PHY2053 Review Book PDF

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Goes through practice problems from past exams all the way back to 2015....

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PHY 2053 Exam Solutions Manual August 23, 2015 Authors: Tenured Associate Professors Ivan Furic and Heather Ray University of Florida

NOTE: Textbook problems referenced in this manual use the numbering system from version 2 of the textbook!

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CONTENTS

Contents 1 How To Succeed in PHY 2053

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2 Basic Math Skills

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3 Problem Solving Techniques

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4 Chapter 1: Introduction 4.1 Spring 2015 Exam 1, Prob. 7-9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 Chapter 2: Motion Along a Line 5.1 Spring 2015 Final Exam, Prob. 24-26 . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Chapter 3: Motion in a Plane 6.1 Spring 2015 Exam 1, Prob. 13-15 . . . . 6.2 Spring 2015 Exam 1, Prob. 16-18 . . . . 6.3 Spring 2015 Exam 1, Prob. 34-36 . . . . 6.4 Spring 2015 Makeup Exam, Prob. 25-27 6.5 Fall 2014 Final Exam, Prob. 37-39 . . . 6.6 Fall 2014 Makeup Exam, Prob. 22-24 . .

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12 12 13 14 16 17 19

7 Chapter 4: Force and Newton’s Laws of Motion 7.1 Spring 2015 Exam 1, Prob. 22-24 . . . . . . . . . 7.2 Spring 2015 Final Exam, Prob. 27-29 . . . . . . . 7.3 Fall 2014 Makeup Exam, Prob. 19-21 . . . . . . . 7.4 Spring 2015 Exam 1, Prob. 31-33 . . . . . . . . . 7.5 Spring 2015 Makeup Exam, Prob. 28-30 . . . . . 7.6 Spring 2015 Exam 1, Prob. 28-30 . . . . . . . . . 7.7 Spring 2015 Exam 1, Prob. 19-21 . . . . . . . . . 7.8 Spring 2015 Exam 1, Prob. 40-42 . . . . . . . . . 7.9 Spring 2015 Exam 1, Prob. 37-39 . . . . . . . . .

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20 20 21 22 23 24 25 26 28 31

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8 Chapter 5: Circular Motion 8.1 Fall 2015 Makeup Exam, Prob. 7-9 . . . 8.2 Fall 2014 Exam 2, Prob. 25-27 . . . . . . 8.3 Fall 2014 Final Exam, Prob. 19-21 . . . 8.4 Spring 2015 Exam 2, Prob. 7-9 . . . . . 8.5 Spring 2015 Final Exam, Prob. 30-32 . . 8.6 Spring 2015 Exam 2, Prob. 28-30 . . . . 8.7 Spring 2015 Makeup Exam, Prob. 31-33 8.8 Fall 2014 Exam 2, Prob. 7-9 . . . . . . .

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33 33 34 36 38 41 43 44 46

9 Chapter 6: Conservation of Energy 9.1 Spring 2015 Exam 2, Prob. 10-12 . . . . 9.2 Fall 2014 Final Exam, Prob. 22-24 . . . 9.3 Spring 2015 Makeup Exam, Prob. 34-36 9.4 Fall 2014 Makeup Exam, Prob. 37-39 . . 9.5 Spring 2015 Final Exam, Prob. 33-35 . .

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47 47 48 49 50 51

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CONTENTS 9.6 Fall 2014 Exam 2, Prob. 10-12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.7 Spring 2015 Exam 2, Prob. 22-24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.8 Spring 2015 Exam 2, Prob. 34-36 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Chapter 7: Linear Momentum 10.1 Spring 2015 Exam 2, Prob. 19-21 10.2 Fall 2014 Final Exam, Prob. 7-9 . 10.3 Spring 2015 Exam 2, Prob. 43-45 10.4 Fall 2014 Exam 2, Prob. 22-24 . . 10.5 Spring 2015 Exam 2, Prob. 37-39

