Elementary Mechanics Using Matlab

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1 Anders Malthe-S0renssen Elementary Mechanics Using Matlab A Modern Course Combining Analytical and Numerical Techniques ^ Springer

2 Contents 1 Introduction Physics Mechanics Integrating Numerical Methods Problems and Exercises How to Learn Physics How to Use This Book 7 2 Getting Started with Programming A Matlab Calculator Scripts and Functions Plotting Data-Sets Plotting a Function Random Numbers Conditions Reading Real Data Example: Plot of Function and Derivative 22 3 Units and Measurement Standardized Units Changing Units Uncertainty and Significant Digits Numerical Representation 36 4 Motion in One Dimension Description of Motion Example: Motion of a Falling Tennis Ball Calculation of Motion Example: Modeling the Motion of a Falling Tennis Ball 64 ix

3 x Contents 5 Forces in One Dimension What Is a Force? Identifying Forces Newton's Second Law of Motion Example: Acceleration and Forces on a Lunar Lander Force Models Force Model: Gravitational Force Force Model: Viscous Force Example: Falling Raindrops Force Model: Spring Force Example: Motion of a Hanging Block Newton's First Law Newton's Third Law Example: Weight in an Elevator Motion in Two and Three Dimensions Vectors Description of Motion Example: Mars Express Calculation of Motion Example: Feather in the Wind Frames of Reference Example: Motion of a Boat on a Flowing River Forces in Two and Three Dimensions Identifying Forces Newton's Second Law Force Model Constant Gravity Example: Motion of a Ball with Gravity Force Model Viscous Force Example: Path Through a Tornado Force Model Spring Force Example: Motion of a Bouncing Ball with Air Resistance Force Model Central Force Example: Comet Trajectory Constrained Motion Linear Motion Curved Motion Example: Acceleration of a Matchbox Car Example: Acceleration of a Rotating Rod Example: Normal Acceleration in Circular Motion

4 Contents xi 9 Forces and Constrained Motion Linear Constraints Example: A Bead in the Wind Force Model Friction Example: Static Friction Forces Example: Dynamic Friction of a Block Sliding up a Hill Example: Oscillations During an Earthquake Circular Motion Example: A Car Driving Through a Curve Example: Pendulum with Air Resistance Work Integration Methods Work-Energy Theorem Work Done by One-Dimensional Force Models Example: Jumping from the Roof Example: Stopping in a Cushion Work Done in Two- and Three-Dimensional Motions Example: Work of Gravity Example: Roller-Coaster Motion Example: Work on a Block Sliding. Down a Plane Power Example: Power Exerted When Climbing. the Stairs Example: Power of Small Bacterium Energy Motivating Examples Potential Energy in One Dimension Example: Falling Faster Example: Roller-Coaster Motion Example: Pendulum Example: Spring Cannon Energy Diagrams Example: Energy Diagram for the Vertical Bow-Shot Example: Atomic Motion Along a Surface The Energy Principle Example: Lift and Release Example: Sliding Block 335

5 xii Contents 11.5 Potential Energy in Three Dimensions Example: Constant Gravity Example: Gravity in Three Dimensions 338 in Three Dimensions Example: Non-conservative Force Field Energy Conservation as a Test of Numerical Solutions Momentum, Impulse, and Collisions Motivating Example Meteor Impact Translational Momentum Impulse and Change Example: Ball Colliding in Momentum 356 with Wall Example: Hitting a Tennis Ball Isolated Systems and Conservation of Momentum Collisions Example: Ballistic Pendulum Example: Super-Ball Modeling and Visualization of Collisions Rocket Equation Example: Adding Mass to a Railway Car Example: Rocket with Diminishing Mass Multiparticle Systems Motion of a Multiparticle System The Center of Mass Example: Points on a Line Example: Center of Mass of Object with Hole Example: Center of Mass by Integration Example: Center of Mass from Image Analysis Newton's Second Law for Particle Systems Example: Ballistic Motion with an Explosion Motion in the Center of Mass System Energy Partitioning Example: Bouncing Dumbbell Energy Principle for Multi-particle Systems Rotational Motion Rotational State Angle of Rotation Angular Velocity Angular Acceleration Example: Oscillating Antenna Comparing Linear and Rotational Motion Solving for the Rotational Motion Example: Revolutions of an Accelerating Example: Angular Velocities of Two Objects Disc 448 in Contact 449

6 Contents xiii 14.6 Rotational Motion in Three Dimensions Example: Velocity and Acceleration of a Conical Pendulum Rotation of Rigid Bodies Rigid Bodies Kinetic Energy of a Rotating Rigid Body Calculating the Moment of Inertia Example: Moment of Inertia of Two-Particle System Example: Moment of Inertia of a Plate Conservation of Energy for Rigid Bodies Example: Rotating Rod Relating Rotational and Translational Motion Example: Weight and Spinning Wheel Example: Rolling Down a Hill Dynamics of Rigid Bodies Motivating Example Spinning a Wheel Newton's Second Law for Rotational Motion Example: Torque and Vector Decomposition Example: Pulling at a Wheel Example: Blowing at a Pendulum Rotational Motion Around a Moving Center of Mass Example: Kicking a Ball Example: Rolling Down an Inclined Plane Example: Bouncing Rod Collisions and Conservation Laws Example: Block on a Frictionless Table Example: Changing Your Angular Velocity Example: Conservation of Rotational Momentum Example: Ballistic Pendulum Example: Rotating Rod General Rotational Motion 536 Appendix A: Proofs 555 Appendix B: Solutions 571 Index 587

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