Unformatted text preview: Physics 2170/2175 a 4 hr elementary physics course MW 10:30
12:30 2025 Science Lecturer: Rajendra Pokharel [email protected] 317 Physics Hours: MW 1:30 – 3:30 Course IntroducKon o Calculus based physics means you need to know calculus o Covers (Chapter 1 – 22): Mechanics: Mo8on, forces, energy, rota8on, gravita8on, oscilla8ons and waves, ﬂuids Thermodynamics: Temperature, thermal energy, ideal gases, entropy How this class works I Lectures: * both PowerPoints and chalk boards lectures will be posted on Blackboard and you need to take notes as well * discuss the basic concepts, applica8ons and problem solving * three 1
hr exams and the comprehensive ﬁnal exam NO MAKE
UP EXAMS! Quiz sec,ons: you will discuss the assigned homework problems there. I will not grade these problems, however you will be evaluated by a number of quizzes in quiz sec8on How this class works II Details are in the syllabus How this class works III You are responsible for your grades No extra credit and no last minute grade adjustments In order to get good grades
do as many problems as possible (at least all assigned homework and solved problems from the text book)
solve problems by yourself, struggle with them unKl you ﬁgure them out
pracKce, pracKce and pracKce! Why physics? Learning physics enable one to analyze physical situaKons, develop suitable (mathemaKcal) models and predict behavior shapes a powerful analyKcal style of thinking requiring concepts reasoning and mathemaKcal problem solving techniques, which is essenKal in all sciences, engineering and other disciplines. Physical quanKKes and measurements I We measures physical quanKKes, like, for example:
mass and height of a person
Kme it takes to go from one place to another
power of an automobile engine
speed of a train the measurement involves these steps:
deﬁning a standard, called unit, that is, agreeing to call a certain length one meter, for example.
comparing to ﬁnd out how many such units are there in the quanKty in quesKon
expressing the measurement in the number and name of the units for example, 5 meters, 10 kilograms, 30 years, 1.5 amperes, etc. Physical quanKKes and measurements II The number alone does not make any sense, you must write what unit you are using. 5 meters and 5 feet are not the same, and 5 alone makes no sense. If you ask your European friend how tall he is and get an answer “I am 2”, it does not make any sense. However, you might guess that he may be talking about 2 meters since an adult cannot be 2 feet tall. Base and derived units? Take the quanKty volume. Whatever be the shape, it really contains the dimensions of lengths. Simplest cases: cube: Volume = length 3 sphere: Volume = 4 π r 3 3 If we measure length or radius in meters, volume will have a units of cubic meter (meter3). Here cubic meter is derived unit. It is derived from the base unit meter. The InternaKonal System of Units Science is internaKonal – need to agree on what units to use. The agreed units, called SI units, are: Basic length: meter (m) mass: kilogram (kg) Kme: second (s) electric current: ampere (A) Derived force: energy: power: newton (N) joule (J) wad (W), etc. 1 N = 1 kgm/s2. Preﬁxes and powers of 10 To denote very small, small, large, very large quanKKes preﬁxes and powers of 10 are use in the units. Examples: 0.000000007 m = 7×10
9 m = 7 nano meters (nm) 50000 wads (W) = 5×104 wads = 50×103 wads = 50 kilowads (kW) 10
15 10
12 10
9 10
6 10
3 10
2 femto (f) pico (p) nano (n) micro (μ) milli (m) cenK (c) 103 106 109 1012 kilo (k) Mega (M) giga (G) tera (T) More examples: 6 μs = 6×10
6 s 9 pF = 9×10
