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Vincent Selhorst-Jones

Vincent Selhorst-Jones

Newton's 2nd Law: Advanced Examples

Slide Duration:

Table of Contents

I. Motion
Math Review

16m 49s

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

26m 2s

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

29m 59s

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

18m 36s

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

16m 34s

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

12m 37s

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

27m 5s

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

27m 47s

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

42m 5s

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

16m 47s

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

50m 11s

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

26m 45s

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

28m 34s

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

39m 7s

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

28m 10s

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

44m 16s

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

28m 54s

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

36m 55s

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

22m 50s

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

40m 55s

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

34m 53s

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

35m 35s

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

52m 57s

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

36m 24s

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

19m 38s

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

42m 52s

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

34m 6s

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

44m 3s

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

27m 30s

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

41m 35s

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

34m 44s

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

29m 12s

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

52m 2s

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

25m 47s

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

2 answers

Last reply by: Peter Ke
Thu Apr 28, 2016 12:35 PM

Post by Peter Ke on February 27, 2016

I don't understand why there's no possibilities for F1 y-axis to go up and down while there is 2 possibilities for F2 y-axis to go up and down, why is that?

1 answer

Last reply by: Professor Selhorst-Jones
Thu Nov 29, 2012 11:04 PM

Post by Abdelrahman Megahed on November 29, 2012

Why can't you just say Fnetx=0; F2cos(theta)-F1cos(57)=0 and then solve for (theta) and finally reapply this in the Fnety=0 eq which would be Fnety=0=F2sin(theta)+F1sin(57)-F3=0, ??

Newton's 2nd Law: Advanced Examples

  • Tension in a rope pulls throughout the rope. With some clever thought, we can use this fact to our advantage.
  • By setting up multiple pulleys, we can cause the same tension to be applied multiple times, effectively multiplying our input force.
  • Why isn't this crazy talk? We'll see why in the lesson on Power when we work on Energy.
  • Making a good free-body diagram to show where all the forces are is incredibly important! Without it, we won't be able to make sense of the problem.
  • Remember, if an object is experiencing an acceleration, it must have a force acting on it.

Newton's 2nd Law: Advanced Examples

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
  • Block and Tackle Pulley System 0:30
    • A Single Pulley Lifting System
    • A Double Pulley Lifting System
    • A Quadruple Pulley Lifting System
  • 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

Transcription: Newton's 2nd Law: Advanced Examples

Hi, welcome back to educator.com, today we are going to be talking about Newton's second law in some really advanced examples.0000

Single dimension is just an introduction to talking multi-dimensionally, now we are going to get the chance to really structure our muscles to see how much we can do with Newton's second law.0006

There are going to be no new specific concepts or major ideas, but it is just going to be the chance to see really advanced complicated problems.0016

We will just be exploring a bunch of examples in this lesson.0025

But first I have got an interesting thing to talk to you about.0029

This is going to be the block and tackle pulley system.0031

You might have heard of block and tackle before.0035

It is used on sailing ships, sometimes on non-sailing ships like motor driven ships.0037

It is a way to be able to use tension to give you mechanical advantage over what you are lifting.0042

You can put less force into your lifting, than it is the actual weight.0048

We will talk about how that is possible, it is pretty interesting.0052

With clever construction, we actually cause the tension in our rope to give us more strength than we first expect.0055

First consider a really basic single pulley lifting system.0061

You have got some weight pulling down, some force of gravity pulling down on our object.0065

If we want to lift this, we going to need a tension pulling here, because this rope is just right here, so it is going to be whatever tension is in that rope.0070

So we are going to have to pull with a force, tension left be equivalent to the force of gravity, for us to be able to lift that block.0078

There is only one direct connection and it is that rope.0086

But, there is a clever thing that we can do.0090

Let us consider a double pulley lifting system like this one right here.0092

So, in this one, we do not have just one rope, we have two ropes.0098

This seems kind of weird, because there is this one connection here, but really what it is, it is the two sides of the pulley.0103

