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Mechanical Energy of a Satellite in Circular Orbit
Flipping Physics posted a video in Circular Motion & Gravity
The mechanical energy of a satellite in circular orbit is solved for in terms of universal gravitational potential energy. And the velocity of the satellite is compared to escape velocity. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:14 Types of mechanical energy of a satellite 1:21 Solving for the velocity of a satellite in circular orbit 2:34 Solving for the mechanical energy of a satellite 3:31 Comparing satellite velocity to escape velocity Next Video: Impulse for Two Objects being Attracted to One Another Multilingual? Please help translate Flipping Physics videos! Previous Video: Deriving Escape Velocity of Planet Earth Please support me on Patreon! Thank you to Jonathan Everett, Christopher Becke, Sawdog, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video.
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Video Discussion: Mechanical Energy of a Satellite in Circular Orbit
Flipping Physics posted a topic in Video Discussions
Name: Mechanical Energy of a Satellite in Circular Orbit Category: Circular Motion & Gravity Date Added: 20180304 Submitter: Flipping Physics The mechanical energy of a satellite in circular orbit is solved for in terms of universal gravitational potential energy. And the velocity of the satellite is compared to escape velocity. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:14 Types of mechanical energy of a satellite 1:21 Solving for the velocity of a satellite in circular orbit 2:34 Solving for the mechanical energy of a satellite 3:31 Comparing satellite velocity to escape velocity Next Video: Impulse for Two Objects being Attracted to One Another Multilingual? Please help translate Flipping Physics videos! Previous Video: Deriving Escape Velocity of Planet Earth Please support me on Patreon! Thank you to Jonathan Everett, Christopher Becke, Sawdog, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video. Mechanical Energy of a Satellite in Circular Orbit
 universal gravitational potential energy
 derive
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Deriving Escape Velocity of Planet Earth
Flipping Physics posted a video in Circular Motion & Gravity
Escape velocity is defined and illustrated. The escape velocity of planet Earth is derived. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:07 Translating the problem 0:42 Defining escape velocity 1:43 Conservation of mechanical energy 3:22 Initial and final mechanical energies 5:38 The escape velocity of planet Earth 6:19 Relating this to binding energy Next Video: Mechanical Energy of a Satellite in Circular Orbit Multilingual? Please help translate Flipping Physics videos! Previous Video: Deriving the Binding Energy of a Planet Please support me on Patreon! Thank you to Dan Burns, Jonathan Everett, Christopher Becke, Sawdog, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video.
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 universal gravitational potential energy
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Video Discussion: Deriving Escape Velocity of Planet Earth
Flipping Physics posted a topic in Video Discussions
Name: Deriving Escape Velocity of Planet Earth Category: Circular Motion & Gravity Date Added: 20180225 Submitter: Flipping Physics Escape velocity is defined and illustrated. The escape velocity of planet Earth is derived. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:07 Translating the problem 0:42 Defining escape velocity 1:43 Conservation of mechanical energy 3:22 Initial and final mechanical energies 5:38 The escape velocity of planet Earth 6:19 Relating this to binding energy Next Video: Mechanical Energy of a Satellite in Circular Orbit Multilingual? Please help translate Flipping Physics videos! Previous Video: Deriving the Binding Energy of a Planet Please support me on Patreon! Thank you to Dan Burns, Jonathan Everett, Christopher Becke, Sawdog, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video. Deriving Escape Velocity of Planet Earth
 potential energy
 universal gravitational potential energy
 (and 4 more)

Deriving the Binding Energy of a Planet
Flipping Physics posted a video in Circular Motion & Gravity
Binding energy of a planet is defined and derived. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:21 Defining binding energy 0:48 Proving change in gravitational potential energy equals work done by force applied 3:03 Universal gravitational potential energy 3:39 The binding energy of a planet 5:16 An alternate way of solving this problem Next Video: Deriving Escape Velocity of Planet Earth Multilingual? Please help translate Flipping Physics videos! Previous Video: Universal Gravitational Potential Energy Introduction Please support me on Patreon! Thank you to Jonathan Everett, Christopher Becke, Sawdog, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video.
