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Vincent Selhorst-Jones

Vincent Selhorst-Jones

Energy: Kinetic

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 (18)

1 answer

Last reply by: Professor Selhorst-Jones
Fri Mar 25, 2016 6:34 PM

Post by Peter Ke on March 12, 2016

For Example 4 at the end, I don't understand the reason why you remove the force that is pushing down including mg. Please explain.

Everything else I understand.

1 answer

Last reply by: Professor Selhorst-Jones
Sun Sep 22, 2013 11:28 AM

Post by Emily Engle on September 22, 2013

Why are there two acceleration formulas? (delta v/t=a and F/m=a).
F/m=a seems a ratio. And delta v/t=a seems to be a rate.

1 answer

Last reply by: Professor Selhorst-Jones
Tue Sep 10, 2013 9:20 AM

Post by Emily Engle on September 10, 2013

In the kinetic energy formula does the v equal speed or velocity?  If it is speed, why do we write a v?

1 answer

Last reply by: Professor Selhorst-Jones
Sun Jul 28, 2013 9:23 PM

Post by KyungYeop Kim on July 27, 2013

I don't understand.. Could you explain why the frictional force is Friction Constant x Normal Force when calculating work done by the frictional force? (34 minute) I know F=MxA or 1/2xmxv2, but am confused about why it's normal force x friction constant.

Thank you

2 answers

Last reply by: Goutam Das
Fri May 31, 2013 11:53 AM

Post by Goutam Das on May 28, 2013

According to the formula : E=mc^2, energy can be created from mass. Does the formula violate conservation of energy rule?

1 answer

Last reply by: Professor Selhorst-Jones
Tue May 7, 2013 2:22 PM

Post by kamal alamrousi on May 6, 2013

can't we use the kinematic equation in example 3 ?


thanx

2 answers

Last reply by: Tanveer Sehgal
Wed Nov 21, 2012 11:01 AM

Post by Tanveer Sehgal on November 21, 2012

Hey,

In example 4, the object has a force of 76.6N in the positive direction. We calculate the work based on this and the kinetic friction. But to move, does the object need to overcome static friction first? So will the object loose 75N to static friction and then have the net force move it?

1 answer

Last reply by: Professor Selhorst-Jones
Thu Sep 6, 2012 4:11 PM

Post by michelle daane on May 27, 2012

I'm confused. The math doesn't make sense... If you just double the velocity you don't get the same answer.... So if from the begining they gave us a velocity of 30, we would get a result of 675,000J
You're doing a great job

Energy: Kinetic

  • One of the central ideas behind energy is the conservation of energy: "Energy cannot be created or destroyed-only changed from one type to another."
  • Work is transferring one type of energy to another type. When we push an object, we change the chemical energy in our muscles into kinetic energy and heat.
  • We will not try to rigorously define the concept of energy in this course: it's a sticky question and beyond the scope of this course. But that's okay! From just living life, we're plenty familiar with energy to use it in this course.
  • The amount of kinetic energy in an object depends on its mass and its speed:
    Ek = 1

    2
    m |

    v
     
    |2.
  • The unit of energy is the joule (J). Notice this is the same unit as the unit for work. It is important that this is the case, because work is the quantity of energy we move from one type to another.
  • The conservation of energy says that the total energy in a system remains constant unless transferred to or from another system (through work):
    Esys,  start + W = Esys,  end
  • Positive work is energy put in to a system. Negative work is energy taken out of a system.
  • Friction always opposes motion, so it will always give a negative work (since W = |F| ·|d| ·cosθ and cos180° = −1). This makes sense, because friction always takes energy out of a system, transforming it into heat.