We have got the two different sides of the pulley.0111

So, whatever tension we put in here, is actually going to be translated all the way through, so we are going to have a tension here, and a tension here, so we are going to get double the lift of that tension that we put in.0113

We might have the force of gravity pulling down here, but we can put in a tension equal to one half the force of gravity, and be able to counter out the force of gravity.0124

We can put it in a static equilibrium, with only half the force of gravity.0133

This is really shocking, it seems sort of like magic.0138

The reason is why you will have to work with the fact that, if you want to lift that, you are going to have to pull double the rope as we would in the single pulley lifting system, to this rope has to go a certain amount, and this rope to go up a certain amount.0141

In the other system, we only had to pull up, if we want pull it up a metre, we only had to pull the rope a metre.0157

In this one, if we want to pull it a metre, we have to pull the rope a metre here, and a metre here, which means 2 m .0161

We will talk about this a little bit later, we will get the chance to revisit this really quickly when we are talking about work and energy, but you can certainly understand that there is a bit of trade off here.0167

Let us consider an even more complicated system.0179

Consider a quadruple pulley lifting system.0182

This time, instead of having to just double up once, we are going to have tension here, tension here, tension here, tension here.0184

So we are actually going to get the 'T' to show up 4 times.0193

For one force of gravity, whatever the force of gravity (the weight is of our object), we can actually put in, T = (1/4)Fg, and we will be able to offset that, put everything into static equilibrium.0197

So, by using these 4 pulleys, we are able to spread that tension in the rope and cause it to occur multiple times.0211

It seems sort of fake, -(and this pulley should actually be connected up here, otherwise it will just fall to the ground)-, and unbelievable, but it does actually work, and you will possibly get the chance to see it if you are in a Science museum, or if you are on an old sailing ship, if you get the chance to play with block and tackle, that is what this set up is called.0221

You can actually see mechanical advantage in motion.0239

Whatever the advantage you are looking at, you have to commensurate more amount of rope, but it could be potentially really useful.0241

You would be able to move really heavy things, which you otherwise would not be able to move.0249

The point of all this, is mot to give us a new formula or something new to do in our problems, it is just to make us realize how important it is to be able to carefully think through what we are doing.0252

If we carefully consider all the forces being involved, with a really good free body diagram, we can see really interesting things happen that we might not notice at first.0261

So, drawing really good diagrams is really important and it is something you got to make sure you do, because otherwise you might miss out on really key piece of information.0271

On to the examples.0279

We are going to have a bunch of examples today, and this is the first one.0282

Say we have got a free hanging mass-less string, and it is holding up three objects of unknown mass.0285

We know the tensions in each section of the string though.0291

First off, let us name these masses.0294

We will call them mass-1 (M1), mass-2 (M2) and mass-3 (M3), and we will say that going up is the positive direction.0296

What are the tensions?0307

The tension in the top section, T1 = 98 N , tension in the middle section, T2 = 49 N, tension in the third one, T3 = 9.8 N .0309

What are the masses of the objects?0334

We would not be able to figure it out, but luckily we have got gravity on our side, so we can use gravity to get the information we need.0335

We do a free body diagram for each one of these.0342

This one is being pulled up with a tension of 98 N, but it is also being pulled down by T2 = 49 N, and also being pulled down by the force of gravity on it.0345

This one is being pulled up by 49 N (because that is what is above it), pulled down by 9.8 N (because that is what is below it), and also being pulled down by its own force of gravity, so Fg2.0358

Finally we have got this one, pulled up by 9.8 N, pulled down by Fg3, but it does not have any tension pulling it down.0372

Let us start figuring out what these masses are.0386

Everything is in static equilibrium, so we know that the acceleration across the board is going to be zero for everything.0388

Let us look at M3 first.0394

We know that Fnet,3, (if it has no acceleration, we know that Fnet is equal to zero.), so Fnet,3 = 9.8 N - Fg3 = 0 (everything inside of it), so, Fg3 = 9.8 N = M3g , M3 = 1 kg .0396