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Video Discussion: Deriving the Binding Energy of a Planet
Flipping Physics posted a topic in Video Discussions
Name: Deriving the Binding Energy of a Planet Category: Circular Motion & Gravity Date Added: 20180218 Submitter: Flipping Physics Binding energy of a planet is defined and derived. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:21 Defining binding energy 0:48 Proving change in gravitational potential energy equals work done by force applied 3:03 Universal gravitational potential energy 3:39 The binding energy of a planet 5:16 An alternate way of solving this problem Next Video: Deriving Escape Velocity of Planet Earth Multilingual? Please help translate Flipping Physics videos! Previous Video: Universal Gravitational Potential Energy Introduction Please support me on Patreon! Thank you to Jonathan Everett, Christopher Becke, Sawdog, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video. Deriving the Binding Energy of a Planet
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Universal Gravitational Potential Energy Introduction
Flipping Physics posted a video in Circular Motion & Gravity
Universal Gravitational Potential Energy is introduced and graphed. It is compared to the force of gravity. And the “zero line” is defined. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:11 “Normal” gravitational potential energy 1:33 Gravitational fields 2:22 Universal Gravitational Potential Energy Equation 3:07 Comparing gravitational potential energy to force of gravity 4:12 Graphing Universal Gravitational Potential Energy 5:35 The “zero line” for universal gravitational potential energy 6:05 Can universal gravitational potential energy ever be positive? 6:49 Gravitational potential energy at the surface of the Earth 7:57 Three things to be careful of. Next Video: Deriving the Binding Energy of a Planet Multilingual? Please help translate Flipping Physics videos! Previous Video: Gravitational Field Introduction Please support me on Patreon! Thank you to Dan Burns, Jonathan Everett, Christopher Becke, Sawdog, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video.
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Video Discussion: Universal Gravitational Potential Energy Introduction
Flipping Physics posted a topic in Video Discussions
Name: Universal Gravitational Potential Energy Introduction Category: Circular Motion & Gravity Date Added: 20180212 Submitter: Flipping Physics Universal Gravitational Potential Energy is introduced and graphed. It is compared to the force of gravity. And the “zero line” is defined. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:11 “Normal” gravitational potential energy 1:33 Gravitational fields 2:22 Universal Gravitational Potential Energy Equation 3:07 Comparing gravitational potential energy to force of gravity 4:12 Graphing Universal Gravitational Potential Energy 5:35 The “zero line” for universal gravitational potential energy 6:05 Can universal gravitational potential energy ever be positive? 6:49 Gravitational potential energy at the surface of the Earth 7:57 Three things to be careful of. Next Video: Deriving the Binding Energy of a Planet Multilingual? Please help translate Flipping Physics videos! Previous Video: Gravitational Field Introduction Please support me on Patreon! Thank you to Dan Burns, Jonathan Everett, Christopher Becke, Sawdog, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video. Universal Gravitational Potential Energy Introduction
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AP Physics C: Universal Gravitation Review (Mechanics)
Flipping Physics posted a video in Oscillations & Gravity
Calculus based review of Universal Gravitation including Newton’s Universal Law of Gravitation, solving for the acceleration due to gravity in a constant gravitational field, universal gravitational potential energy, graphing universal gravitational potential energy between an object and the Earth, three example problems (binding energy, escape velocity and orbital energy), and Kepler’s three laws. For the calculus based AP Physics C mechanics exam. Want Lecture Notes? At 6:01 this video addresses an error in the Universal Gravitational Potential Energy Graph from the video's previous iteration. Content Times: 0:10 Newton’s Universal Law of Gravitation 1:52 Solving for the acceleration due to gravity 2:02 Universal Gravitational Potential Energy 4:52 Graph of Universal Gravitational Potential Energy between an object and the Earth 6:01 Correcting the Universal Gravitational Potential Energy Graph 7:30 Binding Energy Example Problem 9:41 Escape Velocity Example Problem 11:19 Orbital Energy Example Problem 13:52 Kepler’s Three Laws 14:17 Kepler’s First Law 16:19 Kepler’s Second Law 16:42 Deriving Kepler’s Third Law Multilingual? Please help translate Flipping Physics videos! AP Physics C Review Website Next Video: AP Physics C: Simple Harmonic Motion Review (Mechanics) Previous Video: AP Physics C: Rotational vs. Linear Review (Mechanics) Please support me on Patreon! Thank you to Aarti Sangwan, Sawdog, and Frank Geshwind for being my Quality Control team for this video.