Energy: Kinetic

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
  • Types of Energy 0:04
    • Types of Energy
  • Conservation of Energy 1:12
    • Conservation of Energy
  • What is Energy? 4:23
    • Energy
  • What is Work? 5:01
    • Work
  • Circular Definition, Much? 5:46
    • Circular Definition, Much?
  • Derivation of Kinetic Energy (Simplified) 7:44
    • Simplified Picture of Work
    • Consider the Following Three Formulas
  • Kinetic Energy Formula 11:01
    • Kinetic Energy Formula
  • Units 11:54
    • Units for Kinetic Energy
  • Conservation of Energy 13:24
    • Energy Cannot be Made or Destroyed, Only Transferred
  • Friction 15:02
    • How Does Friction Work?
  • 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

Transcription: Energy: Kinetic

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

Just to begin with, you have definitely been exposed to the idea that there is a lots of different types of energy out there.0005

You probably have been hearing about this from a very young age.0010

You have talked about this, almost as early as kindergarten.0012

There is lots of different kinds of motion, energy, and ways for things to be energetic out there.0016

Some examples: there is kinetic motion energy, gravitational potential, if you lift something up and drop it, or lift it even higher, it is going to wind up having more energy.0022

Chemical energy, say hydrocarbons like gasoline inside of your car, light energy: the sun casting all that light energy at us, heat energy: if you are near fire, there is heat energy in the air.0032

Nuclear energy: radioactive Uranium is going to be able to put out energy in a form, electricity: moving electrons, and even more things than what I am talking about right now.0046

There is lots of different ways to have energy out there.0058

It is really useful to us as physicists to be able to understand how energy works, and get a really strong grasp on it, if you are going to be able to solve a lot of things, and model stuff, to be able to have control over environment.0060

Another idea you have probably been exposed to is this one:0073

Energy cannot be created or destroyed, only changed from one type to another.0076

The conservation of energy, you have almost certainly heard this.0081

It is not possible to get rid of energy in a system, it is only possible to change it from one form to another.0083

If you have a car driving along and hits the breaks, it is not that its kinetic energy goes into nothing, the kinetic energy goes into the squeal of the breaks.0089

The friction of the brake pads, the friction of the tyres on the road.0097

There is various different kinds of heat, the heat energy is what is going to come out of it instead.0101

Or you could have that chemical energy burning, it is not that the chemical energy goes away, it gets turned into heat, it gets turned into sound, it gets turned into kinetic energy, if say it is a rocket or a space ship.0106

All these sorts of things.0116

We can think of energy through this metaphor of a bucket full of sand.0118

We have got a bunch of different buckets, and each one has an amount of sand.0122

Say we are looking at a rocket on a launch pad.0126

It has some amount of chemical energy, it has got lot of chemical energy.0130

All of the fuels in these rockets, it has got no kinetic energy, it is just right at the bottom, no kinetic energy, and it has got some amount of gravitational energy, it is currently sitting on a pad, and it is also, maybe we are at some high place, wherever we are launching it from.0133

So, it is slightly higher up.0149

What happens when we ignite those rockets?0150

When we ignite the rockets, we use that chemical energy up, so we wind up burning all that chemical energy.0153

And that energy instead cause the rocket to move upwards, we causes an increase in kinetic energy, it is now moving up.0160

Now we have got an increase in kinetic energy, and the gravitational energy will go up as it moves up.0171

But the total amount of sand, the amount that the chemical goes down by, is the total amount that the kinetic and gravitational go up together.0179

If we look at the total amount of sand in all the buckets, all use the same.0187

It is just we change the location from one bucket to the other.0191

We either want our sand or energy in our chemical bucket or we want it in our kinetic bucket, or we want it in our gravitational bucket, but these are only different ways of swapping it around.0194

Or may be what will happen is, the rocket would run into a satellite, now we are having two system interact.0203

Now, swapping from the kinetic energy of the rocket, it is getting that kinetic energy swapped into the kinetic energy of the satellite, because the satellite gets knocked out of the orbit, and it hurdles away.0209

These sorts of things, it is not that we destroy energy or we change it inherently, it just gets changed from form to form, or from one object to another object, it gets transferred from systems, or gets transferred from types with in a system, or it gets transferred from types between systems.0218

But it does not get lost, does not get destroyed, it is always there, it is moved around in different ways.0235

Now, we will talk a little bit more about what specifically, why we can guarantee this, why we believe in it, why we think that this is one of the fundamental laws of the universe, but that is for thermodynamics, and that is while down the road.0241

But for now we can trust in the fact that the conservation of energy works, and that is going to be incredibly key to be able to solve all sorts of different things.0252

It gives us a lot of power over the understanding of how the world around us works.0260

What is energy?0264

We have talked about it having these different forms, we have not really talked about what it is.0266