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11 Chapter 8: Torque and Angular Momentum 11.1 Spring 2015 Exam 2, Prob. 16-18 . . . . . . . 11.2 Fall 2014 Exam 2, Prob. 16-18 . . . . . . . . . 11.3 Spring 2015 Exam 2, Prob. 25-27 . . . . . . . 11.4 Fall 2014 Final Exam, Prob. 31-33 . . . . . . 11.5 Spring 2015 Final Exam, Prob. 36-38 . . . . . 11.6 Spring 2015 Exam 2, Prob. 13-15 . . . . . . . 11.7 Fall 2014 Exam 2, Prob. 19-21 . . . . . . . . . 11.8 Spring 2015 Makeup Exam, Prob. 37-39 . . . 11.9 Spring 2015 Exam 2, Prob. 40-42 . . . . . . . 12 Chapter 9: Fluids 12.1 Fall 2014 Makeup Exam, Prob. 10-12 . . 12.2 Spring 2015 Final Exam, Prob. 6-8 . . . 12.3 Spring 2015 Makeup Exam, Prob. 7-9 . . 12.4 Spring 2015 Final Exam, Prob. 18-20 . . 12.5 Spring 2015 Makeup Exam, Prob. 10-12 12.6 Fall 2014 Makeup Exam, Prob. 28-30 . . 12.7 Spring 2015 Final Exam, Prob. 9-11 . . 12.8 Spring 2015 Makeup Exam, Prob. 40-42 12.9 Spring 2015 Final Exam, Prob. 39-41 . . 13 Chapter 10: Elasticity and Oscillations 13.1 Fall 2014 Final Exam, Prob. 13-15 . . . 13.2 Fall 2014 Makeup Exam, Prob. 16-18 . . 13.3 Spring 2015 Makeup Exam, Prob. 13-15 13.4 Spring 2015 Final Exam, Prob. 12-14 . . 14 Chapter 11: Waves 14.1 Spring 2015 Makeup Exam, Prob. 16-18 14.2 Spring 2015 Final Exam, Prob. 15-17 . . 14.3 Fall 2014 Makeup Exam, Prob. 25-27 . . 14.4 Fall 2014 Final Exam, Prob. 10-12 . . . 14.5 Fall 2014 Final Exam, Prob. 16-18 . . . 14.6 Spring 2015 Makeup Exam, Prob. 19-21

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57 57 58 59 61 62

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65 65 66 67 68 70 72 73 74 77

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96 96 97 98 100 101 103

4 15 Chapter 12: Sound 15.1 Fall 2014 Makeup Exam, Prob. 13-15 . . 15.2 Spring 2015 Final Exam, Prob. 21-23 . . 15.3 Fall 2014 Final Exam, Prob. 28-30 . . . 15.4 Spring 2015 Makeup Exam, Prob. 22-24 15.5 Spring 2015 Makeup Exam, Prob. 43-45 15.6 Fall 2014 Final Exam, Prob. 25-27 . . . 15.7 Spring 2015 Final Exam, Prob. 42-44 . .

CONTENTS

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104 104 106 107 109 110 111 112

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1

How To Succeed in PHY 2053

Previously, this class had high instances of academic fraud (students purchasing homework solutions before the due date thus buying a perfect score for the homework, and students bring pre-purchased formula sheets with solutions to common types of problems on them to the exams). As a result exams had to be excessively difficult, to allow us to separate those who truly mastered the material (ie deserve an A) from those who did not. Therefore, as of Fall 2014 the grading components and structure of the exams and quizzes for this class has changed. Homework is no longer worth any points toward your final grade. A large part of learning physics is being able to identify common situations and to intuitively know how to approach these problems. This intuition is best built through practicing problems. To reinforce basic concepts and problem types that are offered in the homework, quizzes and exams are now based on homework problems. This handbook offers solutions to many of the exam problems given in Fall 2014 and Spring 2015. As this is intended as a tutoring device to carefully walk you through the thought process behind solving physics problems, these solutions contain many, many more steps than a C-level student would need to use to solve these problems. Please do not be frightened! Tips for succeeding in this course: • Keep up with the course! Once you get behind in reading chapters and doing problems you will have a very difficult time catching up • Attend lecture. We often do problem solving in lecture, and perform demos that most students say help them to visualize the physics concept we’re learning. • Attend both recitation sessions each week. Teaching Assistants who lead recitations are tutors. You have paid for them with your credit hours. Recitations are smaller, TAs provide small group tutoring and one-on-one tutoring. Make use of them! • Attend office hours of anyone teaching this course - you do not need to only go to office hours of your TA. Attend them all if you want! This is another environment that provides small group tutoring and one-on-one tutoring, already paid for by you! • Watch our free videos of solutions to homework problems • Do the homework

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2 BASIC MATH SKILLS

Basic Math Skills

To succeed in this class you must be fluent in the following basic math skills (note: these are all covered by the required pre-reqs for this course): • right triangles and trig functions (sin, cos, tan) taken with respect to any axis • vector math: addition, subtraction • use of variables as unknowns in equations • linear algebra: being able to solve several equations simultaneously These skills are used extensively in this class and in this solutions manual. Please make sure you are extremely capable in them all.

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Problem Solving Techniques 1 Write down all known or given quantities, in variable form 2 Write down the variable that you are asked to solve for 3 Include units on all variables. Make note of ones that are not in our standard set of units (ie not meters, seconds, or kilograms). These will need to be converted before calculating your final answer. 4 Identify the type of situation - is this projectile motion, rotation, a combination of linear and rotational motion? 5 Look through your equations specific to this situation. Find the one(s) that include your known and what you are asked to solve for. You may need to combine multiple equations to find the final answer

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4 CHAPTER 1: INTRODUCTION

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Chapter 1: Introduction

4.1

Spring 2015 Exam 1, Prob. 7-9

This exam question is based on problem 4 from Chapter 1.