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Video Discussion: AP Physics C: Universal Gravitation Review (Mechanics)
Flipping Physics posted a topic in Video Discussions
Name: AP Physics C: Universal Gravitation Review (Mechanics) Category: Oscillations & Gravity Date Added: 20171222 Submitter: Flipping Physics Calculus based review of Universal Gravitation including Newton’s Universal Law of Gravitation, solving for the acceleration due to gravity in a constant gravitational field, universal gravitational potential energy, graphing universal gravitational potential energy between an object and the Earth, three example problems (binding energy, escape velocity and orbital energy), and Kepler’s three laws. For the calculus based AP Physics C mechanics exam. Want Lecture Notes? At 6:01 this video addresses an error in the Universal Gravitational Potential Energy Graph from the video's previous iteration. Content Times: 0:10 Newton’s Universal Law of Gravitation 1:52 Solving for the acceleration due to gravity 2:02 Universal Gravitational Potential Energy 4:52 Graph of Universal Gravitational Potential Energy between an object and the Earth 6:01 Correcting the Universal Gravitational Potential Energy Graph 7:30 Binding Energy Example Problem 9:41 Escape Velocity Example Problem 11:19 Orbital Energy Example Problem 13:52 Kepler’s Three Laws 14:17 Kepler’s First Law 16:19 Kepler’s Second Law 16:42 Deriving Kepler’s Third Law Multilingual? Please help translate Flipping Physics videos! AP Physics C Review Website Next Video: AP Physics C: Simple Harmonic Motion Review (Mechanics) Previous Video: AP Physics C: Rotational vs. Linear Review (Mechanics) Please support me on Patreon! Thank you to Aarti Sangwan, Sawdog, and Frank Geshwind for being my Quality Control team for this video. AP Physics C: Universal Gravitation Review (Mechanics)
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AP Physics C: Work, Energy, and Power Review (Mechanics)
Flipping Physics posted a video in Work Energy & Power
Calculus based review of work done by constant and nonconstant forces, Hooke’s Law, Work and Energy equations in isolated and nonisolated systems, kinetic energy, gravitational potential energy, elastic potential energy, conservative vs. nonconservative forces, conservation of mechanical energy, power, neutral, stable, and unstable equilibrium. For the calculus based AP Physics C mechanics exam. Want Lecture Notes? Content Times: 0:11 Work done by a constant force 2:25 Work done by a nonconstant force 3:58 Force of a Spring (Hooke’s Law) 4:52 Calculating the work done by the force of a spring 6:26 Net work equals change in kinetic energy 7:02 Gravitational Potential Energy 7:50 Nonisolated systems work and energy 8:29 Isolated systems work and energy 9:02 Conservative vs. Nonconservative forces 10:10 Conservation of Mechanical Energy 10:45 Power 12:09 Every derivative can be an integral 13:00 Conservative forces and potential energy 13:46 Deriving Hooke’s Law from elastic potential energy 14:22 Deriving the force of gravity from gravitational potential energy 15:17 Neutral, stable, and unstable equilibrium Multilingual? Please help translate Flipping Physics videos! AP Physics C Review Website Next Video: AP Physics C: Integrals in Kinematics Review (Mechanics) Previous Video: AP Physics C: Dynamics Review (Mechanics) Please support me on Patreon! Thank you to Aarti Sangwan for being my Quality Control help.
