Enter your Sign on user name and password.

Forgot password?
Sign In | Subscribe
Start learning today, and be successful in your academic & professional career. Start Today!
Use Chrome browser to play professor video
Vincent Selhorst-Jones

Vincent Selhorst-Jones

Power & Simple Machines

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
Loading...
Educator®

Please sign in to participate in this lecture discussion.

Sign-In OR Create Account

Enter your Sign-on user name and password.

Forgot password?

Start Learning Now

Our free lessons will get you started (Adobe Flash® required).
Get immediate access to our entire library.

Sign up for Educator.com

Membership Overview

  • Unlimited access to our entire library of courses.
  • Search and jump to exactly what you want to learn.
  • *Ask questions and get answers from the community and our teachers!
  • Practice questions with step-by-step solutions.
  • Download lesson files for programming and software training practice.
  • Track your course viewing progress.
  • Download lecture slides for taking notes.
This is a quick preview of the lesson. For full access, please Log In or Sign up.
For more information, please see full course syllabus of High School Physics
  • Discussion

  • Study Guides

  • Download Lecture Slides

  • Table of Contents

  • Transcription

  • Related Books & Services

Lecture Comments (2)

1 answer

Last reply by: Professor Selhorst-Jones
Mon Dec 10, 2012 1:23 PM

Post by Abdelrahman Megahed on November 30, 2012

Example 4:

How come when you use other method not COE you end up with 7.4s?

Power & Simple Machines

  • Power is a measure of how quickly we put work into a system. Mathematically,
    P = W

    t
    .
  • Since work is a transfer of energy (W=∆E), we can also formulate power as
    P =∆E

    t
    .
  • Finally, we can also formulate it as
    P =

    F
     
    ·

    v
     
    [Note: this requires you to use the dot product for vectors. If you aren't familiar with dot products, this is equivalent: P = |F| |v| cosθ.]
  • Power has the unit of joule per second ([J/S]). We call this a watt (W).
  • Simple machines are based on the idea of conservation of energy. Instead of using a large force over a small distance, we can use a small force over a large distance and still put in an equivalent amount of work.

Power & Simple Machines

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
  • Introduction to Power & Simple Machines 0:06
    • What's the Difference Between a Go-Kart, a Family Van, and a Racecar?
    • Consider the Idea of Climbing a Flight of Stairs
  • Power 2:35
    • P= W / t
  • Alternate Formulas 2:59
    • Alternate Formulas
  • Units 4:24
    • Units for Power: Watt, Horsepower, and Kilowatt-hour
  • Block and Tackle, Redux 5:29
    • Block and Tackle Systems
  • Machines in General 9:44
    • Levers
    • Ramps
  • 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

Transcription: Power & Simple Machines

Hi, welcome back to educator.com, today we are going to be talking about power and simple machines.0000

Let is just start off with, what would you say is the difference between a go-kart, a family car and a race car is?0006

I will be honest, there are a lot of differences, but I would say their main difference is their top speed.0013

It is high fast they can go.0020

How quickly they can get in going a certain speed.0022

You are going to get a lot of difference in how fast a race car can get from 0 to 60, ad how fast the family van can get from 0 to 60.0025

The major issues here are, how fast they can go at their maximum, how much power can they put out.0032

What is the idea of power?0037

So far we have talked about speed and its connection to energy, but we have not talked about different rates of gaining that kinetic energy, we have just talked about it being there.0040

We have not talked about the difference between getting it to going fast quickly, we have only been talking about going fast versus going really fast.0049

There has been, the speed that you are going at, there has been no talk about how fast you can get to go in that speed, what is your acceleration has had no effect on this.0057

That is where power is going to come in, we are going to start talking about how quickly an object or system gains energy.0066

Consider the idea that we are climbing a flight of stairs.0074

Let us assume that we weigh 50 kg, for me 50 kg is fairly well under my weight.0077

The stairs are 5 m high.0090

There are two scenarios.0092

In one of them, you climb the stairs in 5 s you really hustle.0093

But in the other one, it take you 30 s.0097

In both these scenarios, we are going to have the exact same amount of energy at the end, the same amount of potential energy, (not develop the same power.)0099

We climb the same height, we are dealing with the same gravity, we have the same mass.0108

But, very different scenarios.0113

How fast you climb those stairs, that is something we should talk about, and care about.0115

