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Unformatted text preview: Why Study Physics? Physics 317K G General l Physics Ph i I TTH 9:30-11 AM (#56695) TTH 2-3:30 2 3 30 PM (#56700) • • utexas edu • Physics attempts to discover the physical laws that govern the natural world. These laws apply equally to living and nonliving systems and form the basis of all other sciences sciences. • In future courses you will encounter materials that depend on understanding basic physics. • Modern technologies such as computers, cell phones, lasers, and MRI have been made possible by advances in physics, and this will continue to be true for future innovations. innovations • Gaining knowledge in basic physics has become an integral part of a complete p p education. • A training in physics prepares one to solve problems regardless of the subject matter. Outline of Course Contents Textbook • Recommended: Richard Wolfson, Essential U i University it Ph Physics, i 3rdd Edition, Editi V Volume l 1 1. • You may also use other standard introductory physics books. Check out the large collection in the PMA library. • Free textbook from Rice University’s OpenStax College: . • Mechanics • Oscillations and Waves – 1D and 2D Motion – Simple p Harmonic – Newton’s Laws Oscillations – Energy Conservation – Wave Motion – Momentum Conservation – Sound – Rotational Motion and angular momentum • Heat and Thermodynamics – Thermal Physics • Fluid Mechanics – Energy Transfer − Statics of Fluids – Laws of Thermodynamics − Dynamics of Fluids Instructor and TA • Instructor – Zhen Yao, [email protected], 471-1058, RLM 13.208 – Office Hours: • Right after each class outside PAI 2.48 • Tuesday and Thursday11:30 am – 12:30 pm in RLM 13 208 13.208 • Other times by appointment • Teaching Assistant(s) – TBA – Discussion Sessions: TBA – Office Hours: TBA Administrative Issues • Course Pre- and Co-Requisites: Credit with a grade of at least C C- in Mathematics 408C or 408R; or credit with a grade of at least C- in 408K or 408N and registration in 408L or 408S; credit with a grade of at least C- or registration in Physics 117M. • Any questions – see Ms. Ms Kelly McCoy, McCoy Undergraduate Office, RLM 5.214, 471-8856 How to Do Well in Class • Basic Learning Steps – Read about the topic (Textbook): Before coming to class you are expected to have read the relevant materials from the t tb k for textbook f that th t day. d Ideally Id ll you should h ld come tto class l with ith many questions. – Untangle g it ((Lectures): ) The lectures will not simply p y regurgitate g g what you have read, rather they will focus on resolving the misconceptions and difficulties that you may have, with the help of demonstrations and interactive quiz questions and examples. – Challenge yourself (Homework): Try yourself before getting h l help. – Close the loop (Discussion sessions and office hours) • Your participation is required both prior to and during each lecture • Make sure to understand not memorize the materials • It is essential to keep up! Grading • Homework 25% • Midterm Exams 40% • Final Exam 35% • Semester grades will be determined by a class curve at the end of the semester and no prescribed cutoff values should be assumed. Typical Grade Scale • • • • • • • • • • • • A A AB+ B BC+ C CD+ D DD F >90 >85 >80 >75 >70 >65 >60 >55 >50 >45 >40 40 <40 Midterm Exams and Final Exam • Three evening midterm exams from 8 to 10 pm on Tuesdays February 14, March 21, and April 18. • The lowest midterm grade will be dropped. • No makeup midterm exam will be given. If you miss a midterm exam, the th missing i i one will ill b be th the one th thatt will ill b be d dropped. d • The final exam will be held on Tuesday May 16, 9 am to noon for the TTH 9:30-11 section section, or on Friday May 12 12, 9 am to noon for the TTH 2-3:30 section, as scheduled by the Registrar’s Office; no early final exam will be given • The final exam is comprehensive and mandatory • All exams are closed book. • A