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 potential energy
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 conservative force
 nonconservative force
 conservation of energy
 power

Video Discussion: AP Physics C: Work, Energy, and Power Review (Mechanics)
Flipping Physics posted a topic in AP Physics C
Name: AP Physics C: Work, Energy, and Power Review (Mechanics) Category: Work Energy & Power Date Added: 20170330 Submitter: Flipping Physics Calculus based review of work done by constant and nonconstant forces, Hooke’s Law, Work and Energy equations in isolated and nonisolated systems, kinetic energy, gravitational potential energy, elastic potential energy, conservative vs. nonconservative forces, conservation of mechanical energy, power, neutral, stable, and unstable equilibrium. For the calculus based AP Physics C mechanics exam. Want Lecture Notes? Content Times: 0:11 Work done by a constant force 2:25 Work done by a nonconstant force 3:58 Force of a Spring (Hooke’s Law) 4:52 Calculating the work done by the force of a spring 6:26 Net work equals change in kinetic energy 7:02 Gravitational Potential Energy 7:50 Nonisolated systems work and energy 8:29 Isolated systems work and energy 9:02 Conservative vs. Nonconservative forces 10:10 Conservation of Mechanical Energy 10:45 Power 12:09 Every derivative can be an integral 13:00 Conservative forces and potential energy 13:46 Deriving Hooke’s Law from elastic potential energy 14:22 Deriving the force of gravity from gravitational potential energy 15:17 Neutral, stable, and unstable equilibrium Multilingual? Please help translate Flipping Physics videos! AP Physics C Review Website Next Video: AP Physics C: Integrals in Kinematics Review (Mechanics) Previous Video: AP Physics C: Dynamics Review (Mechanics) Please support me on Patreon! Thank you to Aarti Sangwan for being my Quality Control help. AP Physics C: Work, Energy, and Power Review (Mechanics)
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 potential energy
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 conservative force
 nonconservative force
 conservation of energy
 power

Introduction to Elastic Potential Energy with Examples
Flipping Physics posted a video in Work, Energy, Power
Mr. Fullerton of APlusPhysics makes a guest appearance as a floating head to help us learn about Elastic Potential Energy. Several examples of objects which store elastic potential energy are shown and one example of stored elastic potential energy is calculated. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:01 Defining Elastic Potential Energy 1:38 The equation for Elastic Potential Energy 2:08 Defining the Spring Constant 3:27 Elastic Potential Energy stored in a rubber band (Mr. Fullerton’s entrance). 3:39 Showing equilibrium position (or rest position). 4:00 Determining the Spring Constant 4:55 Solving for Elastic Potential Energy 5:44 Solving for the units of Elastic Potential Energy 6:29 Can Elastic Potential Energy be negative? Next Video: Introduction to Conservation of Mechanical Energy with Demonstrations Multilingual? Please help translate Flipping Physics videos! Previous Video: Introduction to Gravitational Potential Energy with Zero Line Examples 1¢/minute 
Introductory Conservation of Mechanical Energy Problem using a Trebuchet
Flipping Physics posted a video in Work, Energy, Power
Learn how to use the Conservation of Mechanical Energy equation by solving a trebuchet problem. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:08 The problem 1:08 Why mechanical energy is conserved 1:37 Setting the zero line and initial and final points 2:32 The three types of mechanical energy 3:55 Canceling mechanical energies from the equation 4:54 Solving the equation 6:18 It’s final speed not final velocity 6:51 Why we can’t use the projectile motion equations 7:43 Do we really have to write all that down? Yes. Thank you to my students Will, Jacob, Natalie and Mery; my students who built and let me use their trebuchet! Next Video: Conservation of Energy Problem with Friction, an Incline and a Spring by Billy Multilingual? Please help translate Flipping Physics videos! Previous Video: Introduction to Elastic Potential Energy with Examples 1¢/minute
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Introduction to Conservation of Mechanical Energy with Demonstrations
Flipping Physics posted a video in Work, Energy, Power
