# Homework Help: Given the concurrent forces, Determine the resultant

1. Aug 4, 2015

### hiineko

1. The problem statement, all variables and given/known data
F1 = 10N at 37 N of W
F2 = 15N North
F3 = 14 N toward the negative z-axis
F4 = (8i + 12j + 4k)N
Find the resultant

3. The attempt at a solution
I use 10cos37/sin37 for F1
I use 15cos0/sin0 for F2

But I don't how to use F3
and F4

2. Aug 4, 2015

### BvU

Write all three as $\ \ a \; {\bf \hat\imath} + b\; {\bf \hat \jmath} + c\;{ \hat k}\ \$ and add up the components.
Make a sketch.

3. Aug 4, 2015

### hiineko

hmmm I'll get the magnitude of it?
I got 14.9666

4. Aug 4, 2015

### hiineko

Help pls thankyouuuu

5. Aug 4, 2015

### SammyS

Staff Emeritus
Not right.

6. Aug 4, 2015

### hiineko

Can you please guide me in understanding f3 and f4? Thankyou!!

7. Aug 4, 2015

### SammyS

Staff Emeritus
I assume the unit vectors are aligned as follows:

$\hat{i} \$ points East.

$\hat{j} \$ points North.

$\hat{k} \$ points upward.

Is that what is meant for F3 & F4?

8. Aug 4, 2015

### hiineko

Soooooo I'll just ????

9. Aug 4, 2015

### SammyS

Staff Emeritus
That's a rather incomplete description of what to do.

Add all the vectors component by component.

What form should you use for the resultant?

10. Aug 4, 2015

### hiineko

Okay wait

11. Aug 4, 2015

### hiineko

Btw how could I get the component of F3 and F4 that is my question , I know how to get the compnent of F1 and F2 you use xcosΘ and xsinΘ.

12. Aug 4, 2015

### SammyS

Staff Emeritus

13. Aug 4, 2015

### hiineko

So you mean to say
i = x component
j = y component
k = z component
???

14. Aug 4, 2015

### SammyS

Staff Emeritus
Yes

15. Aug 4, 2015

### hiineko

16. Aug 4, 2015

### SammyS

Staff Emeritus
What would be your interpretation of 5N to the West?, for example.

17. Aug 4, 2015

### hiineko

I say it as 5N 0 degrees from the x-axis

18. Aug 4, 2015

### SammyS

Staff Emeritus

In other words, that's 5N in the direction of -x . that is to say, toward the negative x axis.

19. Aug 4, 2015

### hiineko

Okay so "F3 = 14 N toward the negative z-axis" - What degree? Bc I'm aware of x-axis and y-axis. But I have problems dealing with z-axis

20. Aug 4, 2015

### SammyS

Staff Emeritus
Like you said in post #13:
$\hat{i} \$ is in h x direction, etc.

The vector $\displaystyle \ (5\hat i-7\hat j+3\hat k\, )\text N\$ has an x-component of 5N, a y-component of -7N, and a z-component of 3N .

21. Aug 4, 2015

### hiineko

So you mean to say that F3 has x-component of 0, y-component of 0, z-component of -14?

22. Aug 4, 2015

### SammyS

Staff Emeritus
Yes, -14 Newtons.

23. Aug 4, 2015

### hiineko

Okay I will put the components of F1 F2 F3 F4 before I add it all

F1 = Σx = 10cos37 = 7.99; Σy = 10sin37 = 6.018
F2 = Σx = 15cos90 = 0; Σy = 15sin90 = 15
F3 = sqrt(0^2+0^2+(-14)^2) = 14
F4 = sqrt(8^2+12^2+4^2) = 14.9666

right?

24. Aug 4, 2015

### SammyS

Staff Emeritus
You have found the x & y components of F1 and F2. the z component of each being 0.

The magnitudes of F3 and F4 are correct, but hardly needed.

To find the resultant of all 4 of these forces, add the respective components.

I presume you are to leave the result in the form with i, j, k unit vectors.

25. Aug 4, 2015

### hiineko

I got it right? :) Means I just have to add of these and that is the final answer the resultant?