Addition of Cartesian Vector Forces | Mechanics Statics | (Learn to solve any question step by step)
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- Опубликовано: 22 июл 2024
- Learn to break forces into components in 3 dimensions and how to find the resultant of a force in cartesian form. We talk about coordinate direction angles, azimuth angles, transverse angles, i, j, k, components and much more, step by step with animated examples.
🔹Addition of Coplanar Forces: • Vector Addition of Cop...
Intro (00:00)
The cables attached to the screw eye are subjected to the three forces shown. (01:25)
Determine the magnitude and coordinate direction angles of the resultant force (05:18)
Express each force as a Cartesian vector. (08:09)
Find more at www.questionsolutions.com
Book used: R. C. Hibbeler and K. B. Yap, Engineering Mechanics Statics.
Hoboken: Pearson, 2017.
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I am really glad to hear that! I hope all the statics videos will be helpful to you. Best of luck with your studies. ❤
@@QuestionSolutions thank you bro
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I swear, when I had my first statics class in college, I was regretting choosing engineering, but now that I know I have access to such helpful resources, I am not worried at all. Thank you so much for your help. Please make more videos on mechanic statics, we engineering students can really use it!!
Don't fret, statics is not hard as long as you understand the fundamentals. Once you are comfortable with expressing forces in cartesian form, taking moments, etc, everything else just falls into place. Keep up the good work and best wishes with your engineering degree.
How is it going so far🤣
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That's awesome to hear :) Thank you very much for your nice comment.
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Extremely HELPFUL....I understood the entire concept, hence feeling confident with these kinds of calculations...
Really glad to hear that :) Best wishes with your studies!
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Glad it was helpful and you're very welcome :)
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You're very welcome! Best wishes with your studies.
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You're very welcome. Thank you for taking the time to comment :)
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I am really glad to hear that! Keep up the good work and I wish you the absolute best with your studies. :)
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I am very happy to hear that! Do your best and good luck with your studies.
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Really glad to hear that :) Keep up the awesome work and best wishes with your studies.
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Glad it was helpful! Best wishes with your studies! :)
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Glad to hear it was helpful :)
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May I know the software you are using for visuals/graphics and how you can use it that way, very interesting.
Thank you very much for the nice comment! I use after effects to animate and illustrator to draw the graphics. :)
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Thank you very much, best wishes to you as well :)
@@QuestionSolutions Please explain, how to quickly solve vector algebra in mechanics.........
@@rishikumarshukla986 What do you mean by vector algebra? Solving for components?
Excellent video
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So much better than my teacher
Glad to hear the video was helpful :)
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Hello . You make me clear in a very good way I am the students of Industrial and manufacturing engineering. But I have a question that for F 2 why we have to find the x component. And in F 1 why we dont find the Y component
Please give me a timestamp to your question. I don't know where you're referring to. Thank you :)
I'm in the first grade in engineering and this video helpp me a lottttt please keep going 🥺❤️❤️
I am glad to hear there. There is a playlist of statics that should pretty much cover everything you need for the first year :)
@@QuestionSolutions i will definitely look at this 💪❤️
@@manarawad3339 Great! Leave a comment if you need clarifications on any of the questions covered in the videos. Best wishes with your studies ❤
youre really good at explaining, could you consider explaining other courses e.g calculus and multi variable analasys as well?
Thank you very much. I don't have any plans to do calculus in the near future, but it is on my to-do list. There are already some wonderful and excellent resources for calculus available on RUclips.
Can you make videos on coplanar and 3-d force systems in equilibrium, please? Your videos are awesome.
I think I have a video on 3D equilibrium problems, please see: ruclips.net/video/EzquIxEoHRE/видео.html
You are amazinggg
Thank you :)
In 10 minutes I understood this topic
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this is so freaking detailed summarizes 8 weeks of classes lol
I hope it was helpful to you. Keep up the great work and best wishes with your studies.
sir, I have a doubt ....in 4:02 ...in f3 vector why we are subtracting 108- 45 degree and writing it as 250cos(135) j with respect to positive y axis....why cant we write directly as (minus) -250cos(45) j with respect to negative y axis ...could you please clarify it?
It makes no difference, the only thing is that you need to remember to use a negative sign whenever it's not with respect to a positive axis. It's easier to remember to subtract the angle from 180 since it gives you ability to understand what you're doing. Either way, you will get the same answer. The proper method is to subtract the angle from 180 but it's up to you :)
@@QuestionSolutions thank you sir😇
on 3:15, since the force runs in the negative z axis, shouldn't we subtract 120 from 180 to give us an angle of 60 between the positive z-axis and the force? We did this for the j component, so why not for the k? Thank you!