In both cases, we have that same gain of energy of gravity, 50×9.8×5, so in both cases we have 2450 J, when we make it to the top of the stairs.0120

But they are clearly very different scenarios.0129

So we need a way to talk about the interaction between work and energy, and time.0131

Work and energy, and how fast we are able to put work and energy into a system.0138

How quickly we are able to change the work and energy in a system.0142

This is going to really matter for some applications.0145

For that race car, we want to be in a race car that can put massive quantity of energy into its system, really fast it can get off the starting line and win the race.0147

With this idea, we make a really simple creation to call this power, just, power = work/(amount of time it takes), work/time, that will give us a way to talk about how much work we are able to deal with in how much time.0157

Just like velocity was how much distance we have gone, divided by how much time to do it, we het a very similar idea with work/time for power.0172

With power defined as work/time, we can easily create a few equivalent formulae.0180

First, since work is a measure of how much energy is being shifted around, we know work = change in energy, always.0185

Another formula is, power = Δenergy/time.0191

There is another interesting formula we can create.0199

Alternately, we can look back to how we originally formulated work.0201

Work = F.d = Fdcosθ, in this case it is going to help us to use that dot product.0206

This allows us to use velocity.0222

Power = work/time = F.d/time.0224

We pull off that force, and we get, F.d/time, but distance/time = velocity, so, we get, F.v, so, Power = F.v, which also, if we do not want to use the dot product, Fv×cosθ.0229

That same idea that worked with work, works with power.0253

So, F.v, or ΔEnergy/time, or work/time, these are all same way to say power.0257

What unit is power in?0266

Work and energy are both in joules, time is in seconds, so, power = work/time, implies, J/s is the unit for power.0268

For ease, we can call 1 J/s a watt, watt is in honour of James Watt who has done a lot of work with energy in 1800's.0287

A watt is a measure of weight.0295

Just like 1 m/s is the rate that you are moving at, 1 J/s, 1 watt is the rate that you are putting energy into a system.0298

One moment, you could have a totally different power, the next moment, just like your velocity can change.0307

watt gives us an instantaneous measure of how much energy is going into a system, that is the definition of power.0314

In other unit systems, there is also the horse power, you probably heard cars referred to in terms of horse power, and the kilowatt hour, another way of saying watts×time, watt×1000×time.0324

Horse power, kilowatt hour, all ways of saying power, that is why energy bills involve these things, cars involve these things, you see these things any time you want to talk about how quickly we can get energy into, or out of the system.0343

We are going to make a little tangent here.0356

This does not directly have to do with power, but I know, it has been driving you crazy that we have not discussed block and tackle system more.0359

I know you remember block and tackle problems extremely well, we talked about them in advanced uses of Newton's second law, and they seemed like magic, they seemed absolutely incredible, and it has been blowing your mind, you keep thinking about it, how is it possible, Physics must be lying, fret no more, I am going to make it better for you.0368

Finally we have the understanding of work and energy to see how those systems make perfect sense.0391

There is nothing magical about them, there is nothing insane about them, the world is not coming apart as it seems, it makes perfect sense when you look at it in terms of energy.0394

I know you love thinking about it, but once again, let us talk about it briefly, quick reminder about how the block and tackle system works.0401

Let us say we have got the force of gravity pulling down on this block, Fg, it is pulling down on this block.0411

If we want to keep it still, or move it up, say we want to keep it still, we are going to have to pull with the force of gravity here, put that much tension into it, so we have got canceling it out, the force of gravity over here.0417

But over here, something weird happens.0430

If we pull with a certain tension, then that tension is going to get pulled in here, but it is also going to get pulled in here.0433

So we still got that same mg, that same force of gravity, but over here, we are going to have the tension = (1/2)Fg, because if this is (1/2)Fg, and this is (1/2)Fg, then when we put them together, we are going to wind up combining two, one whole force of gravity.0440

With the block and tackle system, we are able to distribute our forces over multiple pulleys.0460

We are able to distribute the same tension force in multiple places.0466

It seems crazy, we are able to get more force for the same original cost.0470

How is this possible! This seems like madness.0474

The thing to notice here, is that the block and the single pulley system, say we wanted to raise this block 1 m.0479

If we wanted to raise the block by 1 m, how much rope would we have to pull?0488

We would have to pull 1 m of rope.0491

We have to pull, say some force F.0494

Over here, we know that we only have to pull at half of that force, F.0497

To be able to get that raising happening.0501

But, if we want this block to raise up 1 m, we do not just have to get this move by 1 m, if this moves 1 m, we would be lopsided, we have to get this move 1 m as well.0503