formula sheet will be provided to you during each exam. • Calculators may be used for numerical calculations only. Quest Homework Server • Download homework and submit answers at • Cost recovery charge of $30 per course ($60 for two or more courses) to use Quest • No late homework will be accepted accepted. • Lowest 2 homework grades will be dropped. • Do the homework yourself yourself. Copying answers deprives you of the value of homework problems and will hurt your exam grades. • Start working on your homework as soon as possible and as soon as you have obtained an answer to a problem, submit it — do don’t wait a u until you have a e so solved ed a all the eo other e p problems. ob e s. Units, Standards, and the SI System • W We will ill be b primarily i il working ki iin th the SI system, t where h th the b basic i mechanical h i l units are kilograms, meters, and seconds. • The meter is the length g of the p path traveled by y light in vacuum during a time interval of 1/299,792,458 of a second. • The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom. • The kilogram is defined by the mass of a platinum-iridium cylinder kept at the International Bureau of Weights and Measures at Sèvres, Sèvres France. France • Other systems include cgs unit systems and US customary unit systems. PT.3.2448 Scientific Notation and SI Prefixes • The vast range of quantities that occur in physics are best expressed with ordinary-sized numbers multiplied by powers of 10: – 31416.5 31416 5 = 3.1416510 3 14165 104 – 0.002718 = 2.71810–3 • Standard SI prefixes describe powers of 10. Every three powers of 10 gets a different prefix. Clicker Question How many femtoseconds are there in one minute? 1. 2. 3. 4. 5 5. 3.6 × 1018 6.0 × 1016 6.0 × 1015 1.7 × 1013 1 7 × 1014 1.7 Clicker 1-14 Unit Conversion • Units matter! Measures of physical quantities must always have the correct units. • Convert units by multiplying or dividing so that the units you don’t want cancel, leaving only the units you do want. – Example: On an interstate highway, a car is traveling at a speed of 38.0 m/s. Is the driver exceeding the speed limit of 75.0 75 0 mi/h? 38 m s 38 1609 mi 85 mi h 1 3600 h Clicker Question Clicker Question Modern electroplaters can cover a surface area of 60 m2 with one troy y ounce of gold g ((volume = 1.611 cm3 )). What is the thickness of the electroplated gold? 1. 2 2. 3. 4. A cement truck can pour 20 cubic yards of cement per hour Express this in ft3 /min. hour. /min 1. 1 2. 3 3. 4. 2.68 x 10-8 m 1 34 x 10-9 m 1.34 1.67 x 10-6 m 3.33 x 10-7 m Clicker 1-17 1/3 ft3/min 1.0 ft3/min 3 ft3/min 9 ft3/min Clicker 1-18 In this lecture you’ll learn Chapter 2 Lecture • The fundamental quantities that describe motion – Position – Velocity – Acceleration • The difference between average and instantaneous quantities • How to solve problems involving constant acceleration in one d e so dimension – Including the constant acceleration of gravity near E th’ surface Earth’s f Motion in a Straight Line Slide 2-1 Position and Displacement Slide 2-2 Average Velocity • Velocity is the rate of change of position (SI unit: m/s) – Average velocity over a time interval ∆t is defined as the displacement divided by the time: x v t – Average speed is distance divided by time • IIn one dimension, di i position iti can b be described by a positive or negative number on a number line, also called a coordinate system. – Position zero, the origin of the coordinate system, system is arbitrary and you’re free to choose it wherever it is convenient. • Displacement, denoted by ∆x, is change in position: ∆x = x2–xx1 where x1 and x2 are the initial and final positions, respectively. Slide 2-3 Slide 2-4 Instantaneous Velocity Clicker Question • Instantaneous velocity is the limit of the average velocity as the time interval becomes arbitrarily short: − In calculus, this limiting procedure defines the derivative dx/dt Michael rides his bike to a store 6 miles away. He rides at a speed p of 12 mph p for the first half of the trip p and then at 6 mph p for the remainder. What is his average speed for the entire trip? 1. 