Dot Product and Force Vectors | Mechanics Statics | (Learn to solve any question)
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- čas přidán 7. 08. 2024
- Learn to find angles between two sides, and to find projections of vectors, including parallel and perpendicular sides using the dot product. We solve a few examples step by step so you can grasp the material easily.
🔹Force Vectors Along a Line: • Force Vectors Along a ...
Intro (00:00)
Determine the angle θ between the sides of the triangular plate. (01:26)
Determine the magnitudes of the projected components of the force (02:26)
Determine the components of F that act along rod AC (03:45)
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’m thrilled to hear that you’re finding the videos helpful in your studies! It’s always rewarding to know that the content is making a difference. Remember, it’s perfectly normal to find these topics tough at first, but with consistent practice and study, it will become more intuitive. Keep up the great work!
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I hope you did great on your exam! Thanks for taking the time to write a comment like this, it's really nice. Keep up the great work and I wish you the best in your future endeavors.
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In example 2, I heard you say the the negative sign means that the components points in the opposite direction of the unit vectors. The way I observed the picture, and based on the problem I solved, it seem like we can think of as the vector for Force AB pointing towards point B, and the vector for Force AC pointing towards point C.
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Glad to hear :)
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Haha, glad to hear :)
Hi sir I have a question, in your previous video called “force vectors along a line | learn to solve any question” at 5.47 you find the magnitude of the force from the Cartesian by doing the square root of the 12 squared, the 9 squared and the 8 squared to find the mag then times this by the unit vector to equal the force. And I don’t understand why we don’t use this same concept at 3.34 where u times the unit vector not by the magnitude but by the different components of force F to find the force along the cables.
Is it because in this example we have 2 cables instead of one? I still don’t really understand, thanks for any help
Here, this question is related to projected components. We are given a force expressed in cartesian form and we are told to figure out the projected components of that force along each cable. So we use a different method. The process is pretty much the same as before, but instead of multiplying a scalar force value by the unit vector to get a cartesian force, we are already given a cartesian force so we take the dot product between each component and the unit vector. So in other words, we are getting a scalar force value for each cable. We aren't expressing it in cartesian form.
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Hello, for question 3, how do we know that the result of 99.5N is parallel? Thanks!
That's sort of the whole point of going through the dot product. 😅
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Give it your best shot! I wish you the absolute best on your test.
lol im in the exact same position a year after
How can we find the Cartesian form of the perpendicular component?
Please kindly give me a timestamp so I know where to look.
At problem no.2 won't the sum of forces from vector components of AB and AC be equal to F?
Yes, it would, but keep in mind, FAB and FAC values we found were scalar.
why didnt u make it unit vctor for example 1
So you have to look at the equation to get the angle (shown at 2:15). Notice how it doesn't require any unit vectors, just the position vectors.
3:32 why we need to multiply F with uAB and uAC
Please see 0:33. We are doing the same thing, taking the dot product. The only difference is, instead of it being about an axis, we do it about a specific cable (in this case, that is our axis).
Why do you need to find the unit vector in example 2 but not in example 1?
In example 2, it was a force along a line, (the ropes/cables).
I had the exact same question and I got the same answers as you but my prof m asked my answer for parallel wrong and said it should be 82.4N. A
I don't know which question you are referring to. Please use timestamps so I can take a look, thanks!
@@QuestionSolutions it was the third questions 3:45
I am not sure, but the answer shown is correct. Maybe your professor had different values? Not sure :/@@pyroad23
For the 3rd example why is B=-1.5i+2j+2k why is it not B =-1.5i +2j-2k
For it to have a negative k component, it needs to be below the x-y plane, in other words, point B must lie on the negative z axis, but its above.
What exactly unit vector means
Please see: czcams.com/video/CCeWy1kmxMs/video.html
Can i write cos(theta)=rAB(bold)*rAC(bold)/rABrAC as for example: cos(theta)= A(arrow)*B(arrow)/AB
Are you writing position vectors? You have to use the letter "r" to represent a position vector. So instead of bold, you can write rAB with an arrow on top. See: en.wikipedia.org/wiki/Position_(geometry)
@@QuestionSolutions yeah thats what i was trying to ask haha, hard to write mathematical equations on youtube.
just what you write as r(arrow) i got confused with the difference compared to using just vectors ("a" arrow), i think i get it and try to remember r as a reference for where a force is in a space (starting in a certain point o) and the vectors a or something as just vectors telling you your direction in space?
Thanks
@@tristandescamps8419 That is correct. I have a short video on position vectors, if you have time, please take a look, it might help you out: czcams.com/video/CCeWy1kmxMs/video.html
@@QuestionSolutions You don't know what it means to students when you actually respond even after 2 years... Whenever you think its pointless and useless please don't stop because it really helps people alot so they can continue on.
@@QuestionSolutions What got me confused and is very confusing, we use AB(->) not rAB. So after one year i was looking at this rethinking my life. Why is it used in different forms tho?
How did u got 5?
The 5.099? It's the magnitude of rAC. So you take each term, square it, add it all together, and then take the square-root. See: czcams.com/video/CCeWy1kmxMs/video.html
Point C:(3i+5j+(0k)?)m
Teacher z is not zero, it exista
How does the Z became 0k?
Please use timestamps so I know where you're talking about. Also, z is zero because point C lies on the floor, which means z=0.
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@@nimcaandayib6222 Glad to hear :) I wish you the best with your studies!
for BD I have The j component is -4
Never mind, It's D - B. I'm stupid!
You're not stupid, mistakes like that are easy to make and happens to everyone :)
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@@Devinci297 You're very welcome!
اخي هل تعرف تتكلم عربي لدي اسألة كثيرة
I don't know what you said, sorry!
2:24 the angle is 1.29😅
Ah i get it now u solved the magnitude 1st before you put it on the equation
(3.6055)(5.099)=18.38
Then
Cos-1(5\18.38)
Yes, that's why it's all included in a bracket. You can just plug it into your calculator directly and get the angle in degrees.@@josephluzon6391