Both sides of our rope system have to move up a metre, that means we have to get 2 m of motion in our rope.0514

Over on the left side, we are able to use 1 m of motion for 1 m of motion.0524

Over here, if we want to get that 1 m of lift, we have to put 2 m of distance into our rope.0530

Even if we can use half the force, we have to pull double the distance.0536

So, our work, the amount of energy in our system is preserved, the force×distance.0542

This is force × 1 = F, for work.0547

Over here though, we have got, work = (1/2)F × 2 = F, so they wind up being the exact same things, checks out.0555

For us to be able to manipulate how the system works, we still have to maintain that conservation of energy, that conservation of work.0568

It is equivalent work, because the change in the system, the real change in the system, is how high up we are able to change that block's height.0576

If you want to do that, we are going to have to put in the same amount of work, no matter how we go about it.0585

Work that goes in, is equal to F in both cases, because you have to pull double the rope.0590

And if we had a multiply pulley system, where we were able to have four pulleys, we only have to pull with a quarter of force, we would wind up having to pull 4 times the distance.0597

Everything works out, there is nothing magical about it, it makes perfect sense.0605

It is the same idea in place with all of our machines.0610

Let us look at ramps and levers.0613

First we will look at levers.0617

If we want to get some object to move up here, traditionally you have a lever, you stick it under, you got a fulcrum, you got a long lever arm, and you pull, you pry.0618

You put a low pressure here, and you get a really strong force here.0627

High pressure here, low pressure here.0632

How is it being done, it is being done based on work.0634

You got that small force over here, small force, but it covers a really long distance.0637

On the other side, we get this small distance covered, which means, to be that work to be preserved, it is going to be have to put up a massive force.0643

The reason why a lever works, is that the energy is conserved.0651

If you put a slight force over a long distance, and the other side has a slight distance, then it is going to need a big force to compensate.0654

Force×distance has to be equal in any case.0663

Over the lever, if you put that fulcrum really close to one side, we will be able to get a giant force with little distance.0667

So, the amount of work is preserved, it makes perfect sense.0674

You see the exact same thing with a ramp.0677

If we want to get this box up this ramp, then we can push with this little force over this really big distance.0679

But, if we want to get this box directly up, then we will have to lift a whole lot harder, but we wind up going a smaller distance.0685

The ramp works, because we are able to get a small force over a long distance, whereas if you just want to lift it up with brute strength, we need a really powerful force, but we will be able to save some distance.0694

The same idea, force×distance, they are always equal.0706

The way that you are going to distribute, how you are going to put it in, what ratio you want to put it in, that is up to you.0709

But, it is going to have to come out equal when you multiply the two.0715

However you put it in, work is going to be conserved, energy is going to be conserved, the energy that goes into it is going to be the same however you do it.0719

Machines do not allow us to break the rules of Physics, they just allow us to take advantage if the resources that we have on hand.0726

They allow us to use the rules of Physics on our side.0732

If we have a little force, but a lot of distance or time, we can figure out an alternative rather than needing a really big force.0736

Like with the ramp, like with the lever, like with the pulley system, you can have that slight force, and then figure out the way to multiply by using more distance, or more force, or both , so you can take advantage of what you have, by being able to use the same amount of energy.0742

Same amount of energy will go into the system, same work, but it is up to us to figure how to get that work into it, and that is where the cleverness of machines comes into being, at least simple machines.0757

Now we are ready for our examples.0769

How much work is going to be involved here?0771

50 kg block is pushed along a horizontal surface at a constant velocity by a parallel force 47 N.0773

It covers 10 m in 5 s.0779

What is the power of the force?0781

Lets us draw a quick diagram.0783

Do we have to care about the mass?0801

We do not have to care about the mass.0802

Our power formula is, work/time.0804

We can figure out the work, work = F.d = Fdcosθ = Fd (since parallel).0807

So, 47×10 = 470 J of work.0820

What is the time? 5 s, so , Power = 470 J / 5s = 94 J/s = 94 W, that is the power of the force.0828

It does not change, the power remains the same, because we got a constant velocity.0850

Remember, we could have also used, F.v.0855

If you wanted to, we could figure out, it travels 10 m in 5 s, means that we got, 2 m/s = v, and F = 47 N, so, power = 47×2 = 94 W, two different ways.0861

