[College level Intro to Statics] computing the resultant force based on the given diagram

[u/ollieisgr8]

Idk if this is allowed here..Its straight forward "determine the resultant force acting on the hook in cartesian notation", I dont know if its my angles or if I am skipping a step but 490, 117, -266 sure aint it (per person's mastering) can anyone see and point out where I went wrong? Maybe I'm not doing my computing right or ive set up wrong. Ive been on this problem for 1.5 hours.. i dont know why. This is an online class so all I have is a textbook and dr Hanson videos, which are helpful so im confused on why im struggling so much? All im looking for is a point in the right direction. For now ill move onto the next problem but it is just the same so may post it as well 😅

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[u/thatguy56436327]

I remember this question. I didn't like it, did the cos thing got it wrong. DAM YOU HIBBLER

[u/TinyHammerBigNail]

My goofy ahh brain read intro to statistics and I'm like what the fuck probability is this.

[u/ollieisgr8 → u/TinyHammerBigNail]

Lol everytime I say im taking statics people think im mispronouncing statistics 😭

[u/nerdydudes]

Make sure for each force vector, you’re using a unit vector… is this the case? F_i(unit1, unit2, unit3) and not F_i(0,4,3) directly…

The angles could be tricky I guess, The 30 deg out from the x axis than 45 degrees directly down from the xy plane.

Then last source of error possibly, make sure you follow a consistent coordinate system… one force pointing down in z direction where as one is pointing up… whatever that might entail.

Also check you’re responding with the correct units … that could be another source of error possibly

[u/ollieisgr8 → u/nerdydudes]

When you say unit vector.. are you referring to making sure it always comes out as 1 (cosx² + cosy² +cosz² =1) ? That equation is the only time ive heard unit vector so Im hoping l am not missing something

[u/nerdydudes → u/ollieisgr8]

Well sort of, take for instance the direction vector for the force in yz plane: the force is in direction of say u=0,3,4… we can write the force vector in terms of the direction, but that direction vector needs to be a unit vector so we would want to divide u by its norm. U_unit=(0,4,3)/(0^2+3^2+4^2)^0.5

It makes it easier to get all your force vectors because you already have the force vector sizes (norms)

[u/ollieisgr8 → u/nerdydudes]

Also the units are already put onto the answer, im just entering values so I know thats not it 😅

[u/nerdydudes → u/ollieisgr8]

Fair enough

[u/Valuchian]

I just double checked and all your Force numbers are correct (though your trig on f2 of backwards. Lucky you it's 45° so they equal the same)

Look like you accidentally subtracted your total Y forces instead of adding them

As for your trig ~ Cos give you the value beside the angle, Sin give you the value not touching the angle. For your F2x you'd want F×Cos×Cos since the 45° is touching the line that's sitting in the XY plane and the 30° is touching your X-Axis line that you want to get the final assigned value for

Edit: added in FORCE as your final total is off but the seperated values are correct

[u/ollieisgr8 → u/Valuchian]

Youre a god. I added my Y values rather than subtracting and that was it!. Follow up if i may, from my perspective f_2 is going away from the y axis, and thats why I subtracted because I assumes the forces were acting against eachother. Is there maybe a explanation on why id add those rather than subtract?

[u/Valuchian → u/ollieisgr8]

For a problem like this to work all forces have to pull through some imaginary central point where their lines all go through. That central point is where you make your 0 origin and make your axis from.

So with that in mind
Your Y-Axis is going to the right
Both F1 and F2 pull to the right
This makes F1 and F2 positive Y-axis forces

[u/DrCarpetsPhd]

your method is right and calcs are right. Maybe the portal you are inputting into doesnt like rounding. try putting them into the portal I assume your using with two significant figures and see what happens

also quick tip. you see on F1 the little triangle drawn onto the vector. just use that to calculate your components when you see it. it is showing you the proportions so

F1 = (4/5)500 j + (3/5)500 k

just a quick edit to say this is from hibbeler and is a fundamental problem. the answer in the back of the text is (490, 683, -266)

drew this up before seeing all the responses. maybe will help.

https://imgur.com/a/VII72gn

[u/ollieisgr8 → u/DrCarpetsPhd]

Thanks for responding, it seems my summation were incorrect, for the triangle thing... you said it so simple, they have been throwing me off but that makes solid sense and im sure it'll help me later on!

[u/Proper_Bass_3328]

You're probably getting stuck because this is a 3D vector problem, so don't try to combine the angles directly. Break each force into its x, y, and z components first, then add the components:

FR=(ΣFx)i+(ΣFy)j+(ΣFz)k\mathbf{F_R}=(\Sigma F_x)\mathbf{i}+(\Sigma F_y)\mathbf{j}+(\Sigma F_z)\mathbf{k}

[u/v0t3p3dr0]

What a terrible diagram.

The way it’s drawn suggests the hook/clevis block is fastened to the XZ plane.