The Hitchhiker's Guide to Calculus
Problems and Solutions in Elementary Physics by C. Bond The following sections include solutions to a number of my favorite problems in elementary physics. Some of the solutions bear aspects resembling that of a magician pulling a rabbit out of a hat. Others simply demonstrate the remarkable power of a few seminal concepts to reveal the inner workings of the real world. Most of the problems yield to solution strategies other than the ones shown, but these represent my own preference. At some point in time, I expect to post similar documents containing problems of a more advanced nature, but the problems here may interest physicists and students at all levels.
Contents
1 Kinematics Equations 1.1 Miscellaneous Problems in Kinematics . . . . . . . . . . . . . 1.1.1 1.1.2 1.1.3 Minimum Time for a Vehicle to go from 0 to 60 mph. Minimum Stopping Distance . . . . . . . . . . . . . . Flight of the Bumblebee . . . . . . . . . . . . . . . . . 5 7 7 7 8 8 11
2 Bouncing Ball 3 Maximum Velocity in a Quarter Mile 1
4 Rolling Up A Ramp 4.1 4.2 Maximum Height of Ball . . . . . . . . . . . . . . . . . . . . . Hoop, Disk, Cylinder and Sphere . . . . . . . . . . . . . . . .
11 11 13 14 15 17 18 18 19 20 22 24 24 26 27 28 28 30
5 Height of Water in Tank 6 Bead Sliding on Wire 7 James Bond’s Ski Saga 8 Moment of Inertia 8.1 8.2 8.3 8.4 Constant Moment Arm . . . . . . . . . . . . . . . . . . . . . . Moment of Disk or Solid Cylinder About Axis . . . . . . . . Moment of Thin Spherical Shell About Axis . . . . . . . . . . Moment of Solid Sphere About Axis . . . . . . . . . . . . . .
9 Vertical Loop 9.1 9.2 9.3 Ball on String . . . . . . . . . . . . . . . . . . . . . . . . . . . Cart on Track . . . . . . . . . . . . . . . . . . . . . . . . . . . Pole Vault . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10 Cue Ball Slip Problems 10.1 Slip Problem #1 . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Slip Problem #2 . . . . . . . . . . . . . . . . . .
Contents
1 Kinematics Equations 1.1 Miscellaneous Problems in Kinematics . . . . . . . . . . . . . 1.1.1 1.1.2 1.1.3 Minimum Time for a Vehicle to go from 0 to 60 mph. Minimum Stopping Distance . . . . . . . . . . . . . . Flight of the Bumblebee . . . . . . . . . . . . . . . . . 5 7 7 7 8 8 11
2 Bouncing Ball 3 Maximum Velocity in a Quarter Mile 1
4 Rolling Up A Ramp 4.1 4.2 Maximum Height of Ball . . . . . . . . . . . . . . . . . . . . . Hoop, Disk, Cylinder and Sphere . . . . . . . . . . . . . . . .
11 11 13 14 15 17 18 18 19 20 22 24 24 26 27 28 28 30
5 Height of Water in Tank 6 Bead Sliding on Wire 7 James Bond’s Ski Saga 8 Moment of Inertia 8.1 8.2 8.3 8.4 Constant Moment Arm . . . . . . . . . . . . . . . . . . . . . . Moment of Disk or Solid Cylinder About Axis . . . . . . . . Moment of Thin Spherical Shell About Axis . . . . . . . . . . Moment of Solid Sphere About Axis . . . . . . . . . . . . . .
9 Vertical Loop 9.1 9.2 9.3 Ball on String . . . . . . . . . . . . . . . . . . . . . . . . . . . Cart on Track . . . . . . . . . . . . . . . . . . . . . . . . . . . Pole Vault . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10 Cue Ball Slip Problems 10.1 Slip Problem #1 . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Slip Problem #2 . . . . . . . . . . . . . . . . . .