Example 2: 2 kg watermelon starts at rest, and it is lifted vertically, 9 m.0887

It takes time 20 s, and ends at rest.0898

Over that lifting, what was the power developed in lifting that watermelon?0900

You started at some height, you reached another height, how do we deal with that?0905

Potential energy.0909

What is the change in energy?0911

ΔE = mgΔh = 2×9.8×9 = 176.4 J of work.0913

We know that, power = ΔE/t = 176.4 J/20 s = 8.82 W.0933

There you go, the change in energy divided by how much time it takes to put it i n there, just like velocity, just like acceleration, it is what you have got already, distance or speed divided by how much it is altered, how much it is being changed by, how much it is being increased by, that tells us how much the power being developed is.0952

The power of the system is the change of energy, how much work is going into that system.0970

Just like velocity is how much distance is going into an object, whereas the acceleration is how much velocity is going into an object, just a way of thinking how much velocity is going into an object, a way of thinking how much you are putting into a thing.0978

S0, 8.82 W is what is put in, in that 20 s.0987

Example 3: 20 kg block is initially at rest on a flat frictionless surface.0992

Parallel force of 10 N acts on the block.0997

What is the work done on the block in (A) the first second (B) the second second (C) the third second (D) the instantaneous power at the end of 3rd second.0999

First thing to think about, work = F.d.1009

Is this object accelerating?1015

It is on a flat frictionless surface, it has got a force acting on it, of course it is accelerating.1016

The amount of distance it is going to cover is going to change the entire time.1020

It is also going to have a change in velocity.1023

Now we have got two different ways of looking at this.1025

We can approach this by wither thinking about the distance that it has changed, it is going to be able to give us our work, and from the work, we will be able to get our power.1027

But we can also think that the velocity that it has at each time, would be a way to tell us what is the change in energy, and from the change in energy, we can get the amount of power.1040

These are both perfectly good ways to do it, and we will do both of them just to be able to understand two different ways to approach this problem.1055

First way, we are going to go with distance.1060

What is the formula for distance?1066

We got, F = ma, 10 N = 20 kg×a, a = (1/2) m/s/s.1068

What is the other formula for distance?1082

From basic kinematics, d(t) = (1/2)at2 + v0t + d(0) = (1/2)at2 = (1/4)t2, is our distance, (d(0) and v0 are zero).1084

Now we have got a distance formula.1107

Now we want to find out where is it at 1 s, 2 s and 3 s.1112

Plug things in, d(0) = 0, d(1) = (1/4), d(2) = (1/4)×22 = 1, d(3) = (1/4)×32 = (9/4).1122

If you wanted to see what the distance covered in that period of time is, that change in distance, we can say what is the distance between 0 and 1?1149

That is clearly (1/4).1157

What is the distance between 1 and 2? That is (3/4).1159

What is the distance between 2 and 3? That is (5/4).1165

These three changes in distance, if we want to figure out what the work involved is, we know, work = Fd.1171

Then, work that happened from 0 to 1st second is, 10×(1/4) = 2.5 J of work.1180

What was the work done between 1 and 2? That is, (3/4)×10 = 7.5 J.1200

What is the work from 2 to 3 s? That is, (5/4)×10 = 12.5 J.1209

Now, if we want to know how much power, what the average power was, over each one of these, we just go, 2.5 J/1 s = 2.5 W, was the average power in that first second.1218

In the 2nd second, 7.5 J/1 s = 7.5 W.1228

In the 3rd second, 12.5 J/1 s = 12.5 W.1237

Remember, these are going to be the average powers, because this is not going to give us the instantaneous.1244

Clearly, the amount of power is changing the faster it goes, because it is getting the chance to cover more distance, and that is how that force being applied more and more, since work = Fd.1248

If we want to know what the instantaneous power is, we are going to need to know what its speed is at a given moment.1257

Remember, power = F.v, v(3 s) = at = (1/2)×3 = 3/2 is the velocity at the 3rd second.1264

If we want to figure out the instantaneous power, Power at the third second, power (3 s) = 10 N × (3/2) = 15 W. (Dot product becomes multiplication because of one dimension, in dot product we are dealing with more dimensions, in more dimensions, we will have to know how to use the dot product, we will have to multiply the first components together, add them to the second components, multiply and add them to the third components, so on and so forth, for as many components you have. You probably will do with only 2 or 3 since you dealing with Physics, but it will work with any.)1304

