  Vincent Selhorst-Jones

Work

Slide Duration:

Section 1: 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
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
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
Section 2: 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

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
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
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
Section 3: 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
Section 4: 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
Section 5: 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
Section 6: 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
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
Section 7: 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
22:30
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
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
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
Section 8: 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
8:47
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
Section 9: 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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• ## Related Books & Services 1 answer Last reply by: Professor Selhorst-JonesTue Sep 8, 2020 7:56 PMPost by oli642107 on August 31, 2020I love the lectures! Thanks!! :) 2 answers Last reply by: Professor Selhorst-JonesWed Apr 1, 2020 10:06 AMPost by beihur777 on March 31, 2020When you gave the example about the introduction to work, you said that you can exert a force for some distance. Is this the same concept as exerting a force for some time? I know that exerting force for some time is called newton seconds. Is exerting force for some distance something like a "newton meter"? I really need a clarification on this. Thanks. 1 answer Last reply by: Professor Selhorst-JonesThu Jul 25, 2019 6:57 AMPost by Scott Yang on July 24, 2019well what if you push an object with greater force and it moves faster? more work or same amount of work? 1 answer Last reply by: Professor Selhorst-JonesWed Mar 19, 2014 9:11 AMPost by Nathan Lipinski on March 18, 2014How come for example five we don't have to put the little h a negative? The big H is a positive? Thanks 0 answersPost by javier chichil on October 8, 2013Good explanation. Thanks. 1 answer Last reply by: Professor Selhorst-JonesSun Jul 28, 2013 9:18 PMPost by KyungYeop Kim on July 27, 2013Why is work FxDxCos(x) as opposed to just F times D? it seems cosnine is redundant.. cosnine= Adjacent/Hypotaneous.= it ends up being (adjacent)^2 which is also (distance)^2 ??

### Work

• The idea of work is deeply connected to the idea of energy, as we will see in coming lessons.
• Qualitatively, you've done more work on an object if you push with more force than less force. Similarly, you do more work if you push for a longer distance than less distance.
• We want to define work as how much change you put into the world. Even if an object moves a distance, your force has to have some effect on the object's motion. No effect, no work.
• This means that if your force is perpendicular to the movement, it contributes nothing-no work.
• Work is the distance traveled multiplied by the force parallel to the motion. If the angle between them is θ, we can use trigonometry to get
 W = | →F | ·| →d | ·cosθ.
• The unit for work is the newton·meter, which we call a joule (J).

### Work

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
• Equivocation 0:05
• Equivocation
• Introduction to Work 0:32
• Scenarios: 10kg Block on a Frictionless Table
• Scenario: 2 Block of Different Masses
• Work 4:12
• Work and Force
• Paralleled vs. Perpendicular
• Work: A Formal Definition
• An Alternate Formula 9:00
• An Alternate Formula
• Units 10:40
• Unit for Work: Joule (J)
• 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

### Transcription: Work

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

This is going to be our first introduction to energy.0004

Introduction to energy, but we are talking about work, you thought that this is going to be an introduction to energy, so what is going on here!0008

Do not worry, both these things are actually really deeply connected.0015

To be able to talk about energy, we are going to wind up talking about work, and to talk about work, we are going to have to talk about energy.0018

But, first we can tackle the idea of work on its own, it is going to really help us understand energy.0022

Bear with me, and let us just learn about work as its own idea, and then we will move on to using it as part of energy.0026

Before we can rigorously define what work really means, let us look at a couple of scenarios before we try to figure out what we want, how we want to use work, what we want to find it as.0034

Let us say we have got some 10 kg block sitting on a frictionless table.0045

We are going to have a whole bunch of different scenarios, we have four different scenarios in the next page, and each one of those, we are going to slide the block some distance with some force, but these will vary in the scenarios, and we will talk about each one.0051

In our first one, we have got 'f' and 'd'.0062

We push it from here, to here, and we do that with that much force.0068

So, that is one thing, but what if we did it for this much distance?0073

Same force, but a much larger distance.0077

If that is the case, by the end of it, because it is frictionless, it is going to pick up speed.0081

Remember, the longer the force is going, the longer the acceleration, so it is going to have more speed in it.0085

So, it makes more sense to think that, the longer the distance, the more energy, the more work that we put into it.0090

You push for a longer period of time, it makes more sense that you are putting more work.0095

If you had to do something farther, that is more work than having to do it for less distance, if you are putting in the same force every moment.0100

