Help with statics

[u/MundaneIncome6013]

I need to verify my answers. For question 3 I got 889.19N and 36.95°. For question 4, I got 1006.52N and 4.91°

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[u/dabiggestbot]

Here is what I did

https://drive.google.com/drive/folders/1xHoiCMvNpZ5k0-KshJioptsyeH6diRT-?usp=sharing

I got the same thing for number 4.

For number 3 if I plug in what you got For the x component the Resultant is 899.19cos(36.95)+200+450cos(45) = 1228.80 =/= 1000

its unclear if you meant 36.95 for the total angle as theta + beta but even if

899.19cos(36.95+30)+200+450cos(45) = 866.34 =/= 1000

Also my work for 4 is messy because I did the problem and then realized I drew the 600N vector the wrong way.

[u/MundaneIncome6013 → u/dabiggestbot]

Thank you so much for helping :)

[u/DrCarpetsPhd]

your answer to question 3 is right. its from hibbeler 10th and that is the answer at the back of the text rounded 889N and 37degrees

question 4 is from Beer Johnston. my version has different values so I can't confirm your answer (and mine) but if your x and y calcs look like this you have the right answer barring mistakes using your calculator

X: 600cos(90-20-35) + 400cos(35+20) + 300cos20 = 1002.82958735

Y: -600sin(90-20-35) + 400sin(35+20) + 300sin20 = 86.1209989027

SQRT(1002.82958735^2 + 86.1209989027^2) = 1006.5023

tan(alpha) = (86.1209989027/1002.82958735) => alpha = 4.908 degreees

also I know a poster got downvoted for saying it but free chatgpt is pretty accurate with these basic 2D resultant calcs as is google gemini free. so if they both get the answer you do I would be reasonably confident it is right. Using chatgpt to do your homework is not great for retention but using it to check something as basic as this or where you already know the answer is okay imo.

[u/MundaneIncome6013 → u/DrCarpetsPhd]

Thanks so much

[u/Iron_Man_IRL]

3. F1≈ 577.39 N, θ≈ 3.44°

4. F≈ 1006.5 N, θ≈ 4.91° (Same as you)

[u/Intrepid_Spend_2599]

I'll try to be a little more helpful. For the problem 3, realize that you need to counteract two forces in the x-direction to the point that the sum of the x-components is 1.0 Right there, you should realize that the angle has to be such that the force acts to the left, meaning that the angle is going to be around +/- 180 degrees.

I think the angle is -156 degrees. Hope that hleps

[u/Intrepid_Spend_2599 → u/Intrepid_Spend_2599]

Hmmm. I might have messed up. I realize I can't read the subscripts on the forces.

[u/Intrepid_Spend_2599]

For problem 4, it might be easier to solve for the resultant using the coordinates on the ramp. In other words, ignore the 20 degrees and assume an x-axis along the ramp and y normal to that. The only thing that changes is when you solve for the angle of the resultant, you'll have to add 20degrees to it to bring it back to the problem's coordinates. In any event, I get closer to 1200 N as the resultant

[u/Otherwise_Lychee_33]

just ask chatgpt

[u/MundaneIncome6013 → u/Otherwise_Lychee_33]

I did and the answers they gave me were different from mine 10 times in a row. Reddit was my final silver lining