# Systems: Two or More Bodies/3rd Law

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## Video Clips

#### Newton's Third Law

RealVideo®
4:56 minutes (11:04 - 16:00)

Balance of gravity and upward force; statement of Newton's third law.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Examples of Action and Reaction

RealVideo®
6:10 minutes (16:00 - 22:10)

Action and reaction between two blocks, in a garden hose, and in a balloon.

Instructor: Prof. Walter Lewin
Prior Knowledge: Newton's Third Law (11:04 of V6)

#### Hero's Engine

RealVideo®
4:14 minutes (22:10 - 26:24)

Newton's third law demonstrated through spinning engine propelled by steam.

Instructor: Prof. Walter Lewin
Prior Knowledge: Newton's Third Law (11:04 of V6)

#### Third Law Consequences

RealVideo®
4:41 minutes (26:24 - 31:05)

Third law used to calculate acceleration of earth towards and away from tossed apple.

Instructor: Prof. Walter Lewin
Prior Knowledge: Newton's Third Law (11:04 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)

#### 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)

#### Atwood's Machine

RealVideo®
7:51 minutes (7:43 - 15:34)

Calculation of acceleration for two blocks suspended over pulley with friction from masses and moment of inertia.

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

## Lecture Notes

#### Motion Problems

PDF - 1.6 MB#
Page 1 to page 5

Step-by-step strategy for solving motion problems. Ideal pulleys, pegs, and strings are introduced. Includes a number of motion examples.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Newton's Laws

#### Forces in Equilibrium

PDF - 1.6 MB#
Page 1 to page 6

Conditions of equilibrium for particles and rigid bodies; torque axis; center of gravity; center of mass demonstration; stable and unstable equilibrium; coupled forces; equilibrium problem-solving strategy with several examples.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 25

#### Newton's Third Law

PDF - 1.3 MB#
Page 1

Definition, including an example of identifying action/reaction pairs.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Newton's Second Law

#### Motion Problems

PDF#
Page 1 to page 13

Step-by-step strategy for solving motion problems. Ideal pulleys, pegs, and strings introduced. Includes a number of motion examples.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Newton's Laws

#### Forces in Equilibrium

PDF - 1.5 MB#
Page 1 to page 15

Conditions of equilibrium for particles and rigid bodies; torque axis; center of gravity; center of mass demonstration; stable and unstable equilibrium; coupled forces; equilibrium problem-solving strategy with several examples.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 25

#### Newton's Third Law

PDF#
Page 1 to page 3

Statement, including an example of identifying action/reaction pairs.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Newton's Second Law

#### Newton's Laws

PDF
Page 1 to page 2

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

Instructor: Dr. George Stephans
Prior Knowledge: Kinematics

#### Friction

PDF
Page 1

Direction and magnitude of friction; static and kinetic friction; coefficient of friction.

Instructor: Dr. George Stephans
Prior Knowledge: Newton's Laws

#### Springs

PDF
Page 1

Direction and magnitude of spring force; spring constant; springs in parallel and series.

Instructor: Dr. George Stephans
Prior Knowledge: Newton's Laws

#### 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 Third Law

PDF#
Page 20 to page 22

Action-reaction force pairs; tension in a rope; free body force diagram.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: One-Dimensional Motion

## Practice Problems

#### Three Masses on Two Pulleys

PDF
Problem 7

Using special cases and dimensional analysis to determine which acceleration for system is correct.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: None

#### Model Airplane on a Wire

PDF
Problem 6

3-part problem; calculating tension in wire, critical angle, and safe speed for flight.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: None

#### Free Body Diagrams

PDF
Problem 1

Forces acting on systems of two or more bodies. Solution not included.

Instructor: Dr. George Stephans
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

#### Friction

PDF
Problem 1 to problem 2

Forces acting on moving and stationary blocks sitting on a surface. Solution not included.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Friction

PDF#
Problem 1

Forces acting on moving and stationary blocks sitting on a surface. Solution not included.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Springs

PDF#
Problem 2

Forces acting on horizontal and vertical springs. Solution not included.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Energy and Momentum

PDF
Problem 1

Friction and acceleration; which forces must be known to solve for energy and momentum; kinetic energy and momentum in a collision. Solution not included.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Strings and Blocks

PDF
Problem 4

Forces and accelerations acting on two blocks connected by strings.

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

#### Cart and Pulley

PDF
Problem 5

Forces, including friction, acting on a cart connected to a block suspended from a pulley.

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

#### Glass on a Tablecloth

PDF
Problem 10

Static friction between a glass and a tablecloth.

