# Given