Ian Terry, winner of Big Brother 14, makes a special appearance to help us learn about Conservation of Mechanical Energy. See several demonstrations and understand when mechanical energy is conserved. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:01 Reviewing the three different types of mechanical energy 0:23 Mr. Terry drops an object for our first demonstration 0:58 Calculating Kinetic Energy and Gravitational Potential Energy 2:53 Mechanical energy data table 3:37 Conservation of mechanical energy graph 5:10 When is mechanical energy conserved? 7:13 A second demonstration of conservation of mechanical energy Next Video: Introduction to Conservation of Mechanical Energy with Demonstrations Multilingual? Please help translate Flipping Physics videos! Previous Video: Introduction to Elastic Potential Energy with Examples 1¢/minute
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Video Discussion: Introductory Conservation of Mechanical Energy Problem using a Trebuchet
Flipping Physics posted a topic in Video Discussions
Name: Introductory Conservation of Mechanical Energy Problem using a Trebuchet Category: Work, Energy, Power Date Added: 20160112 Submitter: Flipping Physics Learn how to use the Conservation of Mechanical Energy equation by solving a trebuchet problem. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:08 The problem 1:08 Why mechanical energy is conserved 1:37 Setting the zero line and initial and final points 2:32 The three types of mechanical energy 3:55 Canceling mechanical energies from the equation 4:54 Solving the equation 6:18 It’s final speed not final velocity 6:51 Why we can’t use the projectile motion equations 7:43 Do we really have to write all that down? Yes. Thank you to my students Will, Jacob, Natalie and Mery; my students who built and let me use their trebuchet! Next Video: Conservation of Energy Problem with Friction, an Incline and a Spring by Billy Multilingual? Please help translate Flipping Physics videos! Previous Video: Introduction to Elastic Potential Energy with Examples 1¢/minute Introductory Conservation of Mechanical Energy Problem using a Trebuchet
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Video Discussion: Introduction to Conservation of Mechanical Energy with Demonstrations
Flipping Physics posted a topic in Video Discussions
Name: Introduction to Conservation of Mechanical Energy with Demonstrations Category: Work, Energy, Power Date Added: 20151218 Submitter: Flipping Physics Ian Terry, winner of Big Brother 14, makes a special appearance to help us learn about Conservation of Mechanical Energy. See several demonstrations and understand when mechanical energy is conserved. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:01 Reviewing the three different types of mechanical energy 0:23 Mr. Terry drops an object for our first demonstration 0:58 Calculating Kinetic Energy and Gravitational Potential Energy 2:53 Mechanical energy data table 3:37 Conservation of mechanical energy graph 5:10 When is mechanical energy conserved? 7:13 A second demonstration of conservation of mechanical energy Next Video: Introduction to Conservation of Mechanical Energy with Demonstrations Multilingual? Please help translate Flipping Physics videos! Previous Video: Introduction to Elastic Potential Energy with Examples 1¢/minute Introduction to Conservation of Mechanical Energy with Demonstrations
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Introduction to Gravitational Potential Energy with Zero Line Examples
Flipping Physics posted a video in Work, Energy, Power
Mini mr.p helps you learn about Gravitational Potential Energy with examples of different zero line locations. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:08 Defining Gravitational Potential Energy 1:37 Shrinking mr.p 2:09 Zero Line #1 2:47 Zero Line #2 3:25 Zero Line #3 4:41 Typical locations of the zero line 5:06 Determining the units for Gravitational Potential Energy Next Video: Introduction to Elastic Potential Energy with Examples Multilingual? Please help translate Flipping Physics videos! Previous Video: Introduction to Kinetic Energy with Example Problem 1¢/minute
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Video Discussion: Introduction to Elastic Potential Energy with Examples
Flipping Physics posted a topic in Video Discussions
