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Vincent Selhorst-Jones

Vincent Selhorst-Jones

Energy: Gravitational Potential

Slide Duration:

Table of Contents

I. Motion
Math Review

16m 49s

Intro
0:00
The Metric System
0:26
Distance, Mass, Volume, and Time
0:27
Scientific Notation
1:40
Examples: 47,000,000,000 and 0.00000002
1:41
Significant Figures
3:18
Significant Figures Overview
3:19
Properties of Significant Figures
4:04
How Significant Figures Interact
7:00
Trigonometry Review
8:57
Pythagorean Theorem, sine, cosine, and tangent
8:58
Inverse Trigonometric Functions
9:48
Inverse Trigonometric Functions
9:49
Vectors
10:44
Vectors
10:45
Scalars
12:10
Scalars
12:11
Breaking a Vector into Components
13:17
Breaking a Vector into Components
13:18
Length of a Vector
13:58
Length of a Vector
13:59
Relationship Between Length, Angle, and Coordinates
14:45
One Dimensional Kinematics

26m 2s

Intro
0:00
Position
0:06
Definition and Example of Position
0:07
Distance
1:11
Definition and Example of Distance
1:12
Displacement
1:34
Definition and Example of Displacement
1:35
Comparison
2:45
Distance vs. Displacement
2:46
Notation
2:54
Notation for Location, Distance, and Displacement
2:55
Speed
3:32
Definition and Formula for Speed
3:33
Example: Speed
3:51
Velocity
4:23
Definition and Formula for Velocity
4:24
∆ - Greek: 'Delta'
5:01
∆ or 'Change In'
5:02
Acceleration
6:02
Definition and Formula for Acceleration
6:03
Example: Acceleration
6:38
Gravity
7:31
Gravity
7:32
Formulas
8:44
Kinematics Formula 1
8:45
Kinematics Formula 2
9:32
Definitional Formulas
14:00
Example 1: Speed of a Rock Being Thrown
14:12
Example 2: How Long Does It Take for the Rock to Hit the Ground?
15:37
Example 3: Acceleration of a Biker
21:09
Example 4: Velocity and Displacement of a UFO
22:43
Multi-Dimensional Kinematics

29m 59s

Intro
0:00
What's Different About Multiple Dimensions?
0:07
Scalars and Vectors
0:08
A Note on Vectors
2:12
Indicating Vectors
2:13
Position
3:03
Position
3:04
Distance and Displacement
3:35
Distance and Displacement: Definitions
3:36
Distance and Displacement: Example
4:39
Speed and Velocity
8:57
Speed and Velocity: Definition & Formulas
8:58
Speed and Velocity: Example
10:06
Speed from Velocity
12:01
Speed from Velocity
12:02
Acceleration
14:09
Acceleration
14:10
Gravity
14:26
Gravity
14:27
Formulas
15:11
Formulas with Vectors
15:12
Example 1: Average Acceleration
16:57
Example 2A: Initial Velocity
19:14
Example 2B: How Long Does It Take for the Ball to Hit the Ground?
21:35
Example 2C: Displacement
26:46
Frames of Reference

18m 36s

Intro
0:00
Fundamental Example
0:25
Fundamental Example Part 1
0:26
Fundamental Example Part 2
1:20
General Case
2:36
Particle P and Two Observers A and B
2:37
Speed of P from A's Frame of Reference
3:05
What About Acceleration?
3:22
Acceleration Shows the Change in Velocity
3:23
Acceleration when Velocity is Constant
3:48
Multi-Dimensional Case
4:35
Multi-Dimensional Case
4:36
Some Notes
5:04
Choosing the Frame of Reference
5:05
Example 1: What Velocity does the Ball have from the Frame of Reference of a Stationary Observer?
7:27
Example 2: Velocity, Speed, and Displacement
9:26
Example 3: Speed and Acceleration in the Reference Frame
12:44
Uniform Circular Motion

16m 34s

Intro
0:00
Centripetal Acceleration
1:21
Centripetal Acceleration of a Rock Being Twirled Around on a String
1:22
Looking Closer: Instantaneous Velocity and Tangential Velocity
2:35
Magnitude of Acceleration
3:55
Centripetal Acceleration Formula
5:14
You Say You Want a Revolution
6:11
What is a Revolution?
6:12
How Long Does it Take to Complete One Revolution Around the Circle?
6:51
Example 1: Centripetal Acceleration of a Rock
7:40
Example 2: Magnitude of a Car's Acceleration While Turning
9:20
Example 3: Speed of a Point on the Edge of a US Quarter
13:10
II. Force
Newton's 1st Law

12m 37s

Intro
0:00
Newton's First Law/ Law of Inertia
2:45
A Body's Velocity Remains Constant Unless Acted Upon by a Force
2:46
Mass & Inertia
4:07
Mass & Inertia
4:08
Mass & Volume
5:49
Mass & Volume
5:50
Mass & Weight
7:08
Mass & Weight
7:09
Example 1: The Speed of a Rocket
8:47
Example 2: Which of the Following Has More Inertia?
10:06
Example 3: Change in Inertia
11:51
Newton's 2nd Law: Introduction

27m 5s

Intro
0:00
Net Force
1:42
Consider a Block That is Pushed On Equally From Both Sides
1:43
What if One of the Forces was Greater Than the Other?
2:29
The Net Force is All the Forces Put Together
2:43
Newton's Second Law
3:14
Net Force = (Mass) x (Acceleration)
3:15
Units
3:48
The Units of Newton's Second Law
3:49
Free-Body Diagram
5:34
Free-Body Diagram
5:35
Special Forces: Gravity (Weight)
8:05
Force of Gravity
8:06
Special Forces: Normal Force
9:22
Normal Force
9:23
Special Forces: Tension
10:34
Tension
10:35
Example 1: Force and Acceleration
12:19
Example 2: A 5kg Block is Pushed by Five Forces
13:24
Example 3: A 10kg Block Resting On a Table is Tethered Over a Pulley to a Free-Hanging 2kg Block
16:30
Newton's 2nd Law: Multiple Dimensions