It is hard to come with a truly rigorous definition that we can actually make use of, and be able to both play with it, and do cool things and be able to talk about it in a deep rigorous way, all the same time.0270

That is really hard, so we are going to sidestep that, we will be able to think of energy as the capacity to do work.0282

Being able to put work in, being able to make a change in the world.0287

Energy is your ability to change the system around you to build a change in environment, or change yourself with in the environment, it is to do work.0291

Work is change in energy.0299

So, what is work?0300

If work is what energy can do, work is a lot easier to define in fact.0303

Work is just the transfer of energy from one type to another.0309

Doing work is just the act of transferring energy, whereas the quantity if work is the amount of energy transferred.0311

If we had two buckets, and we wind up moving a whole bunch of stuff from one bucket to the other bucket, the amount that we move over, the quantity, is the quantity of the work, and doing work, this is the act of doing work, it is the moving it over.0317

Work is just moving energy from bucket to bucket.0341

That makes sense.0344

Wait!, that was a circular definition.0346

I defined energy with work, and work with energy, but in fact I did not really define either, that is not allowed, you cannot just make circular definitions and expect anyone to trust you.0349

You should not do that, you want to be able to have something where you can stand in, and at least make a definite claim.0358

You got me, that is a really good point, we really should be having something that is a meaningful statement that we can really push against and test and try out.0364

We do not want circular definitions, because they are not scientific statements.0373

But, in my defence, we have actually defined work.0376

Work is the transfer of energy, work is the motion of energy form one of our theoretical bucket to another theoretical bucket, not theoretical but metaphorical.0380

You move energy from one type to another, form one system to another, and that is work.0389

But what we did not really define is, we did not really define energy.0395

We did not do that rigorously.0398

To be honest, to finding energy precisely, in a really rigorous meaningful way, like push against and really scientifically talk about, and it to really mean something, is kind of outside the scope of this course.0400

It is actually kind of tough to talk about what it really means to be able to have a really deep understanding of that, and there is a whole bunch more to learn about energy before we can really have a very strong perfect meaning, to be able to truly say that.0414

But that is okay, we know enough intuitively, we are able to talk about the idea of energy, you know about having rocket fuel, you know about something moving very fast, you know about something being in a high location or stretching out a string.0426

Any of the different ways of storing energy, or seeing a system that has a lot of energy, you got a really good intuition, and that is enough.0438

You will be able to rigorously define and being able to talk about things in a really specific way, for a later advance Physics course, that starts to matter.0445

For now, we are going to be still be able to do plenty of stuff with what we have got,0453

We have got plenty to work with.0457

Being able to define it rigorously, it is something to do down the road, when you study a whole bunch more Physics.0459

With all that behind us, let us talk about how to derive a formula, useful mathematical formulae, we can talk about things quantitatively.0466

How can we get the amount of energy in something's motion.0474

Kinetic energy.0477

From the theoretical point of view, we have seen that putting work into a system is the same as putting energy in.0478

But we have not quantified it yet.0483

Let us fix it.0485

Consider a simplified picture of work, where the force F is parallel to the displacement.0488

That means that θ = 0, so from here on we are just going to pretend that cos θ = 1, we are just going to get rid of it, so for this case, work = force × distance. (normally, work = force × distance × cos θ)0493

We have got a block of mass 'm', and it is on some magical frictionless surface and it starts at rest.0513

This is how things are to begin, let us talk about from here.0520

Consider the following three formulae from all of our previous work.0524

Definition of how we got the force, force = ma, also from kinematics, vf2 = vi2 + 2ad (d is distance), and what we just defined in our last section, work = fdcos θ = fd, because we are looking at a simplified picture.0526

From this, we get, we can talk about the acceleration, because we want to be able to slope things in to our velocity, so we can talk about what velocity means, we need to be able to get a relationship between 'fd' and velocity.0548

What we are going to be doing is to mathematically massaging this, until we are able to get an expression that shows us something that can connect work and this new formula would become kinetic energy.0561

We are going to say that is work, because work is the amount of transferred energy, if we put work into something that starts off with no kinetic energy, that will tell us what the formula for kinetic energy is.0573

If we want to get acceleration, we get that, a = F/m .0581

Also, vi = 0, we said that this thing started at rest, so we can knock that out.0590

