# Single Particle Dynamics/2nd Law

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## Video Clips

#### Newton's Second Law

RealVideo®
4:12 minutes (6:52 - 11:04)

Motivation and statement of Newton's second law; difference between mass and weight.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Statics Problem

RealVideo®
11:38 minutes (31:05 - 42:43)

Statics problem of mass hanging from two angled strings solved and demonstrated.

Instructor: Prof. Walter Lewin
Prior Knowledge: Newton's Laws (beginning of V6)

#### Weight and Free Fall

RealVideo®
9:16 minutes (0:00 - 9:16)

Weight defined; weight on accelerating scales calculated; free-fall defined.

Instructor: Prof. Walter Lewin
Prior Knowledge: F=ma (6:52 of V6)

#### Masses on a Frictionless Pulley

RealVideo®
6:24 minutes (9:16 - 15:40)

Acceleration and tension calculated for two masses suspended over a pulley.

Instructor: Prof. Walter Lewin
Prior Knowledge: Free-fall (beginning of V7)

#### Interpretation of Masses on a Pulley

RealVideo®
4:47 minutes (15:40 - 20:27)

Results interpreted as masses become unbalanced; gain and loss of weight in free-fall.

Instructor: Prof. Walter Lewin
Prior Knowledge: Masses on a Pulley (9:16 of V7)

#### Tension in Revolving String

RealVideo®
6:26 minutes (20:27 - 26:53)

Calculation of tension at top and bottom of loop for mass swinging in vertical plane.

Instructor: Prof. Walter Lewin
Prior Knowledge: Vertically Swinging Mass (42:07 of V5)

#### Weightlessness During Free-Fall

RealVideo®
4:16 minutes (26:53 - 31:09)

Demonstration that a gallon of water is weightless in free fall during jump from table.

Instructor: Prof. Walter Lewin
Prior Knowledge: Free-fall (beginning of V7)

#### Weightless Mass in Free-fall

RealVideo®
8:19 minutes (31:09 - 39:28)

Demonstration that barbell is weightless in free-fall, then very heavy on impact.

Instructor: Prof. Walter Lewin
Prior Knowledge: Weightlessness During Free-fall (26:53 of V7)

#### Weightlessness Video

RealVideo®
10:32 minutes (39:28 - 50:00)

Video demonstration of the Vomit Comet and explanation of its cycle and conditions.

Instructor: Prof. Walter Lewin
Prior Knowledge: Weightlessness During Free-fall (26:53 of V7)

#### Static Friction

RealVideo®
7:01 minutes (0:00 - 7:01)

Definition, including normal force; μs = ∠tan α proven; method for determining μs.

Instructor: Prof. Walter Lewin
Prior Knowledge: F=ma (6:52 of V6)

#### Measuring Static Friction

RealVideo®
4:37 minutes (7:01 - 11:38)

Demonstration of dependence of μs on surface, but not surface area or mass.

Instructor: Prof. Walter Lewin
Prior Knowledge: Static Friction (beginning of V8)

#### Friction in Pulley/Plane System

RealVideo®
9:12 minutes (11:38 - 20:50)

System of block sitting on inclined plane, connected to hanging block; calculation of conditions when block is falling or is static.

Instructor: Prof. Walter Lewin
Prior Knowledge: Friction (beginning of V8)

#### Example of Pulley/Plane System

RealVideo®
9:39 minutes (20:50 - 30:29)

Numerical calculations for pulley/plane system, including interpretation and calculation of acceleration and tension.

Instructor: Prof. Walter Lewin
Prior Knowledge: Friction in Pulley/Plane System (11:38 of V8)

#### Pulley/Plane Demo

RealVideo®
5:53 minutes (30:29 - 36:22)

Demonstration of pulley/plane system; additional mass hangs, then falls; explanation of changing friction.

Instructor: Prof. Walter Lewin
Prior Knowledge: Example of Pulley/Plane System (20:50 of V8)

#### Waterplaning and Air Tracks

RealVideo®
5:19 minutes (36:22 - 41:41)

Explanation of friction elimination by hydroplaning and air tracks, with brief demonstrations.

Instructor: Prof. Walter Lewin
Prior Knowledge: Static Friction (beginning of V8)

#### CO2 Shuttle

RealVideo®
6:26 minutes (41:41 - 48:07)

Video of device that travels on cushion of CO2 on plate glass; friction so low a flea can pull a large book on the device.

Instructor: Prof. Walter Lewin
Prior Knowledge: Static Friction (beginning of V8)

#### Yardstick Puzzle

RealVideo®
1:53 minutes (48:13 - 50:06)

Moving two fingers towards each other under a yardstick causes alternating movement.

Instructor: Prof. Walter Lewin
Prior Knowledge: Static Friction (beginning of V8)

## Lecture Notes

#### Newton's Second Law

PDF - 1.3 MB#
Page 4 to page 6

Statement that F=m*a; definition of mass; superposition of forces; second law examples.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 7

#### Newton's Second Law

PDF#
Page 9 to page 16

Statement that F=m*a; definition of mass; superposition of forces; second law examples.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 7

#### Newton's Laws

PDF
Page 1 to page 2

Newton's first law defined; Newton's second law defined (F = m*a); Newton's third law defined; inertial reference frames defined.