27m 47s

Intro
0:00
Newton's 2nd Law in Multiple Dimensions
0:12
Newton's 2nd Law in Multiple Dimensions
0:13
Components
0:52
Components
0:53
Example: Force in Component Form
1:02
Special Forces
2:39
Review of Special Forces: Gravity, Normal Force, and Tension
2:40
Normal Forces
3:35
Why Do We Call It the Normal Forces?
3:36
Normal Forces on a Flat Horizontal and Vertical Surface
5:00
Normal Forces on an Incline
6:05
Example 1: A 5kg Block is Pushed By a Force of 3N to the North and a Force of 4N to the East
10:22
Example 2: A 20kg Block is On an Incline of 50° With a Rope Holding It In Place
16:08
Example 3: A 10kg Block is On an Incline of 20° Attached By Rope to a Free-hanging Block of 5kg
20:50
Newton's 2nd Law: Advanced Examples

42m 5s

Intro
0:00
Block and Tackle Pulley System
0:30
A Single Pulley Lifting System
0:31
A Double Pulley Lifting System
1:32
A Quadruple Pulley Lifting System
2:59
Example 1: A Free-hanging, Massless String is Holding Up Three Objects of Unknown Mass
4:40
Example 2: An Object is Acted Upon by Three Forces
10:23
Example 3: A Chandelier is Suspended by a Cable From the Roof of an Elevator
17:13
Example 4: A 20kg Baboon Climbs a Massless Rope That is Attached to a 22kg Crate
23:46
Example 5: Two Blocks are Roped Together on Inclines of Different Angles
33:17
Newton's Third Law

16m 47s

Intro
0:00
Newton's Third Law
0:50
Newton's Third Law
0:51
Everyday Examples
1:24
Hammer Hitting a Nail
1:25
Swimming
2:08
Car Driving
2:35
Walking
3:15
Note
3:57
Newton's Third Law Sometimes Doesn't Come Into Play When Solving Problems: Reason 1
3:58
Newton's Third Law Sometimes Doesn't Come Into Play When Solving Problems: Reason 2
5:36
Example 1: What Force Does the Moon Pull on Earth?
7:04
Example 2: An Astronaut in Deep Space Throwing a Wrench
8:38
Example 3: A Woman Sitting in a Bosun's Chair that is Hanging from a Rope that Runs Over a Frictionless Pulley
12:51
Friction

50m 11s

Intro
0:00
Introduction
0:04
Our Intuition - Materials
0:30
Our Intuition - Weight
2:48
Our Intuition - Normal Force
3:45
The Normal Force and Friction
4:11
Two Scenarios: Same Object, Same Surface, Different Orientations
4:12
Friction is Not About Weight
6:36
Friction as an Equation
7:23
Summing Up Friction
7:24
Friction as an Equation
7:36
The Direction of Friction
10:33
The Direction of Friction
10:34
A Quick Example
11:16
Which Block Will Accelerate Faster?
11:17
Static vs. Kinetic
14:52
Static vs. Kinetic
14:53
Static and Kinetic Coefficient of Friction
16:31
How to Use Static Friction
17:40
How to Use Static Friction
17:41
Some Examples of μs and μk
19:51
Some Examples of μs and μk
19:52
A Remark on Wheels
22:19
A Remark on Wheels
22:20
Example 1: Calculating μs and μk
28:02
Example 2: At What Angle Does the Block Begin to Slide?
31:35
Example 3: A Block is Against a Wall, Sliding Down
36:30
Example 4: Two Blocks Sitting Atop Each Other
40:16
Force & Uniform Circular Motion

26m 45s

Intro
0:00
Centripetal Force
0:46
Equations for Centripetal Force
0:47
Centripetal Force in Action
1:26
Where Does Centripetal Force Come From?
2:39
Where Does Centripetal Force Come From?
2:40
Centrifugal Force
4:05
Centrifugal Force Part 1
4:06
Centrifugal Force Part 2
6:16
Example 1: Part A - Centripetal Force On the Car
8:12
Example 1: Part B - Maximum Speed the Car Can Take the Turn At Without Slipping
8:56
Example 2: A Bucket Full of Water is Spun Around in a Vertical Circle
15:13
Example 3: A Rock is Spun Around in a Vertical Circle
21:36
III. Energy
Work

28m 34s

Intro
0:00
Equivocation
0:05
Equivocation
0:06
Introduction to Work
0:32
Scenarios: 10kg Block on a Frictionless Table
0:33
Scenario: 2 Block of Different Masses
2:52
Work
4:12
Work and Force
4:13
Paralleled vs. Perpendicular
4:46
Work: A Formal Definition
7:33
An Alternate Formula
9:00
An Alternate Formula
9:01
Units
10:40
Unit for Work: Joule (J)
10:41
Example 1: Calculating Work of Force
11:32
Example 2: Work and the Force of Gravity
12:48
Example 3: A Moving Box & Force Pushing in the Opposite Direction
15:11
Example 4: Work and Forces with Directions
18:06
Example 5: Work and the Force of Gravity
23:16
Energy: Kinetic

39m 7s

Intro
0:00
Types of Energy
0:04
Types of Energy
0:05
Conservation of Energy
1:12
Conservation of Energy
1:13
What is Energy?
4:23
Energy
4:24
What is Work?
5:01
Work
5:02
Circular Definition, Much?
5:46
Circular Definition, Much?
5:47
Derivation of Kinetic Energy (Simplified)
7:44
Simplified Picture of Work
7:45
Consider the Following Three Formulas
8:42
Kinetic Energy Formula
11:01
Kinetic Energy Formula
11:02
Units
11:54
Units for Kinetic Energy
11:55
Conservation of Energy
13:24
Energy Cannot be Made or Destroyed, Only Transferred
13:25
Friction
15:02
How Does Friction Work?
15:03
Example 1: Velocity of a Block
15:59
Example 2: Energy Released During a Collision
18:28
Example 3: Speed of a Block
22:22
Example 4: Speed and Position of a Block
26:22
Energy: Gravitational Potential

28m 10s

Intro
0:00
Why Is It Called Potential Energy?
0:21
Why Is It Called Potential Energy?
0:22
Introduction to Gravitational Potential Energy
1:20
Consider an Object Dropped from Ever-Increasing heights
1:21
Gravitational Potential Energy
2:02
Gravitational Potential Energy: Derivation
2:03
Gravitational Potential Energy: Formulas
2:52
Gravitational Potential Energy: Notes
3:48
Conservation of Energy
5:50
Conservation of Energy and Formula
5:51
Example 1: Speed of a Falling Rock
6:31
Example 2: Energy Lost to Air Drag
10:58
Example 3: Distance of a Sliding Block
15:51
Example 4: Swinging Acrobat
21:32
Energy: Elastic Potential