That is basically the method we will use for all of these.0439

Fnet,2 = 49 N + 9.8 N - Fg2 = 39.2 N - Fg2 , since this is in static equilibrium, Fnet,2 = 0, Fg2 = 39.2 N = M2g , M2 = 39.2/9.8 = 4 kg .0443

For the last one, we have that Fnet,1 = 98 N - 49 N - Fg = 49 - Fg,1 = 0, Fg1 = 49 N = M1g = 49 N, M1 = 5 kg .0504

That is how we do it.0550

Also, one thing we could have done from the very beginning is, we could have figured it out that there is 10 kg total, because if we consider it as a one big system, then we would have, the tension on the system (in static equilibrium) = 98 N - Fg,system = 0.0551

So, 98 N = Fg,system = Msystemg , Msystem = 98/g = 10 kg, because if we were to add up (5+1+4) = 10.0580

So there are two different ways of doing it, we could have figured out that the total is going to be 10 kg, and if we have two weights, figure out the third, they all work, they are all different ways of doing it.0611

Figure out which one works best for you, and also the specific kind of question you are looking at.0618

On to the next example.0622

Example 2: An object rests on a frictionless surface (we are looking top-down), and is being acted upon by 3 forces.0625

Since we are looking down on it, it is not going to be affected by gravity, so we do not have to worry about gravity for this one.0634

It is being affected by these 3 forces, but it is in static equilibrium, it is not moving.0640

F1 = 250 N (at an angle 147 degrees), F2 = 150 N and F3 is pulling directly down.0645

We want to find out what is F3.0655

First, let us start working on figuring out what the components to F1 are.0659

We know that this is static equilibrium.0663

So, we know that Fnet = (0,0) as a vector, both x and y components are going to be nothing, they are going to cancel out to nothing.0667

What does F1 break down into?0679

What is this angle right here?0681

The whole angle is 147 degrees, and that is a right angle, that means that this is going to be 57 degrees right here.0683

So, we use trigonometry, and we get that (F1 is over here), 250 × sin(57) , and here we have got 250 × cos(57) .0691

We get, F1,x = 136 N , F1,y = 210 N .0711

So we know that 136 N pulling this way, 136 N pulling up as well.0724

Now, what about F2, we know its magnitude = 150 N, but we do not know what its angle is yet, that is an interesting thing we were not given.0730

That means that there is a possibility, but we do know for sure in static equilibrium, the x's have to cancel out.0740

F3 do not have any x component, it is pointing directly down.0745

That means that whatever F2 is, whatever its angle turns out to be, we know that F2,x = F1,x = 136 N, otherwise they will not cancel out, it will have an acceleration, it could not be in static equilibrium.0751

So, F2,x must be 136 N, and that is an interesting thing.0768

But, there is two possibilities, either F2 could point up, or F2 could point down.0773

So if we have got two possibilities, that is going to give us two possible answers.0779

We do not know which one it is going to be yet, we can work on that in just a moment.0783

Let us finish the whole problem out.0786

Finishing this out, we know from what we did before, that we have got that, F1,x = 136 N, and F1,y = 210 N .0792

So, we know F2,x has to be 136 N as well.0818

So, 136 N is what we have got, possibility 1, possibility 2.0831

What has to be the other side?0836

Now we can use the Pythagorean theorem.0840

We know that, 1502 = 1362 + F2,y20842

We get, sqrt(4004) = F2,y, we will get +/- when taking the square root if we are doing it as algebra.0863

Sometimes you can get rid of that, but in this case we know that both (+) and (-) are both possibilities.0882

So, F2,y = +/- 63.3 N .0888

So there is two possibilities.0896

We know that it is either pulling up at 63.3 N and canceling out the x, or itis pulling down at 63.3 N canceling out the x.0898

We know that 210 N,( because we know that F3 is going to cancel out the rest of the y component), 210 N + F2,y + F3 = 0 .0907

You add up all the forces in the y component, we get zero because acceleration of y is zero, just like the acceleration of x is zero, how we got 136 N being pulled both ways.0924