12 F 50 MJ = 50×106 J = 5×107 J ConverKng units I How many minutes are there in 190 seconds? Here you are converKng from seconds to minutes. First you need a conversion factor, which you can get from this relaKon 60 s = 1 min The conversion factor we need here is 1min/60s. MulKply by it: 190s × 1min/60s = 2.5 min If you need to convert the other way round, i.e., from minutes to seconds, the conversion factor is 60s/1min Note: • that the value of conversion factor is just 1, and mulKplying by it does not alter the value as it should not, it simply converts the units. You see diﬀerent number in diﬀerent units, the measurement is not changed. • You need to do the unit conversion very onen – pracKce doing it now. ConverKng units II Now do this yourself: • The speed of light in vacuum is 3×108 m/s. Write this speed in mi/hr. • Speed limit (free way) in Michigan is 70 mi/hr. What is the speed limit in km/hr? In m/s? • A block of aluminum has a volume of 400000 cm3. Convert this volume into m3. • DensiKes of copper is 8.92 g /cm3. What is the density in kg/m3. • Speciﬁc heat capacity of aluminum is 0.215 cal/goC. Convert this into J/kgoC. (hint: the famous Joule’s experiment set this equivalency in 1843: 1 cal = 4.186 J) Unit Conversion
Applied: NASA • In 1999, a $125 million dollar spacecran sent to orbit mars, was destroyed as it adempted to land on Mars’ surface. • The root cause was due to the fact that the American company (Lockheed MarKn), which fabricated the booster rockets, provided informaKon regarding the rocket’s thrust in American units (n). While NASA was under the assumpKon the units were in S.I. units (m). • “Metric mishap caused loss of NASA orbiter”
CNN • Consider the quanKKes
distance, radius, length, height. They all are measured in units of length. We say that all these quanKKes have dimension of length. • Take volume. All volumes are measured in cubic meters (or cubic feet or cubic inches etc). Whatever is the shape, volume consists of three dimensions of lengths. • Dimensions of the base quanKKes length, mass and Kme are usually denoted by L, M and T, respecKvely. Thus the dimension of volume is L3. • Similarly dimension of speed (= distance/Kme) is L/T or LT
1, that of density (=mass/volume) is M/L3 or ML
3. QuesKon: What are the dimensions of force, energy, pressure? (use the deﬁning relaKons force = mass × acceleraKon, energy ~ mass × velocity2, pressure = force/area) Dimensional analysis I Dimensional analysis II • Dimension analysis essenKally consists of checking whether or not a given combinaKon of quanKKes in a formula gives correct units. SomeKmes we use it to derive a formula. • Example: the Kme period (T) of a simple pendulum is given by T = 2π l / g Now suppose you are not sure if you remembered this formula correctly, or got confused whether it was l/g or g/l under the square root. You can check this right away: Len side: [T] = T Right side: √(L/LT
2) = √(1/T
2) = √(T2) = T We see that the formula is right (we can’t say about the factor 2π). Dimension analysis cannot sedle the value of a dimensionless numerical factor. Ques6on: What do you mean by ‘dimensionless’ quan8ty? Examples? Signiﬁcant ﬁgures Examples: • • • 0.5 s has one signiﬁcant ﬁgure, as does 0.0005 s. 5.05 s has 3 signiﬁcant ﬁgures, just like .0505 s 1.500 has 4 signiﬁcant ﬁgure, as does 150.0 Suppose we measured the radius of a circular disk to be 1.5 m. If we want to calculate area (= πr2), what value of π should we plug in? 3.1, 3.14, 3.142 or 3.14159? Ans: 3.1, since radius is given up to 2 signiﬁcant ﬁgures and we really do not get extra accuracy by using π with more than 2 signiﬁcant ﬁgures. Stop pretending that you will get extra accuracy just from maths. It depends on how accurate the radius is given or how accurate you can measure radius with the instruments you used. Signiﬁcant ﬁgures (contd…) In the last example, even if we use π = 3.1, we get area = 6.975 m2, a signiﬁcant ﬁgure of 4. The given radius has only 2 signiﬁcant ﬁgures. So the acceptable answer is 7.0 m2. 6.98 m2 does not represent the fact that we are given only 2 signiﬁcant ﬁgures in radius measurement. Another example: A rectangle with sides of 1.13789 m and 2 m has an area of 2 m2. Uncertainty Example Take the following measurements of a rectangle: length, l = 15.2 cm width, w = 5.0 cm Assume that the accuracy to which these lengths are measured is ±0.01 cm: δ l = δ w = ±0.01cm That is, the length may well be 15.19 cm or 15.21 cm. Ques,on: What is the uncertainty in area? Answer: δA ⎛ δl ⎞ ⎛ δ w ⎞ ⎛ 0.01 ⎞ ⎛ 0.01 ⎞