44m 16s

Intro
0:00
Introduction to Elastic Potential
0:12
Elastic Object
0:13
Spring Example
1:11
Hooke's Law
3:27
Hooke's Law
3:28
Example of Hooke's Law
5:14
Elastic Potential Energy Formula
8:27
Elastic Potential Energy Formula
8:28
Conservation of Energy
10:17
Conservation of Energy
10:18
You Ain't Seen Nothin' Yet
12:12
You Ain't Seen Nothin' Yet
12:13
Example 1: Spring-Launcher
13:10
Example 2: Compressed Spring
18:34
Example 3: A Block Dangling From a Massless Spring
24:33
Example 4: Finding the Spring Constant
36:13
Power & Simple Machines

28m 54s

Intro
0:00
Introduction to Power & Simple Machines
0:06
What's the Difference Between a Go-Kart, a Family Van, and a Racecar?
0:07
Consider the Idea of Climbing a Flight of Stairs
1:13
Power
2:35
P= W / t
2:36
Alternate Formulas
2:59
Alternate Formulas
3:00
Units
4:24
Units for Power: Watt, Horsepower, and Kilowatt-hour
4:25
Block and Tackle, Redux
5:29
Block and Tackle Systems
5:30
Machines in General
9:44
Levers
9:45
Ramps
10:51
Example 1: Power of Force
12:22
Example 2: Power &Lifting a Watermelon
14:21
Example 3: Work and Instantaneous Power
16:05
Example 4: Power and Acceleration of a Race car
25:56
IV. Momentum
Center of Mass

36m 55s

Intro
0:00
Introduction to Center of Mass
0:04
Consider a Ball Tossed in the Air
0:05
Center of Mass
1:27
Definition of Center of Mass
1:28
Example of center of Mass
2:13
Center of Mass: Derivation
4:21
Center of Mass: Formula
6:44
Center of Mass: Formula, Multiple Dimensions
8:15
Center of Mass: Symmetry
9:07
Center of Mass: Non-Homogeneous
11:00
Center of Gravity
12:09
Center of Mass vs. Center of Gravity
12:10
Newton's Second Law and the Center of Mass
14:35
Newton's Second Law and the Center of Mass
14:36
Example 1: Finding The Center of Mass
16:29
Example 2: Finding The Center of Mass
18:55
Example 3: Finding The Center of Mass
21:46
Example 4: A Boy and His Mail
28:31
Linear Momentum

22m 50s

Intro
0:00
Introduction to Linear Momentum
0:04
Linear Momentum Overview
0:05
Consider the Scenarios
0:45
Linear Momentum
1:45
Definition of Linear Momentum
1:46
Impulse
3:10
Impulse
3:11
Relationship Between Impulse & Momentum
4:27
Relationship Between Impulse & Momentum
4:28
Why is It Linear Momentum?
6:55
Why is It Linear Momentum?
6:56
Example 1: Momentum of a Skateboard
8:25
Example 2: Impulse and Final Velocity
8:57
Example 3: Change in Linear Momentum and magnitude of the Impulse
13:53
Example 4: A Ball of Putty
17:07
Collisions & Linear Momentum

40m 55s

Intro
0:00
Investigating Collisions
0:45
Momentum
0:46
Center of Mass
1:26
Derivation
1:56
Extending Idea of Momentum to a System
1:57
Impulse
5:10
Conservation of Linear Momentum
6:14
Conservation of Linear Momentum
6:15
Conservation and External Forces
7:56
Conservation and External Forces
7:57
Momentum Vs. Energy
9:52
Momentum Vs. Energy
9:53
Types of Collisions
12:33
Elastic
12:34
Inelastic
12:54
Completely Inelastic
13:24
Everyday Collisions and Atomic Collisions
13:42
Example 1: Impact of Two Cars
14:07
Example 2: Billiard Balls
16:59
Example 3: Elastic Collision
23:52
Example 4: Bullet's Velocity
33:35
V. Gravity
Gravity & Orbits

34m 53s

Intro
0:00
Law of Universal Gravitation
1:39
Law of Universal Gravitation
1:40
Force of Gravity Equation
2:14
Gravitational Field
5:38
Gravitational Field Overview
5:39
Gravitational Field Equation
6:32
Orbits
9:25
Orbits
9:26
The 'Falling' Moon
12:58
The 'Falling' Moon
12:59
Example 1: Force of Gravity
17:05
Example 2: Gravitational Field on the Surface of Earth
20:35
Example 3: Orbits
23:15
Example 4: Neutron Star
28:38
VI. Waves
Intro to Waves

35m 35s

Intro
0:00
Pulse
1:00
Introduction to Pulse
1:01
Wave
1:59
Wave Overview
2:00
Wave Types
3:16
Mechanical Waves
3:17
Electromagnetic Waves
4:01
Matter or Quantum Mechanical Waves
4:43
Transverse Waves
5:12
Longitudinal Waves
6:24
Wave Characteristics
7:24
Amplitude and Wavelength
7:25
Wave Speed (v)
10:13
Period (T)
11:02
Frequency (f)
12:33
v = λf
14:51
Wave Equation
16:15
Wave Equation
16:16
Angular Wave Number
17:34
Angular Frequency
19:36
Example 1: CPU Frequency
24:35
Example 2: Speed of Light, Wavelength, and Frequency
26:11
Example 3: Spacing of Grooves
28:35
Example 4: Wave Diagram
31:21
Waves, Cont.

