnitude bB = bB The direction of bB depends on the algebraic sign of b If b > 0 then bB has the same direction as B If b < 0 then bB has the opposite direction of B (1-25) How to check whether an xyz coordinate system is right h in addition to ed Rotate the x-axis in the xy-plane along the shortest angle so that it coincides with the y-axis. Curl the fingers of the right h in addition to in the same direction The thumb of the right h in addition to must point along the z-axis (1-32)

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