Maybe I am not understanding your question properly, but we didn't subtract anything for the j component. Since the angles were already given to us with respect to the positive x,y,z axes, nothing needs to be subtracted. We only ever subtract from 180 degrees if the angle was given with respect to a negative axes. For coordinate direction angles to work, we have to use the angle with respect to positive axes. Now if we look at the 120 degrees, we see that it is indeed given to us measured from the positive axis. You can tell the positive sides by looking at the labels for each axes, so for z, it's labeled on top, that's the positive side, for y, it's labeled on the right, so that's the positive side, and so forth. Lastly, when we do the simplification, we see that the the z component is indeed negative, and you can see that at 3:29, it's below the x-y plane. If we had used cosine 60 for the z-component, we would end up with a positive force value, which would be incorrect.
@@QuestionSolutions Ah! I apologize! You are correct, the angle given for k is with respect to the positive z axis. I had a total brain fart and imagined the angle given was with respect to the negative z axis. That was my question, whether we should subtract the given angle 120 from 180 as I thought it was respect to tue negative z axis. Thank you for responding! I love your videos by the way, they have helped me so much!
@@Pguzman42 I am very happy to hear that it's all cleared up. Keep up the awesome work and I wish you the best with your studies! And thank you for your kind words :)
How can I find that the force vector is just in xz plane or xy plane so that its third component is zero?
So you can just look to see what angles are given. If you are given 3 angles, then you have 3 components, if you're given just 1, then it's in a single plane, and that plane is dependent on the angles given. So look at 2:21, you can see we are given just 1 angle, with respect to the positive z-axis, so we know it must lie in the z-y plane. Even though we are given 1 angle, we know that with respect to the y-axis, the angle must be 90-40 = 50 degrees.
Nice can you tell me please what program do you use ?
After Effects for the animations.
In regards to the F2 of the problem in 3:11 , shouldn't the angle with respect to the y axis be 45 degrees as well? Because if we make use of the 45 degree angle that's with respect to the x-axis to look for the x-component, we could also make use of the same 45 degree angle that's with respect to the x-axis to look for the y component with the use of sin. However, it gives us a different result compared to making use of the given 60 degree angle with cos.
if F2x = (100N)cos(45), then F2y = (100N)sin(45). However, F2y = (100N)sin(45) doesn't give the same result as F2y = (100N)cos(60)
help a brudda out.....I'm confused
What you are saying cannot be done, because these angles are given with respect to individual axes. In addition, they must be given with respect to the positive x,y,z axis, or you have to do the math and calculate the angle with respect to the positive axis. They are not interconnected, which is why cosine must be used when solving coordinate direction angles. So you can't use sine, you have to use cosine to figure out the answer. What you are saying can be done with transverse and azimuth angles (like the one shown at 5:37). I hope that helps.
the angle between F' and F1, shouldnt it be 10? because (90-20-60) degrees ? on 6:14
The 20 degrees is between the positive x-axis and F'. It is not related to the angle between F' and F1. 👍
Hi. I keep getting different values for my sin and cosine solving. For example at 6:32 I got 61.70
Your calculator is set to radians, change it to degrees. 👍
Thank you so much. You really are amazz
Great work man, helps a lot with statics.....what's your name fella?
Glad to hear these help, I'm Steven. 👍
Nice
👍
In the third example. Shouldn’t Fx2 equal Fx1 because I observed a rectangle lying on a the xy-plane and the two short sides of a rectangle are the same length and the two long sides are the same length.
I don't know how to answer your question because I am not understanding what you are saying with the observed rectangle. Are you saying components of F1 is shared for the components of force F2? If you can maybe draw a diagram of what you mean? Sorry, I am unable to follow your question.
@@QuestionSolutions okay. So go to the purple triangle in the xy-plane that has the 30 degree angle, and you will see a line on xy-plane that looks to be parallel to the y axis. Follow that line until you stop at the x axis. The line looks to be perpendicular to the x-axis.Then start from that point and follow that line until you get to the origin we’re the hook is. Next, make you way along the y-axis and stop at the line that is perpendicular to the y-axis. Finally, follow that line until it stop that line that parallel to the y-axis. When you go around that path, you will see that it looks like a rectangle was drawn.
@@darrylcarter3691 Okay, I see what you mean. But if you look at the original diagram, you can see that the line parallel to the y-axis lying on the x-y plane ends shorter than the x-component of force F1. So while, it's true, it forms a rectangle, it doesn't line up with force F1, so the x-component of force F1 is not equal to the x-component of F2. That was the original question right?