52m 57s

Intro
0:00
Superposition
0:38
Superposition
0:39
Interference
1:31
Interference
1:32
Visual Example: Two Positive Pulses
2:33
Visual Example: Wave
4:02
Phase of Cycle
6:25
Phase Shift
7:31
Phase Shift
7:32
Standing Waves
9:59
Introduction to Standing Waves
10:00
Visual Examples: Standing Waves, Node, and Antinode
11:27
Standing Waves and Wavelengths
15:37
Standing Waves and Resonant Frequency
19:18
Doppler Effect
20:36
When Emitter and Receiver are Still
20:37
When Emitter is Moving Towards You
22:31
When Emitter is Moving Away
24:12
Doppler Effect: Formula
25:58
Example 1: Superposed Waves
30:00
Example 2: Superposed and Fully Destructive Interference
35:57
Example 3: Standing Waves on a String
40:45
Example 4: Police Siren
43:26
Example Sounds: 800 Hz, 906.7 Hz, 715.8 Hz, and Slide 906.7 to 715.8 Hz
48:49
Sound

36m 24s

Intro
0:00
Speed of Sound
1:26
Speed of Sound
1:27
Pitch
2:44
High Pitch & Low Pitch
2:45
Normal Hearing
3:45
Infrasonic and Ultrasonic
4:02
Intensity
4:54
Intensity: I = P/A
4:55
Intensity of Sound as an Outwardly Radiating Sphere
6:32
Decibels
9:09
Human Threshold for Hearing
9:10
Decibel (dB)
10:28
Sound Level β
11:53
Loudness Examples
13:44
Loudness Examples
13:45
Beats
15:41
Beats & Frequency
15:42
Audio Examples of Beats
17:04
Sonic Boom
20:21
Sonic Boom
20:22
Example 1: Firework
23:14
Example 2: Intensity and Decibels
24:48
Example 3: Decibels
28:24
Example 4: Frequency of a Violin
34:48
Light

19m 38s

Intro
0:00
The Speed of Light
0:31
Speed of Light in a Vacuum
0:32
Unique Properties of Light
1:20
Lightspeed!
3:24
Lightyear
3:25
Medium
4:34
Light & Medium
4:35
Electromagnetic Spectrum
5:49
Electromagnetic Spectrum Overview
5:50
Electromagnetic Wave Classifications
7:05
Long Radio Waves & Radio Waves
7:06
Microwave
8:30
Infrared and Visible Spectrum
9:02
Ultraviolet, X-rays, and Gamma Rays
9:33
So Much Left to Explore
11:07
So Much Left to Explore
11:08
Example 1: How Much Distance is in a Light-year?
13:16
Example 2: Electromagnetic Wave
16:50
Example 3: Radio Station & Wavelength
17:55
VII. Thermodynamics
Fluids

42m 52s

Intro
0:00
Fluid?
0:48
What Does It Mean to be a Fluid?
0:49
Density
1:46
What is Density?
1:47
Formula for Density: ρ = m/V
2:25
Pressure
3:40
Consider Two Equal Height Cylinders of Water with Different Areas
3:41
Definition and Formula for Pressure: p = F/A
5:20
Pressure at Depth
7:02
Pressure at Depth Overview
7:03
Free Body Diagram for Pressure in a Container of Fluid
8:31
Equations for Pressure at Depth
10:29
Absolute Pressure vs. Gauge Pressure
12:31
Absolute Pressure vs. Gauge Pressure
12:32
Why Does Gauge Pressure Matter?
13:51
Depth, Not Shape or Direction
15:22
Depth, Not Shape or Direction
15:23
Depth = Height
18:27
Depth = Height
18:28
Buoyancy
19:44
Buoyancy and the Buoyant Force
19:45
Archimedes' Principle
21:09
Archimedes' Principle
21:10
Wait! What About Pressure?
22:30
Wait! What About Pressure?
22:31
Example 1: Rock & Fluid
23:47
Example 2: Pressure of Water at the Top of the Reservoir
28:01
Example 3: Wood & Fluid
31:47
Example 4: Force of Air Inside a Cylinder
36:20
Intro to Temperature & Heat

34m 6s

Intro
0:00
Absolute Zero
1:50
Absolute Zero
1:51
Kelvin
2:25
Kelvin
2:26
Heat vs. Temperature
4:21
Heat vs. Temperature
4:22
Heating Water
5:32
Heating Water
5:33
Specific Heat
7:44
Specific Heat: Q = cm(∆T)
7:45
Heat Transfer
9:20
Conduction
9:24
Convection
10:26
Radiation
11:35
Example 1: Converting Temperature
13:21
Example 2: Calories
14:54
Example 3: Thermal Energy
19:00
Example 4: Temperature When Mixture Comes to Equilibrium Part 1
20:45
Example 4: Temperature When Mixture Comes to Equilibrium Part 2
24:55
Change Due to Heat

44m 3s

Intro
0:00
Linear Expansion
1:06
Linear Expansion: ∆L = Lα(∆T)
1:07
Volume Expansion
2:34
Volume Expansion: ∆V = Vβ(∆T)
2:35
Gas Expansion
3:40
Gas Expansion
3:41
The Mole
5:43
Conceptual Example
5:44
The Mole and Avogadro's Number
7:30
Ideal Gas Law
9:22
Ideal Gas Law: pV = nRT
9:23
p = Pressure of the Gas
10:07
V = Volume of the Gas
10:34
n = Number of Moles of Gas
10:44
R = Gas Constant
10:58
T = Temperature
11:58
A Note On Water
12:21
A Note On Water
12:22
Change of Phase
15:55
Change of Phase
15:56
Change of Phase and Pressure
17:31
Phase Diagram
18:41
Heat of Transformation
20:38
Heat of Transformation: Q = Lm
20:39
Example 1: Linear Expansion
22:38
Example 2: Explore Why β = 3α
24:40
Example 3: Ideal Gas Law
31:38
Example 4: Heat of Transformation
38:03
Thermodynamics

27m 30s

Intro
0:00
First Law of Thermodynamics
1:11
First Law of Thermodynamics
1:12
Engines
2:25
Conceptual Example: Consider a Piston
2:26
Second Law of Thermodynamics
4:17
Second Law of Thermodynamics
4:18
Entropy
6:09
Definition of Entropy
6:10
Conceptual Example of Entropy: Stick of Dynamite
7:00
Order to Disorder
8:22
Order and Disorder in a System
8:23
The Poets Got It Right
10:20
The Poets Got It Right
10:21
Engines in General
11:21
Engines in General
11:22
Efficiency
12:06
Measuring the Efficiency of a System
12:07
Carnot Engine ( A Limit to Efficiency)
13:20
Carnot Engine & Maximum Possible Efficiency
13:21
Example 1: Internal Energy
15:15
Example 2: Efficiency
16:13
Example 3: Second Law of Thermodynamics
17:05
Example 4: Maximum Efficiency
20:10
VIII. Electricity
Electric Force & Charge

