/sci/ - Science & Math

>>9711974
>is it possible to solve this by breaking the force vectors into orthogonal components?
yes

>>9711979
For the situation illustrated, how would it look though? I feel like the sketch I made is wrong somehow...

if you start with the standard decomposition and then transform it into yours, you will notice that your angle theta will change, as you have to transfer the y-part of your downhill force to your normal force to conserve their sum. thus this decomposition is not possible in the way shown in your sketch.

cos(theta)*g is your downward and sin(theta)*g is your horizontal

>>9711983
Orient y hat to point up the page and x hat to point to the right. Now use Newton's first law to solve the system.

>>9712009
Here's the thing: when you rotate the coordinates system, you will notice Fg is the hypotenuse and the normal force is the adjacent side to theta. In the none rotated coordinate system, the Fg becomes the adjacent side. Now everything ceases to make sense.

>>9711974
>you're normally supposed to solve these by rotating the coordinate system and making the surface of the ramp in line with your x axis
>not normally breaking the force vectors into orthogonal components
What the fuck

>>9712014
For inclined plane problems, I searched all over the internet and all videos/methods/tutorials tell you to rotate the coordinate system because it is the easiest way to do it. I'm trying to figure out how to solve them the "hard" way so that I have a better understanding of how vectors work.

>>9712014

what are you confused about?

>>9712017
Look, any statics problem can be solved by rotating the coordinate system by any amount you choose. It's totally arbitrary. In every single case, however, the sum of the forces in the x,y,z directions are zero per Newton's first law. That's all you need to figure out how to do it the "hard way"

>>9711974
If you don't "rotate the axis" you'd essentially have a system where the normal force is sliding the block to the right, and the friction resisting it to the left. If you know how to represent the force vectors as 2D components you can just do it normally from there.

>>9712001
Does this make more sense to do?

>>9712017
Have you never finished anything beyond primary school? It's literally a high school tier introductory problem
The high schoolers who main humanities can solve this in my country

>>9711974
Anon... you're really overthinking this. In the coordinate system you've defined, weight does not have a horizontal component.

>>9712543
Fny + Ffy = Fg
Fnx = Ffx
Fn = (Fnx^2 + Fny^2)^0.5
Ff = (Ffx^2 + Ffy^2)^0.5

>>9712017
>>9711974
>rotating the coordinate system
>breaking the force vectors into orthogonal components
This is why linear algebra needs to be taught early, often, and emphasized. Those two statements are literally equivalent. Look up stuff like "orthogonal transformation" and "rotation matrix".

>>9712559
Oh and vector space basis if you really don't know what you're doing with vectors (I don't blame you if you don't, these intro physics courses just don't give enough mathematical foundation): https://en.wikipedia.org/wiki/Basis_(linear_algebra)

>>9712013
no, translate the Fg vector such that it's tail contacts the tip of the normal force vector. the Fg vector becomes the hypotenuse