For ease, vf = v.0596

From there, v2 = 2ad, we have 'a' up here, plug that in, v2 = 2F/m × d, we are really close, we got an 'F' and a 'd' already.0607

We move that m and 2 over, multiply both sides by m, we get, mv2, and divide both sides by 2, we get, (1/2)mv2 = Fd = work.0629

So the work, if we start off with no kinetic energy, if we out work into the system, that is all going to become kinetic energy, because we have got nothing resisting it, no friction, it is just freely moving, then all of that just turns into (1/2)mv2.0642

The amount of kinetic energy in the system, is (1/2)mv2.0657

Now, from our derivation, we get this formula, the amount of energy in a moving object, Ekinetic = (1/2)mv2, notice this is using speed, we cannot square velocity, squaring a vector does not mean anything, but we can square a magnitude.0662

So we use the magnitude, its energy is a scalar value, it is not a vector, direction does not affect the energy, you could be going a 100 miles/h to the north, to the east, to the south, up, down, does not matter, 100 km/h, 100 km/s, they are all going to wind up being directionless, it is all about the speed that they are going at.0681

Ekinetic = (1/2)mv2 .0704

Now we have got a formula, now we can really get our hands dirty.0712

Units: We talked about work being the quantity of energy moved, so if work is the quantity of energy moved, if that is the amount that we move, we are going to need energy to be the same as work, in terms of units.0715

So, at the moment, we are just hoping that work and energy are going to wind up having the same units.0728

Let us see if that is the case.0731

Ekinetic = (1/2)mv2, so what is m?, (1/2) is just a scalar, so we get rid of it, we got m is kg, velocity is m/s, but squared, m2/s2, now Fdcos θ , cos θ is a scalar, just a number, changing the amount, but it does not change the units.0733

Force is newtons, and we got metre, we need to figure out what newtons are!0761

F = ma, 'a' is m/s/s, mass is kg, that means, m/s/s × kg, this is the same as, m2/s2kg, everything checks out, we are happy!0765

So the units make sense, so the world is safe, so we can just shorten things easily, we will call it a joule, a joule is both the measurement for energy and for the amount of work moved.0788

Work is joules, energy is joules, joules is energy.0800

Conservation of energy: To be able to really do anything with kinetic energy, we are going to need to talk about the fact that it stays the same, unless it is affected by its environment.0806

We talked about the fact that energy cannot be made or destroyed, it is only transferred from different systems to different systems, or from different types to different types.0815

Energy in a system must stay constant unless some of its energy is transferred, work, that is what work is, to another system, or another type in another system.0823

But, if we look at all the types within a system, the energy of the system, so this is not just kinetic, but all the energies within the system at start, plus the work, the amount of that change, and that is equal to the energy of the system at the end.0834

All the types of energy at once.0850

Notice that energy transferred into the system, if you put work into the system, to increase its energy, that is represented as a positive value, positive work, environment does work on the system, force is going with motion, chemical energy being contributed, things like that.0852

Energy that is transferred out is negative work.0868

If work is taken out of it, if system does work on its environment, or the environment takes energy out of the system, say friction, then that is going to be negative work.0870

Work is positive if it is going into the system, negative if it is coming out of it, it is going to be up to us to pay some attention to what is going on here.0880

Energy of the system at the start + the work = energy of the system at the end, that is the conservation of energy, that guarantee is going to give us so much power in solving an entire new set of problems, allows to really get a good understanding of how the world works.0888

One last thing to talk about: How does friction work!0903

It is really easy in fact, form an intuitive stand point, friction is the environment taking energy out of it, or we can think of as the energy putting energy in the environment, in either case, the object's motion is going to be slow, it is going to lose its kinetic energy, it is not really going to gain anything, we are just going to get heat dispersal.0906

Friction reduces the energy in the system.0922

By how much?0925

It is as simple as using our formula for work, and our knowledge about friction, remember, if we have got something sliding along, friction always works this way.0927

If it goes this distance, then the work is just going to be equal to, (-) × (magnitude of friction) × (distance), that is it.0936

The work in the system will be negative because its losing it, it is just the friction force times the distance that the object travels.0947

Friction always points backwards, and always gives a negative value, and always saps the energy out of the system we are looking at.0953

