physic 1.1.PDF

Chapter 1: Motion, Force, and En*rgy Lesson 1.1 Foundations Introduction In this lesson, two foundational concepts needed throughout a course in physics are reviewed. Physics questions frequently involve equations and algebraically solving these equations for certain variables. Therefore, underst...

Chapter 1: Motion, Force, and En*rgy Lesson 1.1 Foundations Introduction In this lesson, two foundational concepts needed throughout a course in physics are reviewed. Physics questions frequently involve equations and algebraically solving these equations for certain variables. Therefore, understanding that the variables in physics equations have dimensions represented by a system of units is a useful tool in solving problems on the exam. In addition, it is important to recognize that two different types of variables may appear in questions. Scalars are quantities such as mass, volume, density, and temperature. Quantities associated with motion and direction-such as velocity, acceleration, and force-are vectors. Analyzing vector quantities involves the use of basic trigonometry , 1.1.01 Units and Dimensions Physical quantities are expressed in terms of dimensions. For example, an object has mass, temperature, and a size given by its length in each direction. Furthermore, the motion of the object is described in terms of its behavior over an interval of time. These dimensions of mass, temperature, length, and time are expressed in terms of a set of units. In contrast, pure numbers'such as the ratio of an object's length and width, are dimensionless and have no units. A common system of units is the Jnternational System of Units (or Sl system), with base units shown in Table 1.1. Table 1.1 Base Sl units. Physical quantity Unit Length meter (m) Mass kilogram (kg) Time second (s) Temperature Kelvin (K) Electric current ampere (A) Amount of substance mole (mol) lmportant quantities such as force, energy, and pressure are expressed in terms of derived Sl units, which are combinations of the basic Sl units. In physics, very large or very small values of these units are frequently encountered in calculations. To concisely display large or small values, the prefixes shown in Table 1.2 are added to Sl units.  *hapter 1: fu4oti*n, F*rcs, and En*rgY Table 1.2 List of Prefixes' MultiPlicative value Scientific Abbreviation Standard notation notation Prefix 10t2 T 1 ,000,000,000,000 LUI d 10s 1,000,000,000 giga 106 M 1,000,000 mega 103 1,000 kilo n1 10-1 deci 10-2 0.01 centi 1 0-3 0.001 milli 10-6 p 0.000001 micro '10-s 0.000000001 nano 10-12 0.000000000001 (km) and nanometer in the case of the dimension of lengtir' the prefixed units of kilometer For example, i;i#.;nt 103 meters and L0-e meters' respectively' f;oncePt Sheck'1.1 The|ightemittedbyalaserhasawavelengthof600nm.Whatisthiswavelengthinmeters? SmIutimul Note: The appendix contains the answer' for sorving physics problems' In any variabre X is a usefur technique Keeping track of the dimensions of to the dimensions of the right an algebraic ir'" Jimensions [Xl of the left side must be equal side: "qrrr,on, x=Y=[x]=[r] featured in an equation process by which the units of one vaniabre Dimensionar anarysis refers to the canbedeterminedalgebraica||yusingtheunit=ottheothervariab|eswithinthesameequation. 4  Chapter 1: Motion, Force, and Energy NeMon's law of universal gravitation states that the force F between two objects is equal to the product of the gravitational constant G, the masses of the objects (mr, mz), and the inverse of their separation length squared ts; Gmrm2 r- = --iT- The dimensions of force are the product of mass and length divided by time squared. What are the dimensions of G? Solution Note: The appendix contains the answer. * Scalars and Vectors are physical quantities characterized by only a size or a magnitude-for example, the amount of elapsed during an experiment, or the mass of an object. Vector quantities are characterized by a in addition to a magnitude. kinematic variables that describe the motion of an object (displacement, velocity, and acceleration, are discussed in L.esson 1.2) are vector quantities because an object can move in any arbitrary rn in space. Furtliermore, vector fields (eg, the electric field) represent the magnitude and direction a vector at each point in sfiace. can be represented in tvto.equivalent ways, as shown in Figure 1.1. A vector is a quantity that is represenbd by both a magnitude and a direction {eg, displacement, velocity; accoleration, force, momentum) lndicated as i Represented graphically by an arrow. Length = msgn6ufls = lil. Points in a direction Ax = lAl cos 0 co c Ay = lAlsln I o CL E o o +y * 1 I, +x x-componentAx Ll Vector characteristics.  Ohapter 1: Motion, Force, and EnergY shows the magnitude and direction' The one method is to represent the vector with an arrow, which and the direction of the arrow is aligned with the length of the arrow represents the vector's magnitude, direction of the vector. In the second approach, an xy-coordinate system is introduced. The vector (denoted by '4) can then be Av) with respect to this coordinate system: represented in terms of x- and y-components 1n-, A = (Ax, Av) form a right triangre inclined at an angle 0 Furthermore, as shown in Figure 1.1, the vector components of the triangle, and A" and Av are the adjacent above the x-axis. The vector magnitude is the hypotenuse trigonometric ratios can be used to express the vector and opposite legs of the resulting triangle. Hence, cosine functions: components in t,erms of the magnitude l,4l and the sine and A = (lAlcos 9, lAl sin 9) square root of the sum of the squares of the x- Moreover, by the Pythagorean theorem, l,al is bqual to the and y-comPonents: A?+ A1 graphically or via components' The sum of two The addition of twp vectors can be performed either shown in Figure 1'2' vectors ,4 and d can be determined using the tip'to'tail method Vectors i ano d Step 1 Step 2 Move tail of Fto tiP of A Figure 1.2 Graphical addition of two vectors' that it touches the tip (ie, head) of the with this method, the tail of the arrow representing.4 is shifted such represented by the arrow connecting 1."Or"renting B. tne sum (orresultant vector) 1+ F is then "rro* the tail of F to the tip of the shifted A. The components of '4 + E equal the sum of ln terms of components, vector addition is straightforward. the components of each vector (see Figure 1'3): A+E=(Ax+Bx,Ay+By) o  Chapter 1: Motion, Force, and Energy 1.3 Vector addition by components. Vector A = (O m, 1*m) and vector E = @ m, 20 m). What is the difference between the two vectors, A - E , and what ihe magnitude of the difference ;1 - d;Z Solution '. Ibte: The appendix contains the answer.