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K
kylie
11/20/2025
Physics
work and energy (unit 3)
107
•
Nov 20, 2025
•
Understanding Work and Energy: Unit Overview
K
kylie
@kylie_ywwr
1 / 3
Work & Energy Fundamentals
Work happens when a force causes an object to move in the direction of the force. The formula for work is work = force × displacement × cosθ. Remember, work only occurs when the force causes displacement, and the force must have at least some component in the direction of motion.
Energy comes in different forms. Kinetic energy is the energy of motion, calculated as KE = ½mv². This equals the work needed to accelerate an object from rest to its current speed. Potential energy is stored energy, with gravitational PE = mgh. Together, kinetic and potential energy make up mechanical energy.
Forces can be either conservative (like gravity, which tends to restore objects to their original position) or non-conservative (like friction, which involves thermodynamic processes). When only conservative forces act, mechanical energy is conserved, meaning ME₁ = ME₂.
⚡ Energy Insight: The work-energy theorem states that total work equals the change in kinetic energy. If total work is positive, an object speeds up; if negative, it slows down; if zero, its speed doesn't change.
Simple Machines & Springs
Simple machines help us do work more easily by trading force for distance. The six basic machines are levers, inclined planes, pulleys, wheel and axles, wedges, and screws. Most complex machines are variations of levers or inclined planes.
For any machine, input work equals output work when no friction exists . When friction is present, input work plus work done by friction equals output work. The output force is usually the weight of an object, and output distance is how far it's raised.
Springs follow Hooke's Law, which states that the force needed to stretch a spring is proportional to the distance stretched: F = kx, where k is the spring constant. A larger k means a stronger spring. The potential energy stored in a spring is PE = ½kx².
🔄 Balancing Act: When solving spring-mass problems, remember this equation: mghₒ + ½kxₒ² + ½mvₒ² = mghₑ + ½kxₑ² + ½mvₑ². This shows how energy transforms between gravitational potential, spring potential, and kinetic energy.
Mechanical Advantage & Efficiency
Ideal Mechanical Advantage (IMA) depends only on a machine's geometry and equals the ratio of input distance to output distance: IMA = dᵢₙ/dₒᵤₜ. For pulley systems, IMA equals the number of supporting strands.
Actual Mechanical Advantage (AMA) accounts for energy lost to friction and is found by measuring the ratio of output force to input force: AMA = Fₒᵤₜ/Fᵢₙ. If MA > 1, the machine makes work easier; if MA < 1, it makes work harder.
Efficiency compares energy output to energy input in a system: efficiency = AMA/IMA. This ratio helps us understand how much energy is lost in the process of using a machine.
🔧 Real-World Application: No machine is 100% efficient due to friction and other energy losses. When designing or choosing a machine, consider the trade-off between mechanical advantage and efficiency based on your needs.
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
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This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
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Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
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I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
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Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Understanding Work and Energy: Unit Overview
K
kylie
@kylie_ywwr
Work and energy are powerful concepts that describe how forces change the motion and position of objects. Understanding these principles helps explain everything from how machines make tasks easier to why a roller coaster can complete its track without a... Show more
Work & Energy Fundamentals
Work happens when a force causes an object to move in the direction of the force. The formula for work is work = force × displacement × cosθ. Remember, work only occurs when the force causes displacement, and the force must have at least some component in the direction of motion.
Energy comes in different forms. Kinetic energy is the energy of motion, calculated as KE = ½mv². This equals the work needed to accelerate an object from rest to its current speed. Potential energy is stored energy, with gravitational PE = mgh. Together, kinetic and potential energy make up mechanical energy.
Forces can be either conservative (like gravity, which tends to restore objects to their original position) or non-conservative (like friction, which involves thermodynamic processes). When only conservative forces act, mechanical energy is conserved, meaning ME₁ = ME₂.
⚡ Energy Insight: The work-energy theorem states that total work equals the change in kinetic energy. If total work is positive, an object speeds up; if negative, it slows down; if zero, its speed doesn't change.
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Simple Machines & Springs
Simple machines help us do work more easily by trading force for distance. The six basic machines are levers, inclined planes, pulleys, wheel and axles, wedges, and screws. Most complex machines are variations of levers or inclined planes.
For any machine, input work equals output work when no friction exists . When friction is present, input work plus work done by friction equals output work. The output force is usually the weight of an object, and output distance is how far it's raised.
Springs follow Hooke's Law, which states that the force needed to stretch a spring is proportional to the distance stretched: F = kx, where k is the spring constant. A larger k means a stronger spring. The potential energy stored in a spring is PE = ½kx².
🔄 Balancing Act: When solving spring-mass problems, remember this equation: mghₒ + ½kxₒ² + ½mvₒ² = mghₑ + ½kxₑ² + ½mvₑ². This shows how energy transforms between gravitational potential, spring potential, and kinetic energy.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Mechanical Advantage & Efficiency
Ideal Mechanical Advantage (IMA) depends only on a machine's geometry and equals the ratio of input distance to output distance: IMA = dᵢₙ/dₒᵤₜ. For pulley systems, IMA equals the number of supporting strands.
Actual Mechanical Advantage (AMA) accounts for energy lost to friction and is found by measuring the ratio of output force to input force: AMA = Fₒᵤₜ/Fᵢₙ. If MA > 1, the machine makes work easier; if MA < 1, it makes work harder.
Efficiency compares energy output to energy input in a system: efficiency = AMA/IMA. This ratio helps us understand how much energy is lost in the process of using a machine.
🔧 Real-World Application: No machine is 100% efficient due to friction and other energy losses. When designing or choosing a machine, consider the trade-off between mechanical advantage and efficiency based on your needs.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user