Ready for our examples.0960

First off, real easy one: Block of mass 10 kg is at rest on a frictionless surface.0962

It has a horizontal force of 20 N, applied to it for a distance of 25 m.0973

What is its velocity afterwards?0980

Notice, if we were doing it the old way of kinematics, and F= ma, it will be a little bit more difficult, we will have to figure out what the acceleration is, and we will have to use that complicated, vf2 = vi2 + 2ad, whereas in this case, we just figure out the work, we plug into our formula, BOOM!, we have got it.0982

How much work is put into the system?0998

The work = force × distance × cos θ = fd (since parallel) = 20 N × 25 m = 500 J, going into the system.1000

The system starts at rest, we have got the block starting at rest on a frictionless surface, so no energy is lost, so, (energy of the system at the beginning) + (work) = (energy of the system at the end).1021

At the beginning, this is zero, there is no energy, it is sitting there still, 0 + 500 J = (1/2)mv2, since we know it is all going to be velocity in the end.1036

From here, we just solve for what 'v' is, we know what 'm' is.1051

2 × 500 = 1000, 1000/m = v2, sqrt(1000/m) = v, m is 10 kg, so, v = sqrt(1000/10) = sqrt(100) = 10 m/s .1058

Do not even need a calculator for this one, because it is so easy, 10 m/s, and we are able to do it by just figuring out the work, and figuring out what the kinetic energy is, what the energy connected to that speed is.1086

We know it starts off with no energy, and then we know that all the energy goes into its kinetic energy, so it is as simple as figuring out how much energy is put into the system, and we are done.1099

Example 2: Two identical cars of mass 1500 kg are driving directly towards one another at 15 m/s, and -15 m/s.1109

They crash into one another in a horrible screaming trash of metal, they come to a complete rest after impact.1118

How much energy is released during the crash?1123

At the end, we have got 0.1127

So, whatever energy beginning is, that is going to be our answer.1132

How much energy is in the system in the beginning?1138

How much is it in each car?1140

For one car, the Ekinetic = (1/2)mv2, and we are going to assume that all the energy is in its kinetic energy, because it is just its motion here, so that makes sense.1142

(1/2)mv2, we know it is 1500 kg, we know what the mass is, we plug these things in, (1/2) × 1500 × 152, and the energy of one of the cars is going to be equal to 168750 J.1157

That is a pretty fair amount.1180

But we got to remember that, also the car is going to have that released, because it is in each one of the case, we do not just have that +15, we have that -15 velocity.1182

Since it is speed that we are looking at, we know that they are each going to have the same kinetic energy, so for the crash, it is going to be , the energy of the car × 2, so 2 ×, Ekinetic(of one car), which is = 337500 J.1196

So that is how much energy gets released during the crash.1220

That is a fair bit of energy.1227

Now, what would happen if we double their velocities, instead of driving at 15 m/s, and -15 m/s and hitting one another, they were at 30 m/s each when they crash into one another in completely opposite directions.1228

If that is the case, then we are going to have to change what the velocity is.1244

We know that the crash at double speed (in red, since it is going to be a lot more dangerous), is going to be, 2 × (1/2)mv2 = 1500 × 302 = 1350000 J.1249

Notice that 1350000 is way more than double 337500 J, in fact it is quadruple, because it is going up with the squared of the velocity, the squared of the speed here.1282

It is not just about going double the speed, that means you have quadruple the energy, and that is why freeway accidents are so dangerous.1295

Because everyone is traveling at such a high speed, it is more dangerous, it is 4 times more dangerous in terms of the energy given out, to have an impact when you are driving at 40 m/s than at 20 m/s.1302

Those are reasonable freeway speeds, and those are like normal city speeds.1317

So, it is much more dangerous to get in a collision on the freeway, it is simply because the energy involved to stop those cars, at any reasonable rate is going to take a whole lot of more energy, so the energy is a lot more dangerous for the freeway impact.1322

And that is why it is so important to be careful on driving on the freeway, it is because it is way more dangerous, potentially, if you get into an accident.1335

Example 3: What if we got a block of mass 20 kg, once again sliding on a frictionless table, no air resistance, nothing like that, so it is just about the energy being put into it, with vi = 4 m/s.1343

Then acted upon by a force of 35 N at an angle of 20 degrees above the horizontal for a distance of 15 m.1360

