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Leonel
11/26/2025
AP Physics 1
STATICS OF RIGID BODIES - PROBLEMS WITH COMPLETE SOLUTION
83
•
Nov 26, 2025
•
Understanding Statics of Rigid Bodies: Solved Problems for Engineering Mechanics
L
Leonel
@leonel_dyzi
1 / 4
Force Component Analysis
When working with forces in engineering, we often need to break them down into their component parts along different axes. This helps us analyze complex force systems more easily.
For any force, we can find its x-component (horizontal) and y-component (vertical) using trigonometry. The direction of the force determines which trigonometric functions to use.
In problem 1, we have two forces: a 150 N force at 30° and a 200 N force at 35° from their respective axes. These forces need to be resolved into their x and y components for analysis.
Pro Tip: When finding components, always pay attention to the direction! A force pointing down and to the right will have a positive x-component but a negative y-component.
Solving Force Components Step-by-Step
Breaking down forces into components requires clear understanding of coordinate systems. For the 150 N force at 30° from the y-axis, we need to find what portion acts horizontally and vertically.
For the horizontal (x) component:
- The force is angled 30° from vertical, so we use sine: Fx = -(150 N) × sin 30° = -75 N
- The negative sign indicates the force points left along the x-axis
For the vertical (y) component:
- We use cosine: Fy = (150 N) × cos 30° = 129.9 N
- This is positive, showing the force points upward
The same process applies to the 200 N force, where Px = 163.8 N and Py = 114.7 N. These component values tell us exactly how much force acts in each direction.
Finding Force Components in Applied Situations
In real-world engineering problems, we often need to determine force components based on geometry. When a 300 N force pulls on a rope attached to a building, we must find the horizontal and vertical effects.
First, we need to identify the angle of the rope. Since it runs from point A to point B (8m horizontally and 6m vertically), we can calculate the angle using the inverse tangent: α = tan⁻¹(6/8) = 36.87°.
Once we know the angle, we can find the force components:
- Horizontal component: Fx = (300 N) × cos 36.87° = 240 N
- Vertical component: Fy = -(300 N) × sin 36.87° = -180 N
Remember: The negative sign in the vertical component shows the force pulls downward, which makes sense given the rope's direction!
Calculating Force Resultants
When multiple forces act on a single point, we need to find the resultant force - the single force that would have the same effect as all forces combined.
To find the resultant of the four forces acting on point A:
- Calculate the x and y components of each force
- Add all x-components together: Rx = 129.9 N + + 0 N + 96.6 N = 199.1 N
- Add all y-components together: Ry = 75 N + 75.2 N + + = 14.3 N
The resultant force magnitude is found using the Pythagorean theorem: R = √ = √(199.1² + 14.3²) = 199.6 N
The direction is determined using the inverse tangent: θ = tan⁻¹ = tan⁻¹(14.3/199.1) = 4.1°
This means the resultant force of 199.6 N acts upward and to the right at an angle of 4.1° from the x-axis.
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Brad T
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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
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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
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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
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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
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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
Understanding Statics of Rigid Bodies: Solved Problems for Engineering Mechanics
L
Leonel
@leonel_dyzi
Engineering mechanics explores how forces act on rigid bodies and how to solve force-related problems. Understanding how to break down forces into their components and find resultants is essential for analyzing structures and solving engineering challenges.
Force Component Analysis
When working with forces in engineering, we often need to break them down into their component parts along different axes. This helps us analyze complex force systems more easily.
For any force, we can find its x-component (horizontal) and y-component (vertical) using trigonometry. The direction of the force determines which trigonometric functions to use.
In problem 1, we have two forces: a 150 N force at 30° and a 200 N force at 35° from their respective axes. These forces need to be resolved into their x and y components for analysis.
Pro Tip: When finding components, always pay attention to the direction! A force pointing down and to the right will have a positive x-component but a negative y-component.
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Solving Force Components Step-by-Step
Breaking down forces into components requires clear understanding of coordinate systems. For the 150 N force at 30° from the y-axis, we need to find what portion acts horizontally and vertically.
For the horizontal (x) component:
- The force is angled 30° from vertical, so we use sine: Fx = -(150 N) × sin 30° = -75 N
- The negative sign indicates the force points left along the x-axis
For the vertical (y) component:
- We use cosine: Fy = (150 N) × cos 30° = 129.9 N
- This is positive, showing the force points upward
The same process applies to the 200 N force, where Px = 163.8 N and Py = 114.7 N. These component values tell us exactly how much force acts in each direction.
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Finding Force Components in Applied Situations
In real-world engineering problems, we often need to determine force components based on geometry. When a 300 N force pulls on a rope attached to a building, we must find the horizontal and vertical effects.
First, we need to identify the angle of the rope. Since it runs from point A to point B (8m horizontally and 6m vertically), we can calculate the angle using the inverse tangent: α = tan⁻¹(6/8) = 36.87°.
Once we know the angle, we can find the force components:
- Horizontal component: Fx = (300 N) × cos 36.87° = 240 N
- Vertical component: Fy = -(300 N) × sin 36.87° = -180 N
Remember: The negative sign in the vertical component shows the force pulls downward, which makes sense given the rope's direction!
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Calculating Force Resultants
When multiple forces act on a single point, we need to find the resultant force - the single force that would have the same effect as all forces combined.
To find the resultant of the four forces acting on point A:
- Calculate the x and y components of each force
- Add all x-components together: Rx = 129.9 N + + 0 N + 96.6 N = 199.1 N
- Add all y-components together: Ry = 75 N + 75.2 N + + = 14.3 N
The resultant force magnitude is found using the Pythagorean theorem: R = √ = √(199.1² + 14.3²) = 199.6 N
The direction is determined using the inverse tangent: θ = tan⁻¹ = tan⁻¹(14.3/199.1) = 4.1°
This means the resultant force of 199.6 N acts upward and to the right at an angle of 4.1° from the x-axis.
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