So, because the acceleration of the y is zero, we are able to get this formula right here.0937

Now we are going to split into the two different possibilities.0945

We have got 210 N + 63.3 N + F3 = 0 and 210 N - 63.3 N+ F3 = 0.0948

The possibilities of when F2 is pulling up, or when it is pulling down, it is going to be pulling either a little bit up or little bit down.0963

It is mainly pulling to the side, because of how strong it has to the side, the F1's x component, but it has to pull up or down just like we talked about up here.0971

210 + 63.3 + F3 = 0, 273.3 + F3 = 0, F3 = -273.3 N, or F3 = -146.7 N .0981

They are both answers, both are possibilities, we do not have enough information to be sure of which one of the two possibilities the answer is, but we have the answer for what the question is asking for here, and we could if we were given a little more information, if we knew that F2 is pointed up or pointed down, we will be able to figure out whether or not, we would able to figure out which of these answers we would go with.1010

But these are the two possibilities for the third force.1031

Third example: We have got a chandelier that is suspended by a cable from the roof of an elevator, in a fancy hotel.1034

There is a bottom for our elevator, right there.1041

Assuming that the cable is mass-less, and the chandelier weighs 10 kg, what is going to be the tension in the cable when the elevator is at rest?1054

Also, what happens when the elevator starts moving around?1061

So the elevator is moving up, do you think the tension is going to increase or decrease?1064

If the elevator is moving up, have you ever stood in an elevator and paid attention what the floor felt like under your feet?1069

As the elevator starts to move up, you feel slightly heavier.1076

That is because the floor of the elevator has to push against you.1079

The floor of the elevator actually pushes against you to be able to give you an acceleration.1083

It then just maintains the standard normal force that you are used to so you do not go through the floor, but to be able to accelerate you, it has to put a force on you.1087

So, it puts an acceleration through the floor.1096

That acceleration comes by putting in extra force.1100

What happens when the elevator wants to go down?1103

If you are trying to go down in an elevator, you will notice that you experience a brief moment of weightlessness, not weightlessness, but of a less weight, as you start to accelerate down towards the Earth.1105

That is because, normally, you got some normal force pulling you down, but as we accelerate down, we need less normal force, but now we are being allowed to move towards the centre of the Earth.1114

The normal force is receding, because it is allowing you to gain a velocity, it is allowing you to get some acceleration for a brief period of time.1127

Finally, what would the acceleration be necessary, if the elevator were to have no tension in the cable?1135

What is the tension when it is at rest?1142

When is the tension when there is an acceleration of 1 m/s/s?1145

What is the acceleration when it is -1 m/s/s?1150

We will have positive as going up.1153

1 m/s/s will increase the tension because we are going to have to pull that chandelier along.1156

When the acceleration is going down, when it is -1 m/s/s, we will need less tension, because we are going to be able to allow it to go in the direction gravity would normally be taking it, so we just need to give it less force.1161

Finally, what would have to be the acceleration for the elevator to have no tension in the cable whatsoever?1176

We are going to start off with slightly simplified diagrams, so we have got some tension pulling up (elevator is not the important thing here), the elevator is attached up here, we have got some mass of 10 kg which is being pulled down by the force of gravity.1182

Force of gravity = 10 × 9.8 = 98 N, so being pulled down by 98 N.1205

If the acceleration = 0, what is the tension going to be?1213

If a = 0, tension is going to have to cancel out gravity.1218

So, T - Fg = mass × acceleration = 0, because we are completely still, T = Fg = 98 N.1226

So, if the acceleration = 0, if things are static, 98 N.1243

What if the elevator was moving up?1249

That is going to require more tension, so we will expect to see the tension grow.1253

Let us look at this again.1257

If acceleration =1, then T - Fg = Ma, T - 98 N = 10 kg × 1 m/s/s, so, T = 98 + 10 = 108 N .1259

So if you want to make that chandelier accelerate at 1 m/s/s, you are going to need to give it another 10 N past what it takes to stay off gravity, because you have to keep holding off gravity with what would normally be a normal force, but in this case is tension, because it is not resting on anything, it is being pulled up by a cable.1287

