If is measured with respect to the y axis (as in some problems), these equations will be incorrect. QUICK QUIZ 1.3 Which of the following are vector quantities and which are scalar quantities? Figure P7.55 Symbolic  57. Review. In problem solving, we often combine quantities mathematically through multiplication, division, addition, subtraction, and so forth. SOLUTION Convert meters in the speed to miles: 11 1609mim2 5 2.36 3 10 22 (38.0 m/s) mi/s 5 85.0 mi/h 1160mins 2 1601min h 2 Convert seconds to hours: (2.36 3 1022 mi/s) The driver is indeed exceeding the speed limit and should slow down. Approximate Values for Length, Mass, and Time Approximate values of various lengths, masses, and time intervals are presented in Tables 1.1, 1.2, and 1.3, respectively. Review Plan: Sound Properties: Chapters 13, 14 j Sections 13.2, 13.3, 13.6, 13.7, 14.3 j Quick Quizzes 13.2, 13.4, 13.7 j Example 14.3 j Active Figures 13.6, 13.7, 13.9, 13.22, 13.23 Chapter 13 j Problems 11, 15, 28, 34, 41, 45 Chapter 14 j Problem 27 Interference/Beats: Chapter 14 j Sections 14.1, 14.5 j Quick Quiz 14.6 j Active Figures 14.1–14.3, 14.12 j Chapter Problems 9, 45, 46 Circuits Skill Objectives: To understand mirrors and lenses, to calculate the angles of reflection, to use the index of refraction, and to find focal lengths. • Now focus on the expected result of solving the problem. Because of these factors, the roadways were ruled by gasoline-powered cars almost exclusively by the 1920s. What is the y component of the vector (3ˆi 2 8k (a) 3 m/s (b) 28 m/s (c) 0 (d) 8 m/s (e) none of those answers 5. (a) A particle moves in the 1x direction without reversing. Models are needed because the actual operation of the Universe is extremely complicated. Find unit-vector notation for the resultant displacement and its magnitude. The average velocity vx, avg of the particle is defined as the ratio of its displacement Dx to the time interval Dt during which the displacement takes place: vx,avg ; xf 2 x i Dx 5 Dt tf 2 ti 2.2b Pitfall Prevention | 2.1 Average Speed and Average Velocity The magnitude of the average velocity is not the average speed. The signs of Ax and Ay also are evident from Figure 1.18. : Bx 5 B cos 60.08 5 (40.0 km)(0.500) 5 20.0 km Find the components of B using Equation 1.10: By 5 B sin 60.08 5 (40.0 km)(0.866) 5 34.6 km : : (B) Determine the components of the hiker’s resultant displacement R for the trip. Assuming a familiarity wit, Routledge 2004 1. (a) What is its displacement? It is consistent with the mathematical representation, Equation 2.5, which is the equation of a straight line. The quantity x on the left side has the dimension of length. On the other hand, the magnitude of the displacement vector is the length of a straight line from your home to work or school. Principles of Physics: A Calculus-Based Text, Hybrid (with WebAssign Printed Access Card) Raymond A. Serway. Once we have introduced these analysis models, we shall see that they appear over and over again later in the book in different situations. Find the horizontal and vertical components of the 100-m displacement of a superhero who flies from the top of a tall building following the path shown in Figure P1.40. In this case, the velocity of the car has changed from an initial value of 30 m/s to a final value of 15 m/s in a time interval of 2.0 s. The average acceleration during this time interval is ax,avg 5 15 m/s 2 30 m/s 5 27.5 m/s2 2.0 s 2.4 | Acceleration 49 The negative sign in this example indicates that the acceleration vector is in the negative x direction (to the left in Figure 2.9). If s is a negative scalar quantity, the : : : vector s A is directed opposite to A . (Analysis models will be introduced in Chapter 2.) (This equation is a very common functional form.) The two most important developments in this modern era were the theories of relativity and quantum mechanics. Therefore, there are one and two significant figures, respectively, in these two values. Despite the word compact in the name, the detector is 15 meters in diameter. We will be substituting numerical values into definitions that we have seen, so this problem will be categorized as a substitution problem. (b) The average velocity for the motion of the race car cannot be evaluated unambiguously with the information given, but its magnitude must be some value between 0 and 100 m/s. In addition, you will only need to round once, on the final result. The following is a general problem-solving strategy to guide you through the steps. 