What is its speed afterwards?1366

We do not have to worry about the force of friction, so we do not have to worry about the normal force, so we do not have to break down that force of 35 N into its components, we just have to figure out how much work does it put into our system.1367

The work = fdcos θ = 35 × 15 × cos(20) = 493.3 J.1378

Conservation of energy formula, we know that the energy at the beginning in our system + work put in = the energy at the end in our system.1407

What is the energy in the beginning?1421

Remember, it did not start at rest this time, this time, it had an initial velocity of 4 m/s.1422

So, we have to include that.1428

(1/2)mvi2 + 493.3 = (1/2)mvf2 (work is positive because the environment acted on the object, not the object losing energy to the environment), (also, these are actually the magnitudes, since we are talking about speeds.)1429

Plug things in, (1/2) × 20 × 42 + 493.3 = 653.3 J.1465

So, that means our energy at the end, is equal to just the motion in the velocity, just the energy in the velocity, Ekinetic, is going to be, (1/2)mvf2 = 653.3 J.1490

We solve the algebra, we get, vf = sqrt(2 × 653.3 / 20) = 8.08 m/s.1517

We know what the starting energy is, we know how much work goes into the system, we put those things together, that gives us the ending energy, and then we figure out what energies are going to be being used in the end, it is just the kinetic energy, that is the only energy that is going to be in our system at this point, so we know that the total ending energy is equal to the kinetic energy at the end.1559

And we just solve for it.1580

Final one: This one is going to take a bunch of ideas.1583

Block of mass 3 kg, is resting on a surface, where it does have friction.1586

Friction coefficients are, μs = 0.8, and μk = 0.4.1591

It is acted upon by a force of 100 N, at an angle of 40 degrees below the horizontal, so it is pushing down on to the block.1598

Does it move?1607

The force acts on it for a distance of 50 m, what is its speed after 50m, how far will it slide afterwards?1608

First things first, we need to figure out if it is able to move.1614

How do we do that?1618

To be able to figure out if it is able to move, we need to compare the force acting on it horizontally, to the maximum static frictional force, that it has.1619

First, we are going to break this down, into its component pieces.1629

Actually, we probably would be better off by looking at it in the other point of view, because we know what the 40 degrees are, so, we look at it, over here, so, 100 N is the hypotenuse, 40 degrees here, so cos(40) × 100 will give us what the horizontal action is.1634

That is going to be 76.6 N, and the vertical is going to 64.3 N, pointing down, pointing to the right.1652

If we want to split this into a vector, we know that the force vector is going to be 76.6 N, and -64.3 N.1665

Before we are able to figure out what the normal force acting on the block is, we need to figure out what the force of gravity is, because this block is being supported by the table.1677

If the block is not falling through the table, then that means all the vertical forces on it are in equilibrium.1685

The normal force, the force contributed by the table is going to have to beat out, not just the force of gravity now, but also the force of pushing down into block.1689

What is the force of gravity?1699

Force of gravity = mg = 3 × 9.8, plug that in later.1701

If we want to know what the normal force is, we know that the normal force is going to have to be equal to cancelling out both of those.1718

It is going to have to be positive, pointing in the up direction, it is going to be equal to 63.3, so it can cancel out the force pushing down on the block, and then also, plus mg, so it can cancel out gravity.1725

We put those together, and that gives us 93.7 N.1740

So, the normal force is 93.7 N.1744

Now we are ready to calculate what our maximum static friction is.1747

Maximum friction static = μs × FN = 0.8 × 93.7 = 75.0 N.1751

That is the maximum friction static.1773

Now, we need to compare that to the force of our pushing on the block, what is the force pushing on the block?1776

Its horizontal force is 76.6 N, is greater.1785

That means, YES!, it moves.1798

That means , we can actually pay attention, we do have to care about the rest of the problem, because we are able to beat out static friction.1805

Now, let us work on everything else.1813

If friction static is able to be defeated, then we can now figure out how much work gets put into it by the force.1816

The work of the force = magnitude of force × magnitude of displacement × cos θ = 100 × 50 × cos(40) = 3830 J.1824

Now, remember, this entire time it is moving, it is also being hit by friction.1863