41m 35s

Intro
0:00
Charge
1:04
Overview of Charge
1:05
Positive and Negative Charges
1:19
A Simple Model of the Atom
2:47
Protons, Electrons, and Neutrons
2:48
Conservation of Charge
4:47
Conservation of Charge
4:48
Elementary Charge
5:41
Elementary Charge and the Unit Coulomb
5:42
Coulomb's Law
8:29
Coulomb's Law & the Electrostatic Force
8:30
Coulomb's Law Breakdown
9:30
Conductors and Insulators
11:11
Conductors
11:12
Insulators
12:31
Conduction
15:08
Conduction
15:09
Conceptual Examples
15:58
Induction
17:02
Induction Overview
17:01
Conceptual Examples
18:18
Example 1: Electroscope
20:08
Example 2: Positive, Negative, and Net Charge of Iron
22:15
Example 3: Charge and Mass
27:52
Example 4: Two Metal Spheres
31:58
Electric Fields & Potential

34m 44s

Intro
0:00
Electric Fields
0:53
Electric Fields Overview
0:54
Size of q2 (Second Charge)
1:34
Size of q1 (First Charge)
1:53
Electric Field Strength: Newtons Per Coulomb
2:55
Electric Field Lines
4:19
Electric Field Lines
4:20
Conceptual Example 1
5:17
Conceptual Example 2
6:20
Conceptual Example 3
6:59
Conceptual Example 4
7:28
Faraday Cage
8:47
Introduction to Faraday Cage
8:48
Why Does It Work?
9:33
Electric Potential Energy
11:40
Electric Potential Energy
11:41
Electric Potential
13:44
Electric Potential
13:45
Difference Between Two States
14:29
Electric Potential is Measured in Volts
15:12
Ground Voltage
16:09
Potential Differences and Reference Voltage
16:10
Ground Voltage
17:20
Electron-volt
19:17
Electron-volt
19:18
Equipotential Surfaces
20:29
Equipotential Surfaces
20:30
Equipotential Lines
21:21
Equipotential Lines
21:22
Example 1: Electric Field
22:40
Example 2: Change in Energy
24:25
Example 3: Constant Electrical Field
27:06
Example 4: Electrical Field and Change in Voltage
29:06
Example 5: Voltage and Energy
32:14
Electric Current

29m 12s

Intro
0:00
Electric Current
0:31
Electric Current
0:32
Amperes
1:27
Moving Charge
1:52
Conceptual Example: Electric Field and a Conductor
1:53
Voltage
3:26
Resistance
5:05
Given Some Voltage, How Much Current Will Flow?
5:06
Resistance: Definition and Formula
5:40
Resistivity
7:31
Resistivity
7:32
Resistance for a Uniform Object
9:31
Energy and Power
9:55
How Much Energy Does It take to Move These Charges Around?
9:56
What Do We Call Energy Per Unit Time?
11:08
Formulas to Express Electrical Power
11:53
Voltage Source
13:38
Introduction to Voltage Source
13:39
Obtaining a Voltage Source: Generator
15:15
Obtaining a Voltage Source: Battery
16:19
Speed of Electricity
17:17
Speed of Electricity
17:18
Example 1: Electric Current & Moving Charge
19:40
Example 2: Electric Current & Resistance
20:31
Example 3: Resistivity & Resistance
21:56
Example 4: Light Bulb
25:16
Electric Circuits

52m 2s

Intro
0:00
Electric Circuits
0:51
Current, Voltage, and Circuit
0:52
Resistor
5:05
Definition of Resistor
5:06
Conceptual Example: Lamps
6:18
Other Fundamental Components
7:04
Circuit Diagrams
7:23
Introduction to Circuit Diagrams
7:24
Wire
7:42
Resistor
8:20
Battery
8:45
Power Supply
9:41
Switch
10:02
Wires: Bypass and Connect
10:53
A Special Not in General
12:04
Example: Simple vs. Complex Circuit Diagram
12:45
Kirchoff's Circuit Laws
15:32
Kirchoff's Circuit Law 1: Current Law
15:33
Kirchoff's Circuit Law 1: Visual Example
16:57
Kirchoff's Circuit Law 2: Voltage Law
17:16
Kirchoff's Circuit Law 2: Visual Example
19:23
Resistors in Series
21:48
Resistors in Series
21:49
Resistors in Parallel
23:33
Resistors in Parallel
23:34
Voltmeter and Ammeter
28:35
Voltmeter
28:36
Ammeter
30:05
Direct Current vs. Alternating Current
31:24
Direct Current vs. Alternating Current
31:25
Visual Example: Voltage Graphs
33:29
Example 1: What Voltage is Read by the Voltmeter in This Diagram?
33:57
Example 2: What Current Flows Through the Ammeter When the Switch is Open?
37:42
Example 3: How Much Power is Dissipated by the Highlighted Resistor When the Switch is Open? When Closed?
41:22
Example 4: Design a Hallway Light Switch
45:14
IX. Magnetism
Magnetism

25m 47s

Intro
0:00
Magnet
1:27
Magnet Has Two Poles
1:28
Magnetic Field
1:47
Always a Dipole, Never a Monopole
2:22
Always a Dipole, Never a Monopole
2:23
Magnetic Fields and Moving Charge
4:01
Magnetic Fields and Moving Charge
4:02
Magnets on an Atomic Level
4:45
Magnets on an Atomic Level
4:46
Evenly Distributed Motions
5:45
Unevenly Distributed Motions
6:22
Current and Magnetic Fields
9:42
Current Flow and Magnetic Field
9:43
Electromagnet
11:35
Electric Motor
13:11
Electric Motor
13:12
Generator
15:38
A Changing Magnetic Field Induces a Current
15:39
Example 1: What Kind of Magnetic Pole must the Earth's Geographic North Pole Be?
19:34
Example 2: Magnetic Field and Generator/Electric Motor
20:56
Example 3: Destroying the Magnetic Properties of a Permanent Magnet
23:08
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Lecture Comments (5)

2 answers

Last reply by: javier chichil
Wed Oct 9, 2013 1:29 PM

Post by javier chichil on October 8, 2013

hi Vincent:

Hope this question finds you well.

quick question, in minute 27:00, there is this formula T-mg= Fc.