2 2 2 2 A = ⎜ ⎟ +⎜ =⎜ + = 0.021 ⎝l⎠ ⎝ w⎟ ⎠ ⎝ 15.2 ⎟ ⎜ 5.0 ⎟ ⎠⎝ ⎠
2 2 2 2 δA ⎛ δl ⎞ ⎛ δ w ⎞ ⎛ 0.01 ⎞ ⎛ 0.01 ⎞ = ⎜ ⎟ +⎜ + = 0.021 ⎟=⎜ ⎝l⎠ ⎝ w⎠ ⎝ 15.2 ⎟ ⎜ 5.0 ⎟ ⎠⎝ ⎠ A Note: δ is uncertainty in area while δ A is rela8ve uncertainty in A A area. δ A = 0.021 × A = 0.021 × 76 cm 2 = 0.1596 cm 2 = 0.26 cm 2 And ﬁnally, before we move on to next topics… • Always include units in your ﬁnal answer. The car was not traveling at 10, the car was traveling at 10 m/s. • Always include units during each intermediate step. This will help you determine whether or not you need to include a conversion factor to change the units. OR If you plug in all values in SI, your ﬁnal answer is certain to be in SI and you need not worry about conversion in the intermediate steps. • Always check that your answer has units appropriate for expressing the physical quanKty (dimensional analysis). The car was not traveling at 10 kg m/s2. MoKon in one dimension Some basic concepts and terms • Here we are studying one dimensional kinemaKcs (kinemaKcs = the branch of physics concerned with describing the moKon of objects). One dimensional moKon means moKon along a straight line. • In physics we onen refer to a parKcle. A parKcle is an idealizaKon of a massive body as a point in order to simplify the analysis. By parKcle we always mean a point like object that has a mass but is of inﬁnitesimally small size. • MoKon of a parKcle is completely known if its posiKon in space is known at all Kmes. PosiKon and displacement • A parKcle’s posiKon is its loca8on with respect to a chosen reference point, which we can take it to be the origin of a coordinate system. • For one dimensional moKon, we can use the x
coordinate for posiKon of a parKcle. If the parKcle is at origin at Kme t = 0 (i.e., the clock started at that instant), we describe this situaKon as x(t=0) or x(0) = 0. The parKcle may well start from some other posiKon at t = 0. We may label this iniKal posiKon as xi. Aner some Kme interval, Δt, the parKcle is in some new posiKon xf. In this case the parKcle has undergone a displacement Δx = xf
xi. Note that displacement is a signed quanKty. t = 0 xi t =Δt xf x 0 Velocity Average velocity of a parKcle is its displacement divided by Kme: Δx x f − xi vavg = = Δt Δt In other words, it is a measure of in what rate posiKon changes with Kme, or rate of change of displacement. If displacement changes at constant rate, we do not need to talk about average. Then this is the case of constant velocity and we drop the subscript avg. If we want us to remind ourselves that we are actually talking about 1D moKon along x (or in to disKnguish from moKon is other direcKon in Δx x f − xi case of 2D or 3D moKon), we label v with x: vx = = Δt Δt If velocity is not constant, the approximaKon of velocity by the average velocity is the beder the smaller Δt we chose. In the limit , we Δt → 0 get the instantaneous velocity, which is the velocity at the given instant. Δx dx vx = lim = Δt → 0 Δt dt PosiKon vs Kme graphs x Δx x t t Δt slope = lim • What to the colored lines mean? • IdenKfy instantaneous velocity with the slope. Note how secant line becomes a tangent when Δt approaches zero. x (m) • Interpret the following graph. 3 2 2 3 6 8 Δx dx = = vx Δt → 0 Δt dt t (s) ...
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