What if we had an acceleration of -1?1310

Very easy, just the same thing.1315

We have got, T - Fg = Ma, T - 98 N = 10 × (-1), T = 98 - 10 = 88 N, so we need a little less tension, 10 N less tension to be able to allow it to get that bit of acceleration, because gravity will take it the rest of the way, gravity puts in 98 N, and the tension needs to only bring it 10 N of down force, so that it will be accelerated at 1 m/s/s down.1318

Finally, if we want no tension whatsoever, what would the acceleration have to be?1360

If T = 0, T - Fg = Ma, - Fg = Ma, -98 = 10 × a, a = -9.8 m/s/s, same thing as gravity.1368

If we want to have no tension, we need to let the elevator go into complete free-fall.1397

You just drop the elevator, and there is going to be no tension, because the cable is going to be accelerating with gravity, the chandelier is going to be accelerating with gravity, the elevator is going to be accelerating with gravity, gravity is going to be taking over all the work.1401

So, the only way to get rid of the tension completely is to let gravity do all the work, it does not have to be resisting anything, there is no longer any resistance, you are letting gravity take over.1412

Example 4: A 20 kg baboon climbs a mass-less rope attached to a 22 kg crate.1428

The 22 kg crate on the ground is over a frictionless tree limb, so the baboon climbs the rope with an acceleration of 3 m/s/s, what acceleration will the crate have?1446

What is the maximum acceleration that the baboon can achieve without moving the crate?1455

Our baboon is pulling up, he is putting in some tension, just like if you are climbing a rope to a ceiling, you would be putting in a tension into the rope as it pulls you up, as you use your arms, and the rope resists it, you would be able to yourself up the rope.1460

That is exactly what our baboon is doing here, he is climbing the rope just as you might have to in gym class.1476

He is climbing, so he is putting in a tension.1482

At the same time, that tension is going to pull in here, and it is going to start pulling on the crate.1484

So either it is going to lower its effect of weight so much that the tension is actually going to lift it, so the box will be easier for somebody else to come along and lift, or it is going to get so much tension in the rope that it is actually pulled off the ground, as the baboon is climbing.1490

That is our basic idea, let us start working on it.1506

We will just consider our tree limb to a perfect pulley, mass-less and frictionless, and our baboon is going to climb up things, so if the acceleration of the baboon is 3 m/s/s, what will the acceleration of the crate be?1511

He is going to climb up with some acceleration, which is going to cause some tension in the rope.1524

So, over here, that tension gets canceled out, pulled the other way, rope is always pulling off position, that tension is going to be the same here.1533

Free body diagram for the monkey, he is going to be pulled up, by the tension he is putting into the rope, and he is also being pulled down by his weight.1540

So his force of gravity = 20 × g =196 N.1551

What is the tension?1560

We do not know what the tension is yet, but we do know that his acceleration = 3 m/s/s.1562

So, we can figure out what the tension must be.1570

If we make up positive, and keep in mind, that is going to turn out to be that 'down' from the crate's point of view is positive, that is really strange, because we are actually wrapping it, flipping it all the way, we have to keep in mind that positive stays the same around the pulley, so positive 'up' for the baboon means negative 'up' for the crate.1572

Positive goes into the ground from the point of view of the crate.1595

T - Fg = Mbaboon × ababoon , we do not know what the tension is, but we know everything else.1598

T - 196 = 20 × 3, T = 256 N.1609

So, 256 N, what would be the acceleration on the crate?1623

The crate has got two things happening on it.1626

It has got T, and its own force of gravity = 22 × g = 215.6 N .1629

So, it experiences Fg - T = Mcrate × acrate, (Tension is negative from the crate's point of view, positive from the baboon's point of view.)1642

So, Fg - T = 215.6 - 256 = 22 × acrate , (Fg and T are not equal, which means we are going to have some lift off.)1687