From the diagram shown, i would have thought that it would be T+Fc= mg,

My idea came to mind because of the directions of the forces, T and Fc going up, and mg going down.

could you please comment on this?

thanks

1 answer

Last reply by: ahmed raza
Mon Nov 5, 2012 12:10 AM

Post by Diana Zafra on November 2, 2012

These examples are awesome. It makes physics more interesting when the examples are fun. Thanks!

Energy: Gravitational Potential

  • We can think of potential energy as energy stored for future use. This isn't perfectly rigorous, but it gives us a good understanding for now.
  • The amount of gravitational potential energy is based off of the mass of the object, the gravity involved, and the height of the object:
    Egravity = mgh.
  • We have to set the "base" height. Remember, as usual, we're the ones who have to impose a coordinate system, so it's up to us to determine what we consider the starting height.
  • Because of this, the important thing isn't the "absolute" height, but instead the relative height between the start and end heights: ∆h.
  • This formula relies on the fact that g is a constant near the surface of Earth (or whatever gravitational body we're dealing with). If g were to vary over the height traveled, we would need a different formula.
  • By the conservation of energy, we can look at the entire energy of the system at the start and end:
    Esys,  start + W = Esys,  end.
    [Remember, positive work puts energy into the system, while negative work takes it out.]
  • It's up to decide when we want to take our start and end "snapshots." Carefully choosing what moments we want to compare is key to solving problems.

Energy: Gravitational Potential

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Why Is It Called Potential Energy? 0:21
    • Why Is It Called Potential Energy?
  • Introduction to Gravitational Potential Energy 1:20
    • Consider an Object Dropped from Ever-Increasing heights
  • Gravitational Potential Energy 2:02
    • Gravitational Potential Energy: Derivation
    • Gravitational Potential Energy: Formulas
    • Gravitational Potential Energy: Notes
  • Conservation of Energy 5:50
    • Conservation of Energy and Formula
  • Example 1: Speed of a Falling Rock 6:31
  • Example 2: Energy Lost to Air Drag 10:58
  • Example 3: Distance of a Sliding Block 15:51
  • Example 4: Swinging Acrobat 21:32

Transcription: Energy: Gravitational Potential

Hi, welcome back to educator.com, today we are going to be talking about gravitational potential energy.0000

In our last section, we mentioned that there is a huge variety of forms that energy can take.0005

Then we explored specifically the idea of kinetic energy.0010

Now we are going to investigate the idea of gravity giving energy to objects.0013

When you lift an object up above the ground, you put gravitational potential energy into it.0017

Why do we call it potential energy?0022

Potential energy is stored energy that can be later released.0024

So, it is something that will allow us to do work later.0027

But, that is kind of true of kinetic energy, right?0030

The very least, it is able to store, in a way, store the energy as kinetic energy, and then release it as frictional work.0032

So, what is the difference between potential energy and kinetic energy?0039

If we really want to get rigorous about this, potential energy is energy associated with position/arrangement of a system of objects, and the forces interacting between them.0043

That is a little hard to use in our work though, so it is more than enough for us to think of it as storing energy for later use, something that we can hold on to indefinitely, or at least for a while.0052

We have got a pretty good understanding intuitively, once again we can appeal to our intuition, and we do not have to worry about having a really rigorous understanding until later Advanced Physics stuff, so for now, we can think about potential energy as just something that, just we are storing energy for a while, and also, we will know about it because we are going to talk about each kind of potential energy very specifically in length.0062

Let us start off by thinking about how potential energy works.0082

If we have got an object dropped from ever increasing heights, the higher the height it is dropped from , the faster it would be moving when it gets to the ground.0086

This means that a higher height implies higher speed at the ground.0096

Higher speed means more energy, that means that more height must be more energy.0104

If we have got a little mass with a little distance, that is going to be less energy than that same little mass, and a much larger distance.0110

Bigger the distance, the greater the energy.0117

If we want to talk about things specifically, quantitatively, how much energy does it have?0123

If we drop an object of mass 'm' from a height 'h', how much work does the force of gravity do on it?0127

The object is going to be pulled down, by a force mg, right?0132

The force of gravity is mg, mg always operates down, it is always pulling directly down, just like our height is directly down.0137

So, the motion down is going to be straight down, that means, work = force × distance × cos θ = mgh, since they are parallel, cos θ knocked down.0145

So, the amount of work is just going to be mgh.0168

If gravity does a work of mgh on our box, that is how much energy we must have stored in it by lifting it to that height.0173

Therefore, the energy of gravity = mgh.0180

Now, think about the fact that, no matter what path we take to get an object up to, say the top of this pillar, if we go directly up, and put it here, or we go like this, and then put it here, once it is still and sitting up there, it is going to have the exact same energy either direction.0190

No matter how we get it there, it winds up having the same energy, once they get to the same height.0211

The only important thing is the height that it has.0216

It matters if it is moving, but once it still, it is just the height.0218

It is completely based on the height.0221

So, mgh gives us potential gravitational energy.0224

Two important things to notice about the formula that we just made:0229

It is up to us to set what that base height means.0231

For that pillow that we just talked about, it is up to us to know that, that is the zero.0234

We could have the zero have up here, and it does not matter, it is all based on a relative idea, so it is comparing the two heights, if we want to talk about what the energy of the ball is here, what the energy of the ball is here, it does not matter if they both have negative, it is still going to have a positive difference, because it would have gone up to get up here.0239

Whereas, if it is down here, it is going to be positive, it does not matter, it is positive either way, because this one is less negative from the point of that zero, and this one is more positive from the point of that zero.0257

But either way, it is the relative difference, it is the change in 'h', not just the starting height on its own.0268

Being at the top of Mt. Everest, and going down 10 feet, is not more energy that starting at the top of Empire State Building, and going all the way to the ground floor.0274

There is way more energy in that tall drop from the top of the building down, even though Mt. Everest starts off higher from the centre of the Earth.0282

Formula also relies on the idea that 'g' is constant.0291

We can do this, because 'g' is reasonably constant near the surface of the Earth.0295

We can trust that we can have 9.8, really close to 9.8, remember, if you are on a really high location, depending on where you are on the Earth, specific loads of, like mineral deposits, so there is going to be minor changes in 'g', but more the most part, gravity is really constant on the surface of Earth, we can trust it to be 9.8.0298

We can use this formula, but if we went into space, or a different planet, the formula would change as 'g' changes, and if we were to go really far from Earth, we would not even be able to use this anymore.0315