2. 3. 4. 5 5. x dx t0 t dt v lim – Instantaneous speed is the magnitude of instantaneous velocity. 7 mph 8 mph 9 mph 10 mph 11 mph h Slide 2-5 Clicker Question Clicker Question The figure Th fi shows h the th position iti off a squirrel i l vs. titime as it runs iin a straight line along a telephone wire. During what time interval does the squirrel q have the g greatest speed? p 1. 2. 3 3. 4. 5 5. Slide 2-6 Which people have the same average velocity during the entire time p period shown? 1. 2. 3 3. 4. 5. From A to B From B to C only F From B to t D From C to D only From D to E Slide 2-7 none Amy and Brad Amy and Cate Brad and Cate all three are the same Slide 2-8 Clicker Question Clicker Question The figure shows position-versus-time graphs for four objects. Which starts slowly and then speeds up? Suppose the position for a moving object is given by: x(t) = 3t2+2t+5, where x is measured in meters and t is measured in seconds seconds. Find the velocity at t = 2 ss. 1. 2. 3. 4. A. B. C. 6 m/s 10 m/s 13 m/s 14 m/s D. Clicker 2-9 Acceleration Example • Acceleration is the rate of change g 2 of velocity (SI unit: m/s ). – Average acceleration over a time interval ∆t is defined as the change in velocity divided by the v time: a t – Instantaneous acceleration is the limit of the average acceleration as the time interval becomes arbitrarily short: a lim t 0 Clicker 2-10 A 50-gram superball traveling at 25 m/s is bounced off a brick wall and rebounds at 22 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.5 ms, what is the magnitude of the average acceleration of the ball during this time interval? 1. 1 2. 3 3. 4. v dv t dt –A Acceleration l ti corresponds d tto th the slope of the velocity vs. time graph. Slide 2-11 13,428 13 428 m/s / 2 6,715 m/s2 857 m/s2 20 m/s2 Slide 2-12 Position, Velocity, and Acceleration Clicker Question • Individual values of position, velocity, and acceleration aren’t aren t related. – Velocity depends on the rate of change of position. – Acceleration depends on the rate of change of velocity. – An object can be at position x = 0 and still be moving. – An A object bj t can h have zero velocity l it and d still till b be accelerating. l ti Ball thrown straight g up: p At the peak of its trajectory, the ball has zero velocity, y, but it’s still accelerating. The graph shows position as a function of time for two trains running on parallel tracks. Which is true? 1. At time tB, both trains have the same velocity. 2. Both trains speed up all the time. 3. Both trains have the same velocity at some time before tB. 4. Somewhere on the graph, both trains have the same acceleration. Clicker 2-14 Slide 2-13 Constant Acceleration Example • With constant acceleration • When acceleration is constant, then displacement, – Velocity is a linear velocity, acceleration, and function of time ti time are related l t db by – Displacement is a quadratic function of time v v at 0 x 1 2 v0 v t x v0 t 12 at 2 An aircraft has a lift-off speed of 120 km/hr. What minimum constant acceleration does this require if the aircraft is to be airborne after a take-off run of 240 m? 1. 2. 3. 4. v 2 v02 2 a x where h x0 and d v0 are initial i iti l values at time t = 0, x and v are the values at an arbitraryy time t, and ∆x = x–x0 is the displacement. Slide 2-15 2.32 3 m/s /s2 3.63 m/s2 4.64 m/s2 5.55 m/s2 Slide 2-16 Example Clicker Question A car traveling at an initial speed v0 brakes and comes to a complete stop in a distance d. With the same braking force, what distance does the car travel before coming to rest if its initial speed is 2v0? An automobile driver puts on the brakes and decelerates from 28 m/s to zero in 12 s. What distance does the car travel? 1. 2 2. 3. 