What if instead, if we had a really big force and a small distance?0107

Clearly, between this box up here, and this box here, we are going to have a much bigger amount of work put in to the yellow box, the bottom box, the big force and the small distance, than the small distance and the small force.0110

It is not going to go as far, it is not going to move as far, at the end of that distance we will put way more work into it, because we are pushing so much harder.0131

If we push lightly on an object for a little distance, versus we put our entire body against it and push as hard as we can for a little distance, at the end of it, the thing is going to be moving a lot faster, makes sense to think of it as putting in more work.0139

What if we put both of them together, if we had a really big force, and a really big distance!0150

Clearly, that is going to be the one that has the most work.0155

We push really hard, for a really long time, that is going to be the most work.0158

So, it is about force and distance together.0162

More force means more work, more distance of pushing that force means more work.0164

Put both of them together, and that is even more work.0169

What if we consider two different blocks with masses that are different?0173

Same force in both cases.0177

So we have got the same force, and the same distance, but in this one, we have got a really big mass, whereas in this one, we have got a really small mass.0179

Notice that, because F = ma, the amount of acceleration is relative to the masses, so one vision: we have got a low mass object traveling really quickly at the end of its distance.0192

The other one, we got a high mass object traveling really slowly at the end of its distance.0202

But, we had to push the same force for the same distance.0207

So from the point of the view of the pusher, it is the same effort that we had to put into it.0212

They changed the system of mass, having to do with the speed that it is going at.0216

The two things are connected.0221

But, from the point of view of the pusher, it is the same work, it is the same amount of push for the same distance.0222

These are the same thing, so even though the result is different and how it comes out, it is a different mass with a different speed, we are going to have the same pushing, the same work in it.0231

So, we are going to think of work as just force and distance connected together.0242

The mass is not going to have direct effect.0246

These are different results, but it is the same force that is put into the system.0249

With this idea in mind, we have got a notion that work is force involved multiplied by the distance.0253

Way more force and way more distance stacks up hugely.0257

More force means more work, more distance means more work, these things that make good intuitive sense.0261

If we had to push a car for 1 foot versus push a car for 1 mile, or push a car for a metre versus pushing the car for a km, clearly the really bug distance is going to be the one that is going to take more work, if you are pushing it with the same force the whole time.0266

But there is one last thing that we have to consider before we really define what work means.0282

Consider the idea that there is a giant 20 tons semi-truck, which I will illustrate with an incredible box as my figure, and you are standing in front of it, and you are pushing as hard as you can, you push so hard on that, but it is this huge 20 tons semi-truck, it does not move at all, it does not budge even a mm, so did you do any work?0287

In one way, you definitely strained, and you put a lot of effort into it, you tried really hard, so the idea of looking from the point of view of the pusher is one thing, but what we really want to define is, we want to look at work as the way you change the world around you.0311

Even in the case of boxes with different masses, we were changing the world, we were putting a velocity into it, which was not there previously.0325

We created acceleration, we created change in velocity, by putting that work in.0330

In this case, you put a lot of effort in, you tried really hard, you push and strain, but nothing happens.0335

So we want to define work as 'change in the world'.0342

You have expended a lot of effort, but you did not change anything.0346

So, we are to going to define work as change in the world, so no distance, if you did not make any distance, even if you had a huge force, no distance means no work.0349

It is force × distance, zero distance means no work, even if it is a giant force.0357

With this idea in mind, there is one thing to consider.0363

We have got a block, and this lock moves in this direction.0368

But the entire time, we have got a force moving this way, perfectly perpendicular to the motion of the block.0373

Does the force do any work on the block?0382

We talked about the fact that, if you did not change anything, then you did not put in any work.0385

If there is no change from the force, then the force does no work.0393

Force has to be connected to the distance.0397

So in this case, no work is done by the force, because it is perpendicular.0400

That motion to the side is going to happen whether or not the perpendicular force does anything or not.0404

It is not able to change its distance, because it is perpendicular.0410

The only way it would be able to change its motion, is if the motion was going somewhere like this, but the entire time it slides along, the effect of the force has no acceleration, because its motion is this way only the entire time.0414

So, this one does not happen.0427

Force and distance are perpendicular, so from that we see that the force does no work, it does not change the motion of the object, no change means no work.0433

Forces perpendicular to displacement, contribute no work.0443

Force has to be at least partially in the direction, the amount that is perpendicular will contribute no work.0447