So, the instantaneous power is 15 W for that third second, which makes sense, we see that our average, 2.5, 7.5, 12.5, it continues to go up, so the at the very end of the third second, we got 15 W of instantaneous power.1344

Remember, the instantaneous power can change just like your instantaneous velocity can change.1358

If you are driving in a car that is accelerating, every instant that you move along, your velocity is getting larger and larger.1364

So, if the car is accelerating, you got a larger velocity instant by instant.1370

In this case, we got a larger and larger power instant by instant.1374

If we have got an alternate method, let us start using it, how will that alternate method work?1378

So, we know, we did distance already, we can figure this out using distance, but we can also use velocity to tell us changes in energy.1382

Now we are going to do this using velocity.1390

If we want to see what its velocity is at 1 s, at 2 s, at 3 s, what is the formula for velocity?1394

We know, v(t) = at = (1/2)t, (since previous values still work), makes sense.1403

In this case, what will be velocity at 0 s? Zero, it is still.1424

v(1 s) = (1/2) m/s, v(2 s) = 1 m/s, and v(3 s) = (3/2) m/s.1431

If you want to see what the energy in its movement at that time is, we know, E(0) = (1/2)mv2 = 0, E(1 s) = (1/2)×20×(1/2)2 = 2.5.1443

E(2 s) = (1/2)×20×1 =10, and E(3 s) = (1/2)×20×(3/2)2 = 22.5.1473

So, we have got, 2.5 J, 10 J, 22.5 J.1495

If we want to figure out what the change in energy is, because we are working towards figuring out what the work is in each of these seconds, change in energy = work, work = ΔE.1500

ΔE(0 to 1) = 2.5 - 0 = 2.5 J, ΔE(1 to 2) = 10 - 2.5 = 7.5 J, ΔE(2 to 3) = 22.5 - 10 = 12.5 J, it is the exact same thing that we saw by doing it the other way.1514

Figuring out through the work, figuring out through the change in energy, of course they are going to give the same answer because they are the same thing.1543

If we want to figure what the power developed at the 3rd second was, we just do the exact same thing we did previously, so we can skip that, because we are just figuring out instantaneous power, and we discussed that on the last slide.1548

But, it is kind of cool to be able to see that we have got two different ways of approaching it.1559

So, whichever way that makes more sense to you, is the way you want to do it.1563

The important thing to think is, "Okay, great! I have got lots of methods, I have got lots of ways I can attempt a problem." Figure out what is the best for you, what is the best possible way to approach a problem, and then do it.1567

There are lots of tools for any given job, and it is up to you to figure out what tool to use.1577

Last example: This one is a fun one.1583

We have got a race car of mass 1500 kg, and it has an engine capable of putting out 700 hp ~ 5.22×105 W of power.1585

Neglecting air friction, and friction on the ground, the air drag, the car begins at rest, and we assume that the car puts out its maximum amount of power, how long will it take the car to accelerate to 50 m/s on flat ground?1595

In this case, what do we want to use, what power formula are we going to use?1608

Do we know what the work is? Do we know what the forces involved are?1612

We do not really.1615

Do we know what the change in energy is?1616

We do know what the change in energy is.1618

It starts at a stop, it stops going at 50 m/s.1619

Do we know what its instantaneous velocity is?1623

No, because that is going to change depending.1625

So, we do not really want to go with that one, because that will give us the force, and the force is not really useful, so the best choice for this one is, power = ΔE/t.1629

We know what the time is, can we figure out what is the change in energy?1639

We do not know what the time is, we are solving for the time.1681

But we do know what the change in energy is, we do know what the power is, so we are good to go.1686

That gives us, t= ΔE/power = (1/2)mv2/power = (1/2)×1500×(50)2/(5.22×105) = 3.59 s, that tells us how long it will take us for that car to accelerate form a dead stop, to going at 50 m/s, and that is equivalent to 110 miles/h.1702

3.59 s to get to 110 miles/h, or 50 m/s, that is pretty darn good, that explains why race cars are so powerful.1725

Hope you enjoyed this lesson, hope power made sense, just think of it as the change in work, the change in energy, and how long it took to get there.1732

There is a great analog between speed and velocity and energy and power, it is the same thing.1739

How fast are we changing, how much are we changing from moment to moment.1752

Hope you enjoyed this.1756