Instructor: Dr. George Stephans
Prior Knowledge: Kinematics

#### Newton's Laws of Motion

PDF#
Page 1 to page 4

Newton's three laws of motion defined with a sentence each.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Newton's Second Law

PDF#
Page 8 to page 12

Definition of force (F=ma); superposition principle; definition of impulse and average impulse; Newton's second law equations for force, acceleration, momentum.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Newton's First Law - derivatives, integrals

#### Force Laws

PDF#
Page 13 to page 19

Newtonian induction; definition of Hooke's law; contact forces between surfaces; kinetic friction; static friction; fundamental forces of nature; definition of universal law of gravitation, with equation.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Newton's Second Law

#### Second Law Methodology

PDF#
Page 23 to page 30

Newton's Second Law in components; step-by-step method for solving second law problems.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Newton's Second Law

#### Applying Newton's Second Law

PDF - 1.3 MB
Page 1 to page 16

Definition of a reference frame; relative and relatively inertial reference frames; law of addition of velocities, with example problem; acceleration in relatively inertial reference frames; principle of relativity; tension in a massless rope; equations of motion, with special cases; constraint conditions in pulley systems.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Newton's Second Law

#### Experiment 3

PDF - 1.3 MB
Page 17 to page 29

Force modeling experiment setup and procedure.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Applying Newton's Second Law

## Practice Problems

#### Work on Sliding Box

PDF
Problem 5

4-part problem; finding work in terms of frictional force; stopping time; work to accelerate the box.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: None

#### Newton's Laws

PDF
Problem 1

Forces acting on two blocks connected and suspended by strings. Solution not included.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Forces and Reference Frames

PDF
Problem 2

Forces acting on a passenger in a turning car. Solution not included.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Forces and Reference Frames

PDF
Problem 1 to Problem 2

Forces acting on systems of multiple bodies. Solution not included.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Painter on a Platform

PDF
Problem 9

Force and acceleration.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Force and Velocity

PDF
Problem 1

Force needed to accelerate a cart to a specified speed. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Force and Velocity

PDF
Problem 2

Final speed of a cart acted on by a force. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Passenger in Car

PDF
Problem 3

Force acting on a passenger in a sharply turning car. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Sensation of Motion

PDF
Problem 1

Detecting motion from inside a windowless, soundproof vessel. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Experiment 3 Pre-Lab

PDF
Problem 4

Magnitude of force between two magnets as a function of distance.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Uniform Circular Motion

PDF
Problem 2

Forces acting on a mass connected to a rotating axle.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Experiment 5 Pre-Lab

PDF
Problem 3

Forces acting on a pivoted beam.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Experiment 5B Analysis

PDF
Problem 1

Motion of two unequal masses suspended by a string over a rod.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Conservation of Mechanical Energy

PDF
Problem 2

Motion of a small object that slides down a large sphere and hits the ground.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Static Friction Coefficient

PDF#
Problem 8

Calculating μs by two methods.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Holding a Book Against a Wall

PDF#
Problem 9

Free-body diagram and forces in pushing a book against a wall at an angle α.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Why Wide Tires?

PDF#
Problem 10

Asks why race cars use wide tires, even though friction is independent of surface area.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Sliding Stick Across Fingers

PDF#
Problem 13

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Spring with Friction

PDF#
Problem 12

Finding maximum extension, time to maximum velocity for spring extended on frictional surface.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Suitcase Dropped on Conveyor Belt

PDF#
Problem 14

Kinetic vs. static friction and sign; magnitude of horizontal force on suitcase.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Two Blocks on Two Slopes

PDF#
Problem 7

Two blocks connected over pulley, on separate slopes; find α of pulley, a, and T.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

## Exam Questions

#### Second Law and Kinetic Energy

PDF#
Problem 1

Relative motion and energy of two objects.

Prior Knowledge: None

#### Ascending Jet

PDF#
Problem 6

Motion of a jet airplane after takeoff.

Prior Knowledge: None

#### Objects in Closed Boxes

PDF
Problem 1

Determining change in weight of person jumping and hummingbird taking off inside a closed box on a scale.

Instructors: Dr. Peter Dourmashkin, Prof. Kate Scholberg
Prior Knowledge: None

#### Ball in a Vertical Circle

PDF#
Problem 2

Speed and tension at the top of the circle for ball swinging around.

Instructors: Dr. Peter Dourmashkin, Prof. Kate Scholberg
Prior Knowledge: None

#### Accelerating Car

PDF
Problem CQ1

Force acting on an accelerating car.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Objects in Orbit

PDF
Problem CQ4

Relative mass of weightless objects.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Newton's Laws

PDF
Problem 1b

Reading a scale in an elevator.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Accelerating Pendulum

PDF#
Problem 2b

Finding the period of a pendulum in a moving elevator.

Instructor: Prof. Walter Lewin
Prior Knowledge: None