4 4. A. B. C. D. E E. 168 m 196 m 336 m 392 m 2d 4d d/2 d/4 d Clicker 2-18 Slide 2-17 The Acceleration of Gravity Clicker Question • The acceleration of g gravity y at any y point is exactly the same for all objects, regardless of mass. • Near N E Earth’s th’ surface, f the th value l off the th acceleration is essentially constant at g = 9.8 m/s2. • Therefore the equations for constant acceleration apply: – In I a coordinate di t system t with ith y axis i upward, they read In the absence of air friction, an object dropped near the surface of the Earth experiences a constant acceleration l ti off about b t 9.8 9 8 m/s / 2. This Thi means that th t the th 1 the rate at which the position of the object changes as 1. a function of time equals 9.8 m/s2. 2. object falls 9.8 meters during each second. 3 speed 3. d off the th object bj t increases i 9 9.8 8 m/s / d during i each h second. 4. object j falls 9.8 meters during g the first second only. y 5. speed of the object as it falls is 9.8 m/s. v v0 gt y 1 2 v0 v t y v0 t 12 gt 2 v 2 v02 2 g y Stroboscopic photo of a falling ball Slide 2-19 Clicker 2-20 Clicker Question Clicker Question On p planet X,, a cannon ball is fired straight g upward. p The p position and velocity of the ball at many times are listed below. Note that y we have chosen up as the positive direction. Time(s) Height(m) A ball is thrown straight up up. At the top of its trajectory trajectory, its Velocity(m/s) 0 0 20 1 17 5 17.5 15 2 30 10 3 37.5 5 4 40 0 5 37.5 -5 6 30 -10 10 7 17.5 -15 8 0 -20 What is the acceleration due to gravity on Planet X? A. B. C. D. E. -5 m/s2 -10 m/s2 -15 15 m/s2 -20 m/s2 None of these. A. velocity A l it iis zero, B. velocity is non-zero, C. velocity is zero, D. velocity is non-zero, acceleration l ti is i zero. acceleration is non-zero. acceleration is non-zero. acceleration is zero. Clicker 2-21 Clicker Question Clicker 2-22 Clicker Question Find the maximum height h of a ball thrown vertically upward with an initial velocity v0 = 30 m/s (assume g = 10 m/s2) A ball is thrown straight upward with an initial velocity vo. Assume no air resistance. If the initial velocity vo is doubled, the time to reach the apex of the trajectory: A) Doubles B) Increases by a factor of 4 A. 45 m B 60 m B. C. 90 m If the initial velocity vo is doubled, the maximum height of the ball: A) Doubles B) Increases by a factor of 4 Clicker 2-23 Clicker 2-24 Clicker Question Summary Standing on a roof, you simultaneously throw one ball straight up and another one straight down with the same initial speed. Neglecting air resistance, which ball hits the ground with greater speed? A. The ball thrown straight down A B. The ball thrown straight up C. Both balls have the same speed. • Position, velocity, and acceleration are the fundamental quantities describing motion. – Velocity is the rate of change of position. – Acceleration A l ti iis th the rate t off change h off velocity. l it • When acceleration is constant, simple equations relate position, velocity, acceleration and time acceleration, time. – An important case is the acceleration due to gravity near Earth’s surface. – The magnitude of the gravitational acceleration is g = 9.8 m/s2. Clicker 2-25 v v 0 at x 1 2 v0 v t x v 0 t 12 at 2 v 2 v 02 2 a x Slide 2-26 In this lecture you’ll learn Chapter 3 Lecture Motion in Two and Three Di Dimensions i Slide 3-1 Vectors • To describe position position, velocity velocity, and acceleration in three-dimensional space using the language of vectors • To resolve a vector into its components • To manipulate vectors algebraically • To transform velocities to different reference frames • To solve problems involving constant t t acceleration l ti in i two t dimensions – Including projectile motion due to the constant acceleration of gravity near Earth’s surface Slide 3-2 Adding Vectors • A vector is a quantity that has both magnitude and direction. direction – In two dimensions it takes two numbers to specify a vector. – In three dimensions it takes three numbers. – A vector can be represented by an arrow whose length corresponds to the