@@QuestionSolutions yes
@@darrylcarter3691 👍
Please at 2:49 I don't understand why the force doesn't have an x component but F2 has a z component even though its in the x y plane
Hi, so you have to look at the diagram really carefully. Specifically, look at the axes shown. Locate where, x, y, and z axes are. After you do that, look at force F1. I draw the components of force F1 at 2:49. See how it has an z-component and a y-component. They are along those axes. It's in the z-y plane. Now look at force F2. It's NOT in the x-y plane, it's also in the z-plane. Look at time 3:30. See how the force is below the x-y plane. That means it's not lying in the x-y plane, but it has all three components. You can also tell because the angle between the force and the z-axis is 120 degrees. That means it goes past the 90 degree mark, so it must be below the x-y plane. Let me know if you need further help. Best wishes with your studies.
Thank you soo much I understand now
I wanted to ask if you have a video on finding position vectors in 3D should I send you a sample question?
@@adwoaaj5925 yes, I think this is what you're looking for: ruclips.net/video/CCeWy1kmxMs/видео.html
@@QuestionSolutions thank you
Why do you use f1 different process from the others.
I assume you are referring to question 1? Please kindly use time stamps when asking questions, it's easier that way :) Force F1 lies on a single plane, so it lies on the zy plane, and is not given with coordinate direction angles. So we can't use it, we just need to break the force into components using sine and cosine. Please watch this video: ruclips.net/video/NrL5d-2CabQ/видео.html Thanks!
7:53 how you have drawn this red dotted lines
They are each of the components, so 575 in the positive x-direction, 131 in the positive y-direction and -153 in the negative z-direction.
@@QuestionSolutions really great u are replying to everyone
@@saiprasadsatya3677 :)
For the last problem, how is f' the hypotenuse?
F' is the hypotenuse of the first triangle, not the second.
@@QuestionSolutions you said f’ is hypotenuse for the triangle with the 30 degree angle. But it looks like the y side is the hypotenuse.
@@yusufmoola6471 Yes, it is the hypotenuse. The diagram might be hard to tell, but draw it out with a protractor, you will see that it is indeed the hypotenuse.
cos-1(575,52/610)=19.36 grados
can you solve the first problem by using F2' and F3' ?
No because the forces are given with coordinate direction angles. The F' method is only applied to forces given with transverse and azimuth angles. Please make sure to realize the difference, or you won't get the correct answers.
@@QuestionSolutions so the sign to use transverse or azimuth angles is when they show a blue triangle?
Pretty much, yeah. 👍
Im not even studying math or anything, this just also help a dumbass like me program stuff im way too underqualified for
I am glad you find these videos helpful. Keep up the great work! Don't think negatively, you got this :)
Understood the concept in just 10 minutes while I struggled understanding it from my prof for weeks already. I hope teachers should also learn how to teach.
I am really glad to hear this helped :) I wish you the best with your studies and keep up the good work!
For real, some lecturers don't know how to teach, sometimes I ask my self what really they are doing.
RUclips is the best platform for well explained lectures
I am sorry but isn't that 45 degree must be 30? Because 60 +45=105 degree but that is a right angle triangle.
Please give me a timestamp so I know where to look, thanks!
@@QuestionSolutions 3:39
@@sanatani_manushy77 No, because the other angle with respect to the y-axis would be 135 degrees. Remember, the 45 degree angle is with respect to the y-axis, so 180-45 = 135 degrees. It's not 30 degrees. You are trying to add up an angle that's with respect to the y-axis with the z-axis :)
2:28 sir i think the angle with y would be 60 degree and why you have taken 40 degree bcz the angle is not mentioned wrt y
That's incorrect. You need to look at it with respect to the angle given. You can use 60 degrees (not sure why you would because that's extra work), but if you do, you need to use cosine for the j component and sine for the k component. Remember, always look with respect to the angle.
Also, "why you have taken 40 degree bcz the angle is not mentioned wrt y" I am not sure what you mean here? You don't need the angle with respect to an axis to solve it. You can use any angle given as long as you know whether to use sine or cosine to get it.
@@QuestionSolutions ok thank you
Let me know if you need further help or if you understand it. Thanks!@@Ashjj1935
i love you please have my firstborn child
Haha 😀 Best wishes with your studies!
5:00 What if the question asks you to find the unit vector? Do we just divide the coefficient of the components with the magnitude? e.g. 195.7/407.03 for x component?
See this video where I cover unit vectors: ruclips.net/video/CCeWy1kmxMs/видео.html
@@QuestionSolutions thanks :)
@@famueduyou You're very welcome :)
I will no longer need to listen to class as long as you're explaining engineering mechanics to me
I am glad these videos are helpful, but you should still listen to your class too :)