You are told the volume changes by some factor, and asked how the surface area changes. First let’s write down what we are told in the problem: Vfinal = (volume f actor) Vinitial Vfinal = (volume f actor ) Vinitial Since the size of the object is changing, that means the radius of the object must also change. You do not need to know the exact equation (ie volume of sphere, square, cone, etc) to answer this question. You only need to remember that the volume of an object is proportional to the radius cubed and the area of an object is proportional to the radius squared. Why don’t we need to know the exact equation for volume of the object? If we write the solution using ratios of initial and final volumes, any numerical factor in the volume equation will cancel. 3 For example, if you have a sphere, the initial and final volumes of a sphere are Vfinal = 34 πrfinal 4 3 4 and Vinitial = 3 πrinitial . The 3 π in each term will cancel when we take the ratio of final to initial volumes. Just as we say the final volume is equal to some factor (number) times the initial volume, we can also say the final radius is equal to some number times the initial radius. R3final Vfinal = 3 Rinitial Vinitial 3 Rfinal ((radius f actor) Rinitial )3 = 3 3 Rinitial Rinitial

Vfinal = (volume f actor ) Vinitial =

((radius f actor) Rinitial )3 3 Rinitial

(volume f actor) = (radius f actor )3

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4.1 Spring 2015 Exam 1, Prob. 7-9

Take the cube root of the volume factor to find the amount that the radius has changed. The surface area of any object is proportional to the radius squared. We now know that the radius changes by an amount (radius factor). That means Rfinal = (radius f actor) Rinitial and R2final Afinal = 2 Rinitial Ainitial =

((radius f actor) Rinitial )2 2 Rinitial

= (radius f actor)2 Afinal = (radius f actor)2 ∗ Ainitial The final answer is that the surface area expands by an amount of radius factor squared.

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5 5.1

5 CHAPTER 2: MOTION ALONG A LINE

Chapter 2: Motion Along a Line Spring 2015 Final Exam, Prob. 24-26

This exam question is based on problem 50 from Chapter 2.

To find the time it takes to reach the maximum height, we first need to calculate the maximum height the stone reaches relative to where it was launched. We’re told the initial speed, and we know that as an object moves upward its speed decreases until it reaches a velocity of zero when it is at its maximum height. To find the distance in y the stone travels, we can use: 2 2 − v initial,y vfinal,y = 2 a ∆y

= 2 (−10

m ) ∆y s2

where ∆y is ymax height - yinitial , yinitial is the distance of the stone above ground when it was 2 fired, and vfinal = 0. Rearranging, we solve for ∆y: 2 2 − v initial,y vfinal,y = 2 (−10

∆y =

m ) ∆y s2

2 −vinitial,y 2 (−10 m ) s2

How do we use this to find the time it takes to go this distance? We apply a second constant acceleration equation:

∆y = vinitial,y ∆t −

1 g ∆t2 2

We could use the ∆y we just calculated, and the initial velocity given in the problem, and solve this as a quadratic. There is an easier way to approach this problem. Consider that the ∆y is the distance it takes to go from where it was fired to the maximum height, and -∆y is the distance it takes to go from the maximum height back down to where it was fired. Similarly, ∆t is the time it takes to go from where it was fired to the maximum height, and the time it takes to go from the maximum height to where it started from. The only force acting on this stone, regardless of which direction it is traveling, is acceleration due to gravity. Thus we can use this equation ∆y = vinitial,y ∆t −

1 g ∆t2 2

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5.1 Spring 2015 Final Exam, Prob. 24-26

for the situation where the rock starts from where it was fired (some initial velocity), OR we can use it for the situation where the rock is starting at the maximum height and falling back down to where it was fired from (no initial velocity). If we say we’re starting from the max height then we can set vinitial,y = 0, greatly simplifying our equation.

∆y = vinitial,y ∆t −

1 g ∆t2 2

1 g ∆t2 2 s 2 ∆y ∆t = 10 m s2

−∆y = −

We now substitute in the equation we found for ∆y, using initial and final velocities:

∆t =

s

2 ∆y 10 m s2

=

s

2 2 vinitial,y ) 2 (10 sm2 ) (10 m s2

=

s

2 vinitial,y ) (10 m ) (10 m s2 s2

=

vinitial,y 10 m s2

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6 CHAPTER 3: MOTION IN A PLANE

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Chapter 3: Motion in a Plane

6.1

Spring 2015 Exam 1, Prob. 13-15

This exam question is based on problem 32 from Chapter 3.

We are told the total time someone has to travel a total distance. We are also given their average speed for part of the distance. To find out the average speed for the rest of the trip we need to know how much distance is left to travel, and...