vector’s magnitude magnitude. • To add vectors graphically, place the tail off the second vector at the head of the first. – Their sum is then the vector from the tail of the first vector to the head of the second. – Here is the sum of and . • Position is a vector quantity. – An A object’s bj position i i iis specified by giving its distance g and its direction from an origin relative to an axis. – Here describes a point 2.0 m from the origin at a 30˚ 30 angle to the axis. Slide 3-3 Slide 3-4 Vector Arithmetic Clicker Question • Vector addition is comm commutative tati e and associati associative e • To subtract vectors, add the negative of the second vector to the first: Which figure shows • To multiply a vector by a scalar, multiply the vector’s magnitude i d b by the h scalar. l – For a positive scalar the direction is unchanged. – For a negative scalar the direction reverses reverses. Clicker 3-6 Slide 3-5 Clicker Question Clicker Question Which figure shows Let the magnitudes of two displacement vectors be 20 m and 40 m, m respectively respectively. If the two vectors are added added, what is the only possible magnitude of the resultant vector out of the following choices? A. B B. C. D D. E. Clicker 3-7 0m 18 m 37 m 64 m 100 m Clicker 3-8 Vector Components Adding Vectors by Components • Any y vector in 2D can be written as the sum of two perpendicular vectors, which are called its components • To add vectors, vectors add the individual components: – , then where iˆ and ˆj are unit vectors in the x and y directions – Similarly, Si il l Ay A sin Ay tan A Ax2 Ay2 Ax • Similarly, a 3D vector can be resolved i t th into three perpendicular di l components: t Ax A cos A Ax2 Ay2 Az2 Clicker 3-9 Clicker Question Slide 3-10 Clicker Question What are the x- and y-components Cx and Cy of vector What is the correct expression for Ay, the y-component of the vector A? y 1) 2) 3) 4) 5) 1) 2) 3) 4) 5) Cx= –3 cm, Cy = 1 cm Cx= –4 cm, Cy = 2 cm Cx= –2 cm, Cy = 1 cm Cx= –3 3 cm cm, Cy = –1 1 cm Cx= 1 cm, Cy = –1 cm Clicker 3-11 A cos A sin -A cos -A sin N None off these th x A Clicker 3-12 Clicker Question Example The figure shows two vectors lying in the xy-plane. Determine the signs of the x- and y-components of A, B, and A+B. 1. Ax and Bx are both positive, the rest negative. 2 2. Ax and Bx are both negative, the rest positive. 3. Ay and Bx are both p positive, the rest negative. An ant on a picnic table travels 30 cm eastward eastward, then 25 cm northward and finally 15 cm westward. What is the magnitude of its net displacement? 1. 2. 3. 4. 29 cm 70 cm 57 cm 52 cm Clicker 3-13 Example Slide 3-14 Displacement and Velocity Vectors • Position of a particle: An ant on a picnic table travels 30 cm eastward, then 25 cm northward and finallyy 15 cm westward. What is its directional displacement with respect to its original position? 1. 2 2. 3. 4 4. • Displacement vector: • Velocity is the rate of change of position − Average e age velocity e oc ty − Instantaneous velocity 59° N of E 29° N of E 29° N of W 77° N of E 77 vx dx dy dz vy vz dt dt dt − Instantaneous velocity is always tangent to the path of the particle at every point Slide 3-15 Slide 3-16 Velocity and Acceleration Vectors Clicker Question • Acceleration is the rate of change g of velocity y An airplane makes a gradual 90 turn while flying at a constant speed of 200 m/s. The process takes 20 s to complete. For this turn, the magnitude of the average acceleration of the plane is: – Average acceleration: – Instantaneous accel.: • How the velocity y evolves depends p on the magnitude g of the acceleration as well as its direction: In general: g both speed and direction change 1. 2. 3. 4. 5. 40 m/s2 14 m/s2 0 m/s2 10 m/s2 20 m/s2 Slide 3-17 Relative Velocity • An object j moves with velocity y relative to one frame of reference, S’. • S’ moves at relative to a second reference f f frame, S. S • From the diagram, Slide 3-18 C...
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