Solving, acrate = -1.84 m/s/s .1701

So, the baboon is able to achieve an acceleration of 3 m/s/s, the crate is also going to have to achieve 1.84 m/s/s .1717

What about when we want to have the baboon climb, but not cause any movement?1735

If we want to have the baboon climb, but not cause any movement, then we are going to have to look for what is the maximum acceleration for the baboon is going to happen when we get the most tension, because tension is what enables it.1740

Keep in mind, unlike our block problems from before, they are not rigidly connected, the baboon is climbing hand over hand, going up the rope, he is not attached to a single fixed point, whereas the two blocks are attached to a fixed point, when one of them moves, the other one has to move, but in this case the baboon is able to climb up it.1764

It still puts a tension, otherwise nothing would be able to move him around, he would not have an external force to cause him to actually go up.1787

But he does not connect directly to the crate, so they are going to be decoupled, our accelerations are decoupled.1794

The maximum acceleration for the baboon will be when there is the most tension in the rope, without moving crate.1801

What is the maximum tension we can have without moving the crate?1812

We have to cancel out the baboon, otherwise he is going to start falling.1816

So we have got, T = 196 + Ta, (196 is what which cancels weight, Ta('a' for acceleration) is what is able to give more than that.)1824

Most of this tension could be, is equal to the force of gravity on the crate, because otherwise the crate is going to start to lift off the ground.1856

196, that which cancels out the baboons weight, and the acceleration he gets in addition to canceling out his weight, cannot exceed the weight of the crate.1864

What is the weight of the crate equal to?1872

The weight of the crate = 215.6, so we get the acceleration part of the tension, Ta = 215.6 - 196 = 19.61874

What is the maximum acceleration our baboon can have?1903

The maximum acceleration the baboon can have is going to be, we have already canceled out, we have got our T, we have got our force of gravity pulling down on the baboon + Tension, we are going to split that tension into the one that cancels weight + the tension that actually does acceleration.1906

These two things cancel one another out, and that leads to, equal to, the mass of the baboon × acceleration.1933

So we have got, Ta = Mbaboonababoon, 19.6 = 20 × a , a = 19/20 = 0.98 m/s/s, is the maximum acceleration, which is still pretty good, 1 m/s/s, that is a tenth of the acceleration due to gravity, which seems kind of low, but if you try to climb a rope faster than that, that would be pretty impressive.1946

Final example: Two block of masses, M1 = 5 kg, M2 = 10 kg, are roped together on an incline, both having different angles.1993

The first box is on an incline of 50 degrees, and second one is on an incline of 20 degrees.2007

They also each have different masses as we said before.2015

Assuming the pulley and rope mass-less, and the pulley is frictionless, what acceleration will they experience?, what will be the tension in the rope?2022

Very first thing to do, we have force of gravity pulling down on both, but force of gravity is not what really matters, what matters is how much they get canceled out, and how much is parallel.2031

We are going to, remember, whatever the force of gravity is perpendicular, Fnormal, they are going to cancel each other out.2044

So, while they are still present, for our purposes, we are not going to pay attention to them, because they are not going to have any effect on what we are doing.2055

Force of gravity perpendicular over here, gets canceled out by the normal force, because the normal force is able to cancel out whatever perpendicular.2061

So the normal force cancel the force of gravity perpendicular to the side of the triangle, once again, we are not going to worry about these for the purpose of our problems.2072

The only thing that we are really concerned about, is what is the parallel component.2082

Up here, we have got a 20 degree angle, over here we have got a 50 degree angle.2089

So, sin(50) × Fg, and over here, sin(20) × Fg.2098

We have not figured out Fg yet, but that will take no time at all.2113

Fg = 5 × 9.8 = 49 N, over here, Fg = 10 × 9.8 = 98 N.2116

If you want to figure out what the parallel components are, we get, sin(50) on this one, it is going to be equal to, the force of gravity on the first block, parallel to the triangle (down the side of the triangle) is equal to 37.5 N .2132

Over here, we are going to get that the force of gravity on the second block, parallel, is going to be equal to 33.5 N.2158

