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Smruti Sannabhadti
11/24/2025
AP Physics 1
Work, Energy, Power
86
•
Nov 24, 2025
•
Understanding Work, Energy, and Power: Exploring Key Concepts
1 / 4
Understanding Work and Force
Ever wonder how much effort it takes to move something? That's what work is in physics! Work happens when a force causes an object to move. It's calculated using the formula W = Fd, where F is force in newtons and d is distance in meters.
Work is measured in joules and is a scalar quantity (it has magnitude but no direction). Remember, work only happens when something actually moves. If you push against a wall and it doesn't budge, you're exerting force but doing zero work!
When forces act at angles, only the component of force parallel to the direction of motion contributes to work. We use W = Fd cosθ where θ is the angle between the force and direction of motion.
Quick Tip: When force and motion go in opposite directions (like friction opposing movement), work is negative! This means energy is being removed from the system.
For example, if someone pulls a 50 kg stone with 250 N of force at a 60° angle for 4 meters, we can calculate the work as W = 250N × 4m × cos(60°) = 500 joules.
Power and Work Problems
Power measures how quickly work is done - it's the rate of doing work. While work tells us the total energy transfer, power tells us how fast that transfer happens. Power is measured in watts (joules per second).
The main equations for power are:
- P = W/t (work divided by time)
- P = Fd/t
- P = Fv (force times velocity)
Let's see this in action: A 65 kg athlete runs 600m up a mountain inclined at 20° in 80 seconds. To find the work done, we need to identify the forces involved. The force moving the athlete uphill is equal to the component of their weight parallel to the slope: mg sin θ.
The work done is calculated as W = Fd cos θ₂ = (mg sin θ)(d)(cos 0°) = 65 kg × 9.8 m/s² × sin(20°) × 600m = 130,720.1 joules.
Remember: In physics problems, breaking forces into their components (like we did with gravity on a slope) makes seemingly complex situations much easier to solve!
The athlete's power is simply work divided by time: P = 130,720.1 J ÷ 80 s = 1,634 watts. This shows the impressive amount of energy the human body can generate!
Force Analysis in Real-World Problems
Physics gets interesting when we apply it to real-world scenarios! In slope problems, gravity always acts downward, but we need to find its component along the incline. For an object on a slope, the force parallel to the incline is mg sin θ.
Consider a truck problem: a 20,000 kg truck travels 500m up a 20° incline in 60 seconds. The work done against gravity is calculated as W = (mg sin θ)(d) = 20,000 kg × 9.8 m/s² × sin(20°) × 500m = 3.35×10⁶ joules.
The power required is P = W/t = 3.35×10⁶ J ÷ 60 s = 55,833 watts. That's why trucks need powerful engines to climb hills!
Physics Insight: When analyzing forces, always start by identifying ALL forces acting on the object, then determine which ones contribute to the work being done.
In these problems, we consistently break down complex situations by identifying forces (like gravity), determining their relevant components, calculating the work done, and then finding the power when time is involved.
Elevator Physics and Force Analysis
Elevators are perfect for studying forces in action! For an elevator carrying passengers, we need to account for all forces involved: tension in the cable , gravity , and friction .
Consider an elevator with a mass of 1,000 kg carrying 800 kg of passengers (total 1,800 kg) with 4,000 N of friction. If it moves at a constant speed of 3 m/s, the acceleration is zero .
The gravitational force is F_G = mg = 1,800 kg × 9.8 m/s² = 17,640 N, always pulling downward. Since the elevator moves at constant speed, F_net = ma = 0, which means the tension in the cable must balance both gravity and friction.
Therefore, F_T = |F_G + F_F| = 17,640 N + 4,000 N = 21,640 N. The power needed to operate this elevator is P = F_T × v = 21,640 N × 3 m/s = 64,920 watts.
Cool Connection: Next time you're in an elevator, think about the massive forces at work! The cable is supporting not just the weight of the elevator and everyone inside, but also overcoming friction in the system.