Name: Introduction to Elastic Potential Energy with Examples Category: Work, Energy, Power Date Added: 20161103 Submitter: Flipping Physics Mr. Fullerton of APlusPhysics makes a guest appearance as a floating head to help us learn about Elastic Potential Energy. Several examples of objects which store elastic potential energy are shown and one example of stored elastic potential energy is calculated. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:01 Defining Elastic Potential Energy 1:38 The equation for Elastic Potential Energy 2:08 Defining the Spring Constant 3:27 Elastic Potential Energy stored in a rubber band (Mr. Fullerton’s entrance). 3:39 Showing equilibrium position (or rest position). 4:00 Determining the Spring Constant 4:55 Solving for Elastic Potential Energy 5:44 Solving for the units of Elastic Potential Energy 6:29 Can Elastic Potential Energy be negative? Next Video: Introduction to Conservation of Mechanical Energy with Demonstrations Multilingual? Please help translate Flipping Physics videos! Previous Video: Introduction to Gravitational Potential Energy with Zero Line Examples 1¢/minute Introduction to Elastic Potential Energy with Examples
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Video Discussion: Introduction to Gravitational Potential Energy with Zero Line Examples
Flipping Physics posted a topic in Video Discussions
Name: Introduction to Gravitational Potential Energy with Zero Line Examples Category: Work, Energy, Power Date Added: 20151207 Submitter: Flipping Physics Mini mr.p helps you learn about Gravitational Potential Energy with examples of different zero line locations. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:08 Defining Gravitational Potential Energy 1:37 Shrinking mr.p 2:09 Zero Line #1 2:47 Zero Line #2 3:25 Zero Line #3 4:41 Typical locations of the zero line 5:06 Determining the units for Gravitational Potential Energy Next Video: Introduction to Elastic Potential Energy with Examples Multilingual? Please help translate Flipping Physics videos! Previous Video: Introduction to Kinetic Energy with Example Problem 1¢/minute Introduction to Gravitational Potential Energy with Zero Line Examples
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Review of the Universal Gravitation topics covered in the AP Physics 1 curriculum. Want [url="http://www.flippingphysics.com/ap1gravitationreview.html"]Lecture Notes[/url]? Content Times: 0:14 Newtonâ€™s Universal Law of Gravitation 1:20 When to use the Two Force of Gravity equations 1:52 Solving for the acceleration due to gravity 2:45 Local and Global Gravitational Fields 3:34 Orbiting Satellite Example 5:03 Universal Gravitational Potential Energy 6:19 Why Universal Gravitational Potential Energy is less than or equal to zero 7:47 Must have two objects for gravitational potential energy Multilingual? [url="http://www.flippingphysics.com/translate.html"]Please help translate Flipping Physics videos![/url] Next Video: [url="http://www.flippingphysics.com/ap1shmreview.html"]AP Physics 1: Simple Harmonic Motion Review[/url] Previous Video: [url="http://www.flippingphysics.com/ap1rotationalkinematicsreview.html"]AP Physics 1: Rotational Kinematics Review[/url] [url="http://www.flippingphysics.com/give.html"]1Â¢/minute[/url]

Video Discussion: AP Physics 1: Universal Gravitation Review
Flipping Physics posted a topic in AP Physics 1/2
Name: AP Physics 1: Universal Gravitation Review Category: Exam Prep Date Added: 03 April 2015  03:42 PM Submitter: Flipping Physics Short Description: None Provided Review of the Universal Gravitation topics covered in the AP Physics 1 curriculum. Want View Video 
Why humans are the best distance runners
running_dry posted a blog entry in Tired and a little dehydrated
In my last post I highlighted some of the incredible things that distance runners are able to do, including very long runs at altitude (lower oxygen) and in extreme conditions. But what allows these people to do these kinds of things? The short answer is training. With enough training almost anyone (for the most part excluding the very elderly) could finish an ultra marathon. But why is this? The answer lies in the fact that humans are better adapted to run for long distances than any other animal on the planet. First of all, humans are bipedal meaning that we move around on two feet, and while other primates are able to walk with two limbs humans are the only primates who walk exclusively with only two legs. Bipedalism in itself isn't incredibly unique as other mammals such as macropods (kangaroos, wallabies...) and large birds like