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

#### Car at Rest

PDF
Problem 4

Comparing the gravitational force on a car and the normal force of the ground on the car. Solution not included.

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

#### Jumping on a Scale

PDF
Problem 5

Forces acting on a scale with a person jumping from it. Solution not included.

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

#### Accelerating Elevator

PDF
Problem 6

Normal force exerted on a person in an accelerating elevator. Solution not included.

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

#### Friction and Surface Area

PDF
Problem 7

Force needed to push a crate across a floor as a function of the surface area in contact with the floor. Solution not included.

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

#### Friction and Inclined Plane

PDF
Problem 8

Motion of an object sliding on an inclined surface, with friction. Solution not included.

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

#### Friction and Tension

PDF
Problem 9

Tension in a rope pulling a block with friction. Solution not included.

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

#### Cart and Hanging Weight

PDF
Problem 10

Tension in a string connecting a moving cart and a hanging weight via a pulley. Solution not included.

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

#### Accelerating Elevator

PDF
Problem 2

Forces acting on a person standing in an accelerating elevator. Solution not included.

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

#### Tension on a Sphere

PDF
Problem 6

Force applied by horse teams to an evacuated hollow metal sphere. Solution not included.

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

#### Tension on a Yo-Yo

PDF
Problem 8

Force acting on the string of a descending yo-yo. Solution not included.

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

#### Tension on a Yo-Yo

PDF
Problem 9

Force acting on the string of an ascending yo-yo. Solution not included.

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

#### Blocks and Pulleys

PDF
Problem 10

Acceleration of a system of multiple masses and pulleys. Solution not included.

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

#### Spring Constant

PDF
Problem 11

Relationship between spring constants of springs used to suspend a mass. Solution not included.

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

#### Turntable

PDF
Problem 21

Forces acting on a cube lying on a spinning turntable. Solution not included.

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

#### Free Body Diagrams

PDF
Problem 3

Drawing free body diagrams for tug-of-war.

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

#### Second Law and Projectile Motion

PDF
Problem 4

Motion of an object sliding off an inclined roof and falling to the ground.

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

#### Experiment 3 Analysis

PDF
Problem 6

Approximating the force law acting between magnets.

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

#### 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

## Exam Questions

#### Stacked Blocks

PDF#
Problem 1

3-part problem; drawing free-body diagram and finding acceleration; force required to slide top block relative to bottom.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: None

#### Newton's Third Law

PDF#
Problem 2

Forces acting in systems of two or more bodies.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Static Friction

PDF#
Problem 4

Dynamics of an astronaut pushing a block on a surface in outer space.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Jumping Man

PDF#
Problem 5

Motion of and forces acting on a jumping basketball player.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Mass on an Accelerating Surface

PDF#
Problem 8

Dynamics of a bead of water on the windshield of an accelerating car.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Suitcase on a Conveyor Belt

PDF#
Problem 9

Dynamics of a suitcase placed on a moving conveyor belt.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Spinning Rod and Mass

PDF#
Problem 10

Dynamics of a system of a mass suspended from a vertical spinning rod by a string and pulley.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Mass Hanging over the Edge

PDF#
Problem 1

4-part problem; finding acceleration, tension, time, and speed for mass on table to reach pulley while other mass hangs.

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

#### Circular Motion in a Cone

PDF#
Problem 2

4-part problem; drawing free-body diagram and finding v, T for object; maximum speed with friction.

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

#### Weight from a Jump

PDF#
Problem 4

Determining upward speed from a jump given force exerted on the floor.

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

#### Weightlifter on a Scale

PDF
Problem CQ2

Effect of lifting a barbell on scale reading.

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

#### Monkey and Pulley

PDF
Problem CQ5

Motion of a monkey climbing a rope that passes over a pulley and connects to a hanging block.

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

PDF
Problem CQ6

Forces acting on a basketball player jumping to take a shot.

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

#### Second Law and Projectile Motion

PDF
Problem 2

Motion of an object sliding off an inclined roof and falling to the ground.

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

#### Inclined Plane and Pulley

PDF
Problem 3

Motion of a block on an inclined plane and connected to a second block via a wire that passes over a pulley.

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

#### Blocks on a Table

PDF
Problem 5

Motion of two touching blocks on a frictionless table.

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

#### Inclined Plane, Friction, Spring

PDF
Problem 4

Motion of a mass that slides down an inclined plane and compresses a spring.

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

#### Inclined Plane and Pulley

PDF
Problem 2

Motion of two blocks on an inclined plane and connected to a third block via a wire that passes over a pulley.

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

#### Scale in an Elevator

PDF
Problem 4

Modeling the forces and acceleration acting on a person riding an elevator.

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