So, we have got what the two parts are parallel.2170

Which direction can we expect to move in?, we know we are going to have to move in this direction because there is more force in the system pulling this way, than this way; this is the smaller one, so this is the side that is going to win.2172

Let us finish this up.2190

So, we know that the parallel force, which is the only force we have to worry about, because we know that gravity perpendicular and normal force cancel one another out, we know that this force of gravity, Fg,1(parallel) = 37.5 N, Fg,2(parallel) = 33.5 N.2193

Now we want to find out what is our acceleration, what is the tension in the rope.2220

So, there are going to be tensions pulling both this way.2225

As we have talked about before, we can actually treat this whole thing as one big system.2227

So, we have got one big system.2232

We can figure out the tensions, come up with a bunch of equations, but there is no reason to, because we know that what are the external forces acting on it, the tensions are not external, those are the things that links our system, that makes our system.2234

So, the tensions are not going to cancel out whether we can treat it as a system, they are what enables us to use it as a system.2246

So we only have to pay attention to what is working outside, if we treat it as a one big system.2251

What forces are acting on the system?2255

That is going to be, = Msystem × a, unlike the baboon and crate problem, we got a rigid connection here, if one thing moves, the other has to move, so we know that we can use the same acceleration for the two of them.2260

What forces are here?, let us make to the right as positive, we got 33.5 - 37.5 = (10+5)a, solving, -4 = 5a, a = -0.27 m/s/s, which makes sense, because as we have talked about before, we are going to see an acceleration pulling things that way.2274

In this case, it is a very small acceleration, but it is still pulling it along.2312

This is what our acceleration is, it is parallel, it is not just some general acceleration, this is the magnitude, and what we know, we know if we were to consider it as a vector, it is the amount parallel to the triangle and pulling to the left.2318

It is going to be parallel from both of their point of views.2332

They are going to have very different acceleration vectors.2334

This one is only going to come up, at a 20 degree incline, while this one is going to go down at a 50 degree incline, so one is rising , the other is falling, but as we talked about before, the only thing effecting this is the parallel component, because remember, the normal force cancel out the perpendicular component of gravity.2337

The only thing we really have to worry about here is, what the total acceleration is, and it is up to us, if we had a problem where we had to consider which direction it is moving, then we would have to work on it, but in this case, it is enough to say that it is -0.27 m/s/s, or really 0.27 m/s/s, and then talk about which direction it is moving in.2354

Now, what if we were to solve for the tension is?2375

If we want to solve for what the tension is, we can look at a single block on its own.2378

So, let us consider looking at the smaller block.2385

The smaller block is being pulled down with 37.5 N, it is being pulled up with the tension (which we will figure out in a second).2388

Another important thing is, because the way we got this constructed, tension is parallel.2403

As we have talked about before, it is possible for the rope to be pulling at a different angle, and cause things to not be parallel to the surface, but in this case, we have set up our problem in such a way, or the problem is given to us in such a way that the rope is going to run parallel to the surface, so we do not have to worry about this.2409

So, it is just going to be these two things acting directly, without having to worry about putting in any more angles.2423

We already figured out that this one was the parallel component, so we are good to go from here.2427

This is the negative direction, so tension is pulling in the positive direction, T- 37.5 = Mlittle block × alittle block = 5 kg × (-0.27 m/s/s), solving, T = 36.15 N, which makes sense, because the tension in the rope is going to be have to be less than the force of gravity parallel, otherwise it is going to go in the direction of the tension.2432

The larger force is the one that will win out, which is going to have the effect, if they are directly opposed.2493

So, the tension is smaller than the force caused by gravity.2497

That gives us everything for this problem, we have got it solved.2505

I hope you learned something, there is a bunch of different possibilities in really advanced examples that you can do with forces, but just by breaking it down into good free body diagram, carefully analyzing the forces involved, putting down all the things that you know, you can work your way through it, and you can figure out what you are going to do.2507

I hope you enjoyed it, and we will see you at educator.com for the next lesson.2520

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