Table of Contents s392

1301 LAB MANUAL TABLE OF CONTENTS

Introduction 5

Laboratory 1: Description of Motion in One Dimension 9 Problem #1: Intro to Measurement and Uncertainty 11 Problem #2: Motion Down an Incline 21 Problem #3: Motion Up and Down an Incline 25 Problem #4: Motion Down an Incline with an Initial Velocity 29 Problem #5: Mass and Motion Down an Incline 33 Problem #6: Motion on a Level Surface With an Elastic Cord 37 Check Your Understanding 41 Laboratory 1 Cover Sheet 43 Laboratory 2: Description of Motion in Two Dimensions 45 Problem #1: Mass and the Acceleration of a Falling Ball 47 Problem #2: Acceleration of a Ball with an Initial Velocity 51 Problem #3: Projectile Motion and Velocity 55 Problem #4: Bouncing 59 Problem #5: Acceleration and Circular Motion 63 Problem #6: A Vector Approach to Circular Motion 67 Problem #7: Acceleration and Orbits 71 Check Your Understanding 75 Laboratory 2 Cover Sheet 77 Laboratory 3: Forces 79 Problem #1: Force and Motion 81 Problem #2: Forces in Equilibrium 85 Problem #3: Frictional Force 89 Problem #4: Normal and Kinetic Frictional Force I 93 Problem #5: Normal and Kinetic Frictional Force II 97 Table of Coefficients of Friction 101 Check Your Understanding 103 Laboratory 3 Cover Sheet 105 Laboratory 4: Conservation of Energy 107 Problem #1: Kinetic Energy and Work I 109 Problem #2: Kinetic Energy and Work II 113 Problem #3: Energy and Collisions When Objects Stick Together 117 Problem #4: Energy and Collisions When Objects Bounce Apart 121 Problem #5: Energy and Friction 125 Check Your Understanding 129 Laboratory 4 Cover Sheet 131 TABLE OF CONTENTS

Laboratory 5: Conservation of Energy and Momentum 133 Problem #1: Perfectly Inelastic Collisions 135 Problem #2: Elastic Collisions 139 Check Your Understanding 143 Laboratory 5 Cover Sheet 145

Laboratory 6: Rotational Kinematics 147 Problem #1: Angular Speed and Linear Speed 149 Problem #2: Rotation and Linear Motion at Constant Speed 153 Problem #3: Angular and Linear Acceleration 157 Check Your Understanding 161 Laboratory 6 Cover Sheet 163 Laboratory 7: Rotational Dynamics 165 Problem #1: Moment of Inertia of a Complex System 167 Problem #2: Moment of Inertia about Different Axes 171 Problem #3: Moment of Inertia with an Off-Axis Ring 175 Problem #4: Forces, Torques, and Energy 179 Problem #5: Conservation of Angular Momentum 183 Problem #6: Designing a Mobile 187 Problem #7: Equilibrium 191 Check Your Understanding 195 Laboratory 7 Cover Sheet 197 Laboratory 8: Mechanical Oscillations 199 Problem #1: Measuring Spring Constants 201 Problem #2: The Effective Spring Constant 205 Problem #3: Oscillation Frequency with Two Springs 209 Problem #4: Oscillation Frequency of an Extended System 213 Problem #5: Driven Oscillations 217 Check Your Understanding 221 Laboratory 8 Cover Sheet 223

Appendix: Equipment 225 Appendix: Software 239 Appendix: Significant Figures 265 Appendix: Accuracy, Precision and Uncertainty – Error Analysis 269 Appendix: Review of Graphs 277 Appendix: Guide to Writing Lab Reports 285 Appendix: Sample Lab Reports 291 Acknowledgments

Much of the work to develop this problem solving laboratory was supported by the University of Minnesota and the National Science Foundation. We would like to thank all the people who have contributed directly to the development of this laboratory manual:

Sean Albiston Heather Brown Jennifer Docktor Andy Ferstl Tom Foster Kaiyan Gao Charles Henderson Ted Hodapp Tao Hu Andrew Kunz Vince Kuo Roman Lutchyn Laura McCullough Michael Myhrom Maribel Núñez V. Jeremy Paschke Leon Steed Tom Thaden-Koch Hao Wang Sean Albiston

And all of the faculty and graduate students who helped to find the 'bugs' in these instructions.

Kenneth & Patricia Heller

Kenneth Heller & Patricia Heller