2 1.4 | Order-of-Magnitude Calculations 9 where the ratio in parentheses is equal to 1. © Images-USA/Alamy in transportation; some experts predict that diminishing supplies of crude oil will push the cost of gasoline to prohibitively high levels within two more decades. We can generate another equation for the particle under constant acceleration model by recalling a result from Section 2.1 that the displacement of a particle is the area under the curve on a velocity – time graph. A surveyor measures the distance across a straight river by the following method (Fig. xviii PREFACE Henry Leap and Jim Lehman Figure 10.28  r v r r r Figure 3.2  r Expansion of the Analysis Model Approach. Rank the following five quantities in order from the largest to the smallest. Plus, get access to millions of step-by-step textbook solutions for thousands of other titles, a vast, searchable Q&A library, and subject matter experts on standby 24/7 for homework help. tan < sin < 5 : : 61. Express the resultant A 1 B in unit-vector notation. You want to move from the information contained in the word problem, through various representations of the problem that allow you to understand what is happening, to one or more equations that represent the situation in the problem and that can be solved mathematically for the desired result. A sidewalk is to be constructed around a swimming pool that measures (10.0 6 0.1) m by (17.0 6 0.1) m. If the sidewalk is to measure (1.00 6 0.01) m wide by (9.0 6 0.1) cm 34. (b) Compute the order of magnitude of the mass of a bathtub half full of copper coins. What is the sum of the measured values 21.4 s 1 15 s 1 17.17 s 1 4.00 3 s? 34 CHAPTER 1 | Introduction and Vectors What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 220 m), A (60 m, 80 m), E (210 m, 210 m), C (40 m, 230 m), and D (270 m, 60 m)? In Active Figure 2.2b, we show the result of drawing the lines representing the average velocity of the car as point is brought closer and closer to point . Now let us take the limit of this expression as the time increments shrink to zero, in which case the approximation becomes exact: Dx 5 lim oDxn 5 Dtlim ovn Dtn :0 n Dtn : 0 n n In this limit, the sum of the areas of all the very thin rectangles becomes equal to the total area under the curve. Expertly curated help for Principles of Physics: A Calculus-Based Text . What is its displacement from its starting point? To an order of magnitude, through how many revolutions will it turn over its lifetime? The limited range of electric cars was not a significant problem because the only roads that existed were in highly populated areas and cars were primarily used for short trips in town. Only 3 left in stock - order soon. The term on the right represents the total area of all the thin rectangles. A skater glides along a circular path. The distance traveled (a scalar quantity) is the length of the path, which in general can be much greater than the magnitude of the displacement. A good rule of thumb to use in determining the number of significant figures that can be claimed in a multiplication or a division is as follows: When multiplying several quantities, the number of significant figures in the final answer is the same as the number of significant figures in the quantity having the smallest number of significant figures. Find the radius of a solid aluminum sphere that balances a solid iron sphere of radius r Fe on an equal-arm balance. That is, what do they each extract from a source, be it a type of fuel or an electric battery? 2.4). Review Plan: Motion in 1 Dimension: Chapter 2 j Sections 2.1, 2.2, 2.4, 2.6, 2.7 j Quick Quizzes 2.3–2.6 j Examples 2.1, 2.2, 2.4–2.9 j Active Figure 2.12 j Chapter Problems 3, 5,13, 19, 21, 29, 31, 33 Motion in 2 Dimensions: Chapter 3 j Sections 3.1–3.3 j Quick Quizzes 3.2, 3.3 j Examples 3.1–3.4 j Active Figures 3.5, 3.7, 3.10 j Chapter Problems 1, 11, 13 Centripetal Acceleration: Chapter 3 j Sections 3.4, 3.5 j Quick Quizzes 3.4, 3.5 j Example 3.5 j Active Figure 3.14 j Chapter Problems 23, 31 Newton’s Laws: Chapter 4 Sections 4.1–4.6 j Quick Quizzes 4.1–4.6 j Example 4.1 j Chapter Problem 7 j Resultant Forces: Chapter 4 Section 4.7 j Quick Quiz 4.7 j Example 4.6 j Chapter Problems 29, 37 j MCAT Test Preparation Guide Welcome to your MCAT Test Preparation Guide Gravity: Chapter 11 j Section 11.1 j Quick Quiz 11.1 j Chapter Problem 5 Equilibrium Skill Objectives: To calculate momentum and impulse, center of gravity, and torque. 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