With all this thinking, we got things down pretty well.0454

It is the length of the displacement times the amount of force parallel to the displacement, the amount that is perpendicular has no effect.0457

Now we can finally create a formula.0465

If we have got some object, it does not matter what the mass is, remember the mass has an effect on the outcome of what happens in the world, but the work that is put in, is going to be the same whether it is a tiny mass or a really large mass.0468

The work = the size of the force × the size of the displacement × cos θ , θ is the angle between the two.0480

Why is that?0490

Remember, basic trick, since this is the hypotenuse, and this is the side adjacent, that side = force × cos θ .0491

So, the amount that is parallel, is going to be F × cos θ , so the amount that is the sin θ , the side opposite has no effect, so we can completely get rid of it.0505

So the only one we have to care about is the force × cos θ and that appears here, and here, and then we take the amount f the displacement in here, so the work = force × the distance × the cosine of the angle between the two, and that tells us what the work is.0515

That is the formal definition of work, it allows us to look at all the ideas that we have talked about so far and make sense of them.0534

One alternate formula you can use, in addition to force × distance × cos θ , we can also formulate it as a dot product from math.0541

The work = (force).(distance), (as vectors).0549

So the dot product is, if you take, a.b = (the x components multiplied with one another) + (the second two components multiplied with one another)0554

It might seem surprising at first, but it turns out actually having the exact same effect.0579

If you look at a formulation where, if one of them is lying on the x axis, then you can actually quickly see why if this is here, then the amount that this is out is the x axis amount here, x-y, well, it is going to wind up being F, if this is F again, then Fcos θ = its x component, because that is how much it is, because we can see that the way the vector breaks down.0582

We can break the vector into its constituent perpendicular and parallel pieces.0608

It will be a little bit more complicated to prove this in a different angle, but you can trust me on this, work = (force vector).(distance vector)0614

We can also use just force × distance × cos θ if we know the magnitudes and the angle.0623

Sometimes one is going to be more useful than the other, it depends on the specific conditions, and what you need to do.0628

As always you got to pay attention to what you are trying to solve fro in Physics, and figure out what is the best thing for you to use right there.0634

Finally, what units does work use?0642

From our formula, work = force × distance × cos θ .0644

cos θ , θ comes in angles, angles do not really have a unit, they are radians, but they are unitless, cos θ is just a scalar.0648

The only things that come with units are our force and our distance.0660

Force's unit is newtons, and distance's units is metres, if we are working in the S.I. system.0664

That means, work = N m , for ease we call this a joule, which we shorten as J.0672

J on its own, that is what we do for work, and later we will find out it is also what we do for energy when we talk about how those two are connected.0679

We call it a joule in honor of James Joule, who did pioneering work in heat and energy, in the 1800's.0685

We are ready for our examples.0694

Real simple, real easy one to start off with.0695

We got a bus, and we push it a distance of 10 m with a parallel force of 20 N.0697

If it is parallel, what is the angle?, the angle = 0, so cos θ = 1.0707

So, work = force × distance × cos θ = 20 N × 10 m × 1 = 200 J, and that is our answer.0713

If we wanted to, we could have also done that in dot product form, because we know that they are parallel, so the force would just have a vector of (20 N,0 N) , and the displacement vector would be (10 m,0 m).0738

So, we wind up getting 200, because 20 × 10 = 200, and 0 × 0 = 0, so we get 200, the exact same answer.0757

Second example: Ball of mass 0.25 kg is dropped at a height of 12 m.0769

When it hits the ground, how much work has the force of gravity done on the ball, what if the mass was 'm,, and the height was 'h'.0775

First off, we have got some ball, and we drop it 12 m, so the ball is up here, and mass = 0.25 kg, what is the force pulling on that ball?0781

Force pulling on that ball is the force of gravity, we assume no air resistance for ease, actually in this problem we can have air resistance, but we are paying attention to just the work done by the force of gravity, if we have to look at the energy later on, we would have to take the air resistance into account, but the force of gravity is going to do the same work no matter what, as far as it does move those 12 m.0796

In any case, force of gravity = mg, so in this case, if it travels 12m, and what is cos θ?, θ = 0 (since parallel).0822

So, work = force × distance × cos θ = mg × 12 × 1 = 0.25 × 9.8 × 12 × 1 = 29.4 J.0841

What if we wanted to solve this in the general case, what if we want to talk about, what if we were dealing with an arbitrary mass 'm', what if the height was just an arbitrary 'h'?0872