It is going to rely on the fact that we can rely on the fairly constant gravity of Earth, within a near area from the surface of the Earth.0325

That is what we are going to trust on, whenever we are working on problems, we trust on the fact that we know what the gravitational constant is, and we know that it is going to be fairly, with the acceleration of gravity is not going to change much, whatever distance we go above the Earth, as long as it is a reasonable distance compared to the size of the Earth.0332

Finally, to be able to use anything in our energy formulae usefully, we are going to have the fact that energy is conserved.0352

We keep talking about hits, and we are going to keep talking about it, energy cannot be created or destroyed, it is always going to be conserved, it is only transferred.0357

This means that energy in a system stays constant, unless it is transferred out of the system.0367

The energy in the system at the start + the work = energy of the system at the end.0370

Positive work means energy is put into the system, work is put into the system, and the energy increases, negative work means energy is taken out, say friction.0376

That is what work is, work that is positive, is energy going in, work that is negative, is energy coming out.0386

We are ready to tackle the examples.0392

If we have a rock dropped from a height of 20 m, and we ignore air resistance, how fast will it be traveling 10 m above the ground?0394

Then how fast we will be traveling just before the impact?0400

Say we have got this rock, and there is 20 m, and there is the 10 m that it falls first.0403

From here to here, what is the change in height?, the change in height = 10, and the change in height here = another 10.0411

How fast is it traveling 10 m above the ground?0420

At beginning, it starts off at rest, so energy at the beginning, kinetic energy (K.E.) = 0, so there is no energy in it other than potential gravitational energy.0422

No work happens, because it does not lose anything to friction, it does not lose anything to air resistance, it is just direct transfer between gravitational potential energy moving directly into K.E.0431

For the first one, there is two ways of approaching this one:0441

We could look at this as either being, mgΔh = (1/2)mv2 (we are talking about speed, since this is single dimension.)0444

mgΔh, we do not know 'm', that might be a problem, but that we can take it for a bit, we do know 'g' and Δh, and we have got 'm' on both sides, so we can strike out our m's, we do not have to worry about that.0458

Remember, gravity works on everything, no matter what the mass is, it has a uniform acceleration, barring air resistance.0478

A uniform acceleration caused by gravity happens in our potential gravity to kinetic transform, because of the fact that, that 'm' constant shows up on both sides of the equation.0486

That means, gΔh = (1/2)v2, sqrt(2gΔh) = v.0499

Plug in numbers, sqrt(2 × 9.8 × 10) = v = 14 m/s, at 10 m above the ground.0512

One other way that we could have done this though, is we could have said, Esystem(beginning) + work = Esystem(end), mghi = mghend + (1/2)mv2, since work = 0, and also it has got some speed at the end.0534

If we move this over, we got, mghi - mghend, which is why we wind up pulling it out, and we look at, mgΔh.0570

It is the relative change that tells us how much energy is put into the system from gravitational potential.0583

That equals our (1/2)mv2, and that is why we did not have to put on both sides.0588

We could though, some case it is going to be useful to do that, we want to keep that tool in our tool box, but for this case, we are just looking at the change in height, gives us how much energy gets put in.0592

If we want to consider what happens when it moves it to all 20, we have got, mgΔh = (1/2)mv2, 2gΔh = v, 2×9.8×20 = velocity = 19.8 m/s.0602

That is the velocity at 0 m above the ground.0638

The things are, when we are at 10 m above the ground, we got 14 m/s, and we are at 0 m above the ground, when we are just touching the ground, just the instant before the impact, just that split second before it lands on the ground, 19.8 m/s.0642

A 100 g is thrown from a height of 1.4 m above the ground at a speed of 10 m/s.0659

At a height of 2.5 m, it has a speed of 7.9 m/s.0664

How much of its energy has been lost to air drag?0668

This is a case where it is actually going to be useful for us to have height on both sides, I think it is easier that way, you might not, but you can definitely do the other way if you felt like it.0670

In this case, we will do my way though.0679

Energysystem(beginning) + work = Energysystem(end), we want to figure out what the work is, how much work does the air drag do, and we should get a negative number, because the air drag is going to sap the energy out of it, it is going to suck energy out.0681

Esystem(beginning) has two things, it has a height above the ground, and it also has an initial speed.0704

What is its initial height?, mghinitial + (1/2)mv2 + work = mghfinal + (1/2)mvfinal2 (again, v is speed, note that it could be a vector as well, the important thing is to understand what you are writing, a useful diagram could be really helpful here.)0711

This frisbee, it starts off flying at some speed, and with some height, hinitial, and then later in time, it is at higher height, but less speed, and we want to figure out how much work is done between those two moments.0751

Those are our two snap shots.0777

At the beginning, we have got, in S.I., 0.1 kg, (sometimes we can use other unit system, but if we use 100 g instead of 0.1 kg, we would not be working with joules anymore, we would be working with something else, and we will completely screw up our ability to do this problem properly, because we have got m/s which is S.I., and we have got grams in there, which is not S.I., and things are going to get really funny, it is going to get bad.)0779

So, vinitial = 10, then, hinitial = 1.4, hfinal = 2.5, and vfinal = 7.9.0822

Plug everything in, we get, 0.1 kg×9.8 m/s/s×1.4 m + (1/2)×0.1×102 + work = 0.1 kg×9.8 m/s/s × 2.5 m + (1/2)×0.1 kg × (7.9)2.0840

We cannot make it easier by canceling 'm', because the work does not involve 'm', but it is important to be able to think about what you are doing and catch them when they happen.0860

Start calculating everything out, eventually, work = -0.802 J.0919

We plug everything in, move things around, put in a calculator, and we get the fact that we get -0.802 J at the end.0931

That is what our answer is, it loses that much energy to air drag, which is not very much, but remember, there is not all that much energy in a very light weight frisbee being thrown, not that fast.0937

Example 3: Block of unknown mass is slid down a frictionless slide of height 5 m.0952

Then it slides along a table where it has a friction coefficient of μk = 0.3, we only have to know the kinetic friction, because it is already starting on motion.0957

It starts on a frictionless incline, but very still, it starts to slide down it, and how far does the block slide on the table?0968

What is the initial energy in it?0977

Ei + work = Eend, so how much energy does it have at the end?0981

It is still, so it has no energy.0994

The work is going to have to suck out, is going to have to cancel out all the initial energy.0996