ostriches and emus rely on bipedal movement as well, however humans have other adaptations to make bipedalism more efficient. You may not realize it but the human foot is a very intricate mechanical structure containing 26 bones, 33 joints and over 100 muscles and tendons. While running the foot, specifically the arch, acts as a spring which absorbs and returns force to the ground which is done as follows: the foot lands on the outside of the forefoot and pronates inward, stretching muscles which absorb and store force. The foot rocks forward while it pronates so that by the time the front pad of the foot is flat on the ground the toes are pushing off the ground with the energy stored in the foot's muscles. In addition to the feet the rest of the muscles act as springs which store energy from the foot strike to be used as propulsion for that step. As a result, running is basically a process of converting kinetic energy (foot strike) into potential energy (stretched muscles) and back into kinetic energy (push off). Of course as in any system, energy is lost as heat thus cells must break down glucose during anaerobic and aerobic respiration to create ATP for your muscles to use to create additional energy to put into the ground.
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Everyone likes trampolines. But how do they even work? It's all about energy, and at the same time, proves Newton's laws of motion. Potential energy (PE) and kinetic energy (KE) are the reason trampolines allow you to jump higher than you can on flat ground. One type of potential energy that is involved with trampolines is the potential energy stored in springs. Another type of energy is gravitational potential energy. There is also kinetic energy because you are moving. The equation that connects potential and kinetic energy to find total energy (E) is: E=PE+KE+Q The total energy of the person jumping on a trampoline equals all of the potential energy (both the spring and gravitational potential), plus the kinetic energy. Q is internal energy, which isn't really important here. Other equations needed to understand the forces and energy of trampolines are: PE=mgh This used to find the potential energy due to gravity. You multiply the mass of the object (or person in this case), by the height they are from the ground, by g, acceleration due to gravity. Which is always 9.81 m/s^2. People with larger masses have a greater potential energy due to gravity if they are at the same height as someone with a smaller mass. However, it is harder for people with larger masses to reach the same heights as people with small masses, because gravity is pulling them down more. PE=(1/2)kx^2 The potential energy stored in a spring: "x" is how much the spring stretches, and "k" is the spring constant. Hooke's law goes along with this: F=kx. The force of the spring is the constant multiplied by the change in the spring length. This demonstrates Newton's third law; every action has an equal and opposite reaction. When the springs are stretched by the person, they have to compress again, making the person jump higher as the trampoline returns to its original position. Because of gravity, larger masses allow the spring to be stretched out more. This can be shown by the equation F=ma, which is Newton's second law of motion. "F" is the force of gravity, "m" is mass, and "a" here is also g, acceleration due to gravity. So when mass increases, so does the force of gravity. This means the object/person is being pulled down harder by gravity. This stretches the springs of the trampoline more, creating a higher spring potential energy. But the mass is usually too heavy for the spring to move you if you just stand there, which is why you don't move unless you start jumping first. Smaller kids usually jump higher than adults, even though they have a lower potential energy due to gravity, because the trampoline can more easily spring them back up, since they are being pulled down by gravity slightly less. This is all a great example of Newton's first law: objects in motion will keep moving, and objects at rest will not move, until acted upon by an outside force. The outside forces that keep you on the trampoline are both gravity, which keeps you down, and the trampoline itself, which keeps you up. You also wont move until you begin jumping. Pushing your feet down makes you go up. (Newton's third law!)
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