If that is the case, the work once again, the fall is parallel to the force of gravity (same direction), so work = F × d = mg × h = mgh, is the work done by the force of gravity for an object dropping.0883

Third example: A box moves a distance 5 m to the right, a force of 10 N pushes on it in the opposite direction.0912

How much work does the force do on the box?0922

The first thing to think about is, what is the angle.0924

Here is the 5 m, what is the angle between those two vectors?0929

5 m is a vector, 10 N is a vector, so what is the angle between them.0935

They are parallel, but they are pointing in opposite directions, we got to pay attention to the fact that they are going opposite.0939

So, 180 degrees.0947

So, if θ = 180 degrees, what is cos(180)?0951

cos(180), remember in your unit circle, it is pointing in the opposite direction, so it is going to be -1.0955

We drop this all in our formula for work, we got, work = force × distance × cos θ = 10 N × 5 m × (-1) = -50 J.0961

This is a totally new idea we have not encountered before.0994

We got the idea that we can actually take work out of a system.0997

If we had it going with it, that means we would be making it go faster, you put in work into it, because you would be making it going with it.1002

Bu this time, we are actually resisting the motion that it has.1009

It is going to move forward 5 m, but this time we are pushing in the opposite direction.1012

If we push in the opposite direction, this means that we are actually resisting it.1016

We are using our work to take the total work in the system out, the total energy in the system out.1022

We will talk more about the connection between energy and work, but right now, before, work was contributing to the distance it was moving, it was contributing to motion.1027

In this case, our force was going against the motion, so it is actually taking away from the motion, so it is a negative work.1035

If we want to do this with the dot product, work = F.d, if we make this the positive direction, then what is our distance vector?1042

It is going to be equal to (+5m,0m), what is the forces?1052

It is going to be going in the opposite direction, so (-10 m,0 m).1059

We put these two together with our dot product, and we got, 5× (-10) + 0 × 0 = -50 J.1064

Two different ways of doing it, both equally valid, gives you the same answer, the idea is the fact that, one you work against the motion of it, you have negative work, you are taking work out.1076

Fourth example: We have got a box traveling a distance of 50 m, 30 degrees South of East.1088

So it is moving South of East by 30 degrees, and it travels 50 m.1094

The box is acted upon during that motion by a force of 50 N, in a direction of 30 degrees North of East.1101

Even though there is a force moving on it, it does not change the displacement.1107

We know the displacement vector beforehand, it is given to us, we can be sure of it.1113

For some reason, there is something keeping it on that track, we are just worried about what the work that force does is.1116

We do not have to worry about the displacement changing, displacement is given to us in the beginning.1123

The work is going at an above direction by another 30 degrees, so it is 30 degrees North of this.1129

How much work does the force do?1134

We are looking at this from above, so it is flat, so we do not have to worry about the gravity, that is what the North and East and South all tell us.1136

In this case, what is θ?1142

The angle between the two is not just 30, it is the total between the two, so it is 60 degrees.1144

So, θ = 60 degrees.1151

Use our formula for work, work = force × distance × cos θ = 60 × 50 × cos(60) = 1500 J, is the answer.1154

Now, in this case, we could also do this in vector mode.1183

For this one, we were given the angles and magnitudes, so it is less useful, but I want to show you how to use the dot product, because sometimes, you are going to get things in vectors, and it is way more useful not have to convert into angles and magnitudes and see if you can do the problem, it is useful to go, "We have got vectors, let us use the dot product!"1186

We will convert this first into vectors.1205

For the top one, if it is 60 N on the hypotenuse, and 30 degrees angle here, then over here, it is going to be 30 N vertical, and what is its horizontal going to be, it is going to be 51.96, which is what we get when we take cos(30) × 60.1209

What about for the triangle representing the displacement?1232

It has got 50 m on its hypotenuse, so what is its vertical, its vertical = 25 (remember, we got 30 degrees here, and in 30-60 triangle, the side opposite to 30 is 1/2), and up here, cos(30) = sqrt(3)/2, is going to be 43.30.1236

In this case, this means that we know our force vector, what is the horizontal component?, it is 51.96, and let us say this (right) is positive, and up is positive, and vertical is +30 N .1265

We look at the displacement vector, and that is going to be equal to, (43.30 m, -25m).1293

This one is pointing down.1306

We take the dot product of these two, force dotted with distance, f.d, that is going to wind up equaling (51.96 × 43.30) + (30 × -25) = (2249.9) - (750) = 1499.9 J .1309