What energy does it have in the very beginning?, is it moving in the very beginning?1001

No!, it just starts, and then slides on a frictionless slide.1006

So, how much energy does it have?, it has mgh, its starting height worth of energy.1010

We have got, mgh = -W, work here is by friction.1018

How much is friction?, force of friction = μk×FN.1026

Remember, we do not have to worry about it once it is on the slide, because there is no friction on the slide, so we only have to worry about the flat plane.1032

On the flat plane, the only thing pulling down on it is mg, and mg is also equal to FN, so, friction = μkmg.1039

We go back to this, we get, mgh = -fdcosθ, θ = 180 degrees, because its motion is this way, but friction is pulling this way, so a 180 degrees.1055

So, mgh = -fdcos(180) = fd (cos(180) = -1).1093

So, mgh = μk×mg×d.1116

Look!, mg gets canceled on both sides.1132

So, h = μk×d, d = h/μk = (5 m)/(0.3) = 16.7 m, is the distance that it slides.1135

All the energy that it starts with, is just going to be its gravitational potential energy, that is all the energy in it, so it slides down the slide, once it gets to the bottom, it then starts to be zapped by friction.1167

So, the distance, starting here, once it gets to the friction table, is going to 16.7 m, because we know that, Ei + W = Eend, (gravitational potential energy) + [(friction force)×(distance it slides)] = 0, since still in the end.1181

Of course it might be still higher, but we know are looking at the change in height from start end to the bottom, and we said our base height as being the table's height, that is a clever thing we did, we did not even point out while we were working on it.1208

One thing I would like to point out: When we worked on this problem, for almost all of it, we did not put in our numbers, we do not need to put in numbers until the very end.1226

It is so much easier to be able to work with μk and sub in at the very end, that is a very useful trick, when you have got a lot of non-sense going around, you only need to substitute in the values until you get to the very end, because you might get the chance to eliminate some of them, it is easier to write letters, than complicated sets of numbers, because you might wind up making a simple error when you are trying to put down five 4 digit numbers, as opposed to 5 letters.1240

It is easier to watch what you are doing and have an understanding of what is going on, have an intuitive understanding of what you are doing, what this represents mathematically, by moving things with letters than just these meaningless numbers that you might not understand as well.1273

It is really helpful to be able to move things around as letters, and at the very end substitute in.1286

Final one: An acrobat of mass, m= 55 kg, swings from a trapeze of length 15 m, starts at rest, and descends 5 m during the sway.1293

The trapeze rope has been sabotaged by an evil villain, and it will snap at 800 N of tension.1303

Will our acrobat make it across safely?1309

This is a question that is important to his life.1312

If it is going to snap, where would be the point it would experience the most tension, when is the most tension going to happen?1316

If we are able to figure out that it is going to not snap at the point it is experiencing the most tension, then we know he will make it across safely, because the entire time the swing occurs, the acrobat is able to swing across without having to worry about the tension snapping it, because if the tension is maximum at one point, then we know that if we can figure out that one point's maximum tension, it will tell us whether or not it snaps.1326

Because everything is going to be at least less than that.1355

If everything is less than that, all we figure out is what the maximum tension put on it is.1360

Where will the maximum tension occur?1365

Now we have to think about, where do we have to get tension from!1367

The tension has to keep it in a circle.1372

So, the tension is going to be connected to keeping it in a circle, so force centripetal for it to be able to go in a circle, forcecentripetal = m×v2/r (again, v is speed)1375

At what point on the circle will he be traveling the fastest?1402

It is going to be the point, where he has converted all of his initial gravitational potential into motion, which is going to be the lowest point on the circle.1411

That is going to have the largest 'v'.1421

The largest 'v' occurs at the bottom, also the largest 'v' is when there is going to be the most fight between the tension of the rope, and the gravity pulling him down.1425

So, mg is going to be pulling down, and the rope is going to have to also give the centripetal force necessary to keep it in the circle, and also beat the gravity force that is trying to pull him down.1435

These two things combined will cause the tension to be highest at the bottom, so that is the point that we have to look at.1447

We know that, Ei + W = Eend, so the moment we have to look at, the snap shot, is going to be the moment of most tension, that is the point we want to check out and figure out if he is going to survive.1454

If he is going to survive, we are going to have to look at that moment of maximum tension.1473

So we are going to make that ending snap shot be, when it is pointing directly down.1478

There is no work, since there is no friction, everything is smooth.1481

So, mgh = (1/2)mv2, m's cancel out, so we do not have to worry about the mass.1491

So, gh = (1/2)v2, v = sqrt(gh) = 9.9 m/s, is the 'v' at the bottom, that is the speed our acrobat would be traveling if the rope were definitely safe.1505

If the rope snaps, it will snap somewhere between here, and here; after this it will wind up being safe, so all we have to do is to test the most extreme point, and we will be able to figure out if it snaps before it gets to the bottom.1528

If the bottom tension is greater than 800 N, we know the rope snaps, somewhere on the way to getting to the most extreme tension.1545

We do not know precisely where yet, we could figure it out, that would be a more difficult question.1553

We know that, vbottom = 9.9 m/s, what is the centripetal force necessary to keep him in a circle?1557

That is what it has to be, on the acrobat, forcecentripetal = m×v2/r, and we know m and r.1564

(55 kg)×(9.9)2/(15 m) = 359 N, is the necessary centripetal force, the necessary sum of forces to be able to keep him in that circle.1577

The centripetal force is pulling this way.1597

We have got tension, is pulling this way, and has to also be able to be some of mg.1602

We know that, T - mg = 359 N = centripetal force.1609

T = 359 + mg, at the moment of maximum tension that that rope would experience if it were a safe healthy rope.1617

Remember, if it is not a safe healthy rope, it might snap before we even get there, so the actual rope might not even ever experience that tension, because the most it is going to experience is 800 N before it snaps.1628

We do not know if he will make it yet, we got to finish this problem.1638

359 + mg = 359 N +(55 kg) × (9.8 m/s/s) = 898 N, SNAP!, he does not make it!1641

But, on the bright side, there is a net underneath it, let us draw a net, the net catches him, and he works later, and he finds the villain who is responsible for it, and he puts him to justice.1670

Hope you enjoyed this, hope you will come back, and we will learn about more about energy, and have an even stronger understanding of how energy works.1684

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