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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
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❗️❗️⚠️
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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, Energy, and Power: Exploring Key Concepts
Physics is all about how things move and why. In this lesson, we'll explore the concepts of work, power, and energy - fundamental ideas that explain everything from lifting a backpack to powering a rocket into space. Understanding these concepts... Show more
Understanding Work and Force
Ever wonder how much effort it takes to move something? That's what work is in physics! Work happens when a force causes an object to move. It's calculated using the formula W = Fd, where F is force in newtons and d is distance in meters.
Work is measured in joules and is a scalar quantity (it has magnitude but no direction). Remember, work only happens when something actually moves. If you push against a wall and it doesn't budge, you're exerting force but doing zero work!
When forces act at angles, only the component of force parallel to the direction of motion contributes to work. We use W = Fd cosθ where θ is the angle between the force and direction of motion.
Quick Tip: When force and motion go in opposite directions (like friction opposing movement), work is negative! This means energy is being removed from the system.
For example, if someone pulls a 50 kg stone with 250 N of force at a 60° angle for 4 meters, we can calculate the work as W = 250N × 4m × cos(60°) = 500 joules.
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Power and Work Problems
Power measures how quickly work is done - it's the rate of doing work. While work tells us the total energy transfer, power tells us how fast that transfer happens. Power is measured in watts (joules per second).
The main equations for power are:
- P = W/t (work divided by time)
- P = Fd/t
- P = Fv (force times velocity)
Let's see this in action: A 65 kg athlete runs 600m up a mountain inclined at 20° in 80 seconds. To find the work done, we need to identify the forces involved. The force moving the athlete uphill is equal to the component of their weight parallel to the slope: mg sin θ.
The work done is calculated as W = Fd cos θ₂ = (mg sin θ)(d)(cos 0°) = 65 kg × 9.8 m/s² × sin(20°) × 600m = 130,720.1 joules.
Remember: In physics problems, breaking forces into their components (like we did with gravity on a slope) makes seemingly complex situations much easier to solve!
The athlete's power is simply work divided by time: P = 130,720.1 J ÷ 80 s = 1,634 watts. This shows the impressive amount of energy the human body can generate!
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Force Analysis in Real-World Problems
Physics gets interesting when we apply it to real-world scenarios! In slope problems, gravity always acts downward, but we need to find its component along the incline. For an object on a slope, the force parallel to the incline is mg sin θ.
Consider a truck problem: a 20,000 kg truck travels 500m up a 20° incline in 60 seconds. The work done against gravity is calculated as W = (mg sin θ)(d) = 20,000 kg × 9.8 m/s² × sin(20°) × 500m = 3.35×10⁶ joules.
The power required is P = W/t = 3.35×10⁶ J ÷ 60 s = 55,833 watts. That's why trucks need powerful engines to climb hills!
Physics Insight: When analyzing forces, always start by identifying ALL forces acting on the object, then determine which ones contribute to the work being done.
In these problems, we consistently break down complex situations by identifying forces (like gravity), determining their relevant components, calculating the work done, and then finding the power when time is involved.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
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Elevator Physics and Force Analysis
Elevators are perfect for studying forces in action! For an elevator carrying passengers, we need to account for all forces involved: tension in the cable , gravity , and friction .
Consider an elevator with a mass of 1,000 kg carrying 800 kg of passengers (total 1,800 kg) with 4,000 N of friction. If it moves at a constant speed of 3 m/s, the acceleration is zero .
The gravitational force is F_G = mg = 1,800 kg × 9.8 m/s² = 17,640 N, always pulling downward. Since the elevator moves at constant speed, F_net = ma = 0, which means the tension in the cable must balance both gravity and friction.
Therefore, F_T = |F_G + F_F| = 17,640 N + 4,000 N = 21,640 N. The power needed to operate this elevator is P = F_T × v = 21,640 N × 3 m/s = 64,920 watts.
Cool Connection: Next time you're in an elevator, think about the massive forces at work! The cable is supporting not just the weight of the elevator and everyone inside, but also overcoming friction in the system.
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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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
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