The only reason this wound up being any different from this answer which they are approximately equal, is because of rounding errors.1347

Rounding errors when we wound up figuring out what these two horizontal components were, we got slight answers off, because when we are using our calculator we wound up having to round it, because we did not use the entire thing, which we should, because remember we want to take some care about how significant digits work when you use an entire 10 digit long expansion.1356

Because that is the kind of extreme amount of accuracy to have, so we wound up having a slight rounding error, but when we consider the fact that this is 5 digits long, and we are only off by the very last digit, that is really close to 1500 J, that is as precise as we will be able to measure anything, in any lab we do.1374

And probably any lab you would wind up doing very long time, unless you are working in seriously experimental Physics.1390

Example 5: This is our last example.1397

Similar to example 2, remember in example 2, we talked about dropping a ball from a height 'h' or 12 m, we have got the same mass and the same height as we did in example 2.1400

We drop a ball 12 m, it is going to be the mass of the ball times gravity because that is the force of gravity times the height that it falls and cos θ just winds up going away turning into 1, because cos(0), because they are parallel is just 1, so we can just pay attention to the force × distance, so mgh.1412

What about this case, a ball of mass 0.25 kg is tossed out of a window at a height of 12 m.1432

Now, it travels up, and then travels down.1439

So, we do not know how high it gets, and I did not tell you precisely what it was.1444

It could be that it winds up getting really tall or it could be practically flat and then falling immediately.1449

It could be either one of these, I did not tell you how it is going to look.1455

So how could we figure out what it is going to be.1459

Remember, we know about how negative work works.1461

Notice that for the amount up here, for this portion right here above the height of the window, no matter what happens, the ball is going to wind up going positive.1466

Let us call it 'H', so there is the h that it falls to the ground, it should be 'h', that is the amount that is guaranteed, and then there is H which is the variable amount that it winds up going depending on how we throw it.1480

It has to go up by H, but then to be able to make it down, it has to also go down by H.1491

We have got a positive H and a negative H.1498

What happens if we look at the work done over the positive H and the negative H section?1500

It is traveling to the side, gravity is only going to be caring about the component, about up and down because everything else is going to be perpendicular, so we can just toss it out.1505

We only have to care about the up and down components.1515

Positive H is the amount that it travels up, that is the parallel amount, the perpendicular amount, the motion sideways we can just get rid off because it does not matter, that is the amount that is perpendicular and we can throw it away because we only care about the parallel amount.1518

In this case, we only have to care about the up by H and down by H, and then h.1534

We already know that the amount of work done in the h is going to be mgh.1542

What about the amount of work done by H?1547

This one, g is negative number.1550

So, +H, if we go this way, they are actually going to have an angle, θ = 180 degrees.1558

This is going to give us, -mgH.1566

What about the direction where it goes down?1572

That is going to be θ = 0, because now they are going in the same direction.1574

So this is going to be, +mgH.1578

We have got the idea that you go up by some amount of height, but you are fighting against gravity, so gravity is taking work out of the system, that means a negative work.1583

-mgH, the amount that you travel up, but then we wind up having travel the exact same amount down if we are going to make it to the ground, so that means, that amount that we just lost in work is going to be regained in work.1592

The H, mgH is going to wind up cancelling the -mgH, the two are just going to hit each other, and they are going to disappear, and we are going to wind up getting, these two things, just cancel each other out, and in the end, the only thing that we are left having to care about, is the h that we got right here.1604

That is the important part, mgh.1626

No matter how crazy a throw we have, if we go way up, or it is really flat, it does not really matter because the amount of work done by the extra arc from where it, the amount that is not just where it starts falling to 12 m we are guaranteed, is going to be canceled out.1630

The two works go opposite to one another, so it just gets canceled out.1647

In the end, it is mgh, the end of our answer is going to be the exact same answer we got for example 2.1651

The work = mgh, which is going to be, 0.25 × 9.8 × 12 = 29.4 J, is what we got.1656

The reason why is because the amount of arc that goes above where we started gets canceled out, because it winds up having to travel up, but then it travels that same amount back down, before it can do the real fall of h.1671

So H is, wind up cancelling one another out, because they do the same thing, they are doing with the same gravity , but they go in opposite directions, so they just cancel one another.1686

All we have to worry about is where we started, if we want to figure out the amount of work that gravity is going to put into it when it hits the ground.1701

Hope you enjoyed this, hope you got a good understanding of work.1708

This is going to be really useful in the next section when we talk about energy.1714

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