We have got friction fighting it.1870

The whole time it is moving that 50 m, it is being fought by friction.1873

So, it moves along, it slides along, but as it is sliding, it is also continually losing energy to friction.1877

The block is giving energy to its environment, it is gaining energy from the force that the environment is putting into it, but it is also winding up giving heat energy through friction.1884

So, it is going to have that much work coming out if it.1894

It moves along that 50 m, and it is going to continue moving, because the force is able to beat out the force of friction.1897

But, once the force stops acting on it, it is going to slide.1904

How far will it slide?1908

It is going to take all of the friction to sap all of the kinetic energy out of it.1909

Once it has lost all of its kinetic energy, it will be still, if we can figure out how far that distance is, we will know what the slide is.1914

What is the speed at 50 m?1921

We need to first figure out how much work has friction done over those 50 m.1924

That is going to be, force × distance × cos θ = μk × FN × 50 m, (cos θ = 1, since perfectly parallel.)1931

One last thing to figure out: which direction is friction working?, it is working negative, it is pulling away from this the whole time.1963

Our work value for the friction is going to be negative.1970

So, -0.4 × 93.7 × 50 = -1874 J.1973

It gains 3830 J from the force acting on it, but it loses 1874 J through the force of friction acting on it.1983

What is its starting kinetic energy?1992

Its starting kinetic energy is nothing, it sits still at first.1994

(Energy at the beginning = 0) + (the work) = (Energy at the end).1999

The work and now our ending snap shot is at this 50 m line, we want to figure out what is the velocity there.2007

The work that goes in, 3830, the work that comes out is 1874, and that is = the kinetic energy at that moment, because all of our energy, all of our work, is going into kinetic energy, (1/2)mv2, where we are talking about the speed really.2013

We figure out what that is, we get, 1956 = (1/2)mv2, solve for v (speed, this whole time we know that v is single dimension, so that is not a problem), v = sqrt(2 × 1956 / 3), solving, we get that it is sliding at a very fast 36.1 m/s, at the end of it push.2037

Now we know how fast it is sliding at the end of the push, how far will it slide after that?2079

Now we need to figure out, the only thing working on it now, is we have got, E(beginning) + Work = E(end).2085

So, for the first one, the one on the left, over here, we had a beginning snap shot, the beginning snap shot was still, and the ending snap shot was the very end of the push.2095

For this one over here, we are talking about, beginning snap shot is the end of the push, when it already has all that energy stored in it, and its ending snap shot is just as it comes to rest, once it is still again.2108

We know that, E(beginning) + Work = E (end), E(beginning) = 1956, we can also figure that out by doing (1/2)m(36.1)2 because that is how much energy is, but that is going to wind up being 1956, because we already solved for that).2119

So, 1956 + work = 0, (when still, it has no energy.)2150

That means, our work = -1956.2160

What is the work in this case?2165

The work is just friction, remember?2166

We know this is friction, because the only thing acting on it now is the work of friction.2169

What is the distance that is slides?2174

We know that friction is negative, so, μk × FN, but now the normal force is actually a different number.2176

FN is equal to just gravity at this point, because now we no longer have it pushing on it, so, -μk × mg × d = -1956.2187

We know what μk and FN are, we do not know what the distance is, that means we only have one variable to solve for, so we can make these positive on both sides.2213

d = 1956 / (mg μk) = 1956 / (3 × 9.8 × 0.4) = 166.3 m, this time it slides a very long distance.2225

It gets pushed for 50 m, and that whole time it has got a very large additional frictional force contributed by the force pushing down.2282

But once we remove that, it is going to be able to slide longer, because it does not have to deal with the force pushing down on it the whole time now.2291

The normal force change between the two different worlds we are looking at, in the second world, we did not have that force pushing down on it now, so we now have a different normal force, and that is a definite trap that you could fall into.2299

If you forget to change that, at which point you get a different answer.2310

Bu tin this case, we caught that, we know that it is going to be 'mg' is just the normal force at this point.2313

μk × FN × d is the work done by friction, so now we need to figure out how much distance it goes, and once it completes that slide, it will manage to take out all of the kinetic energy, and it will come to a rest or come to a zero kinetic energy.2319

So, we get 166.3 m, and there is our answer, that is how far it slides after you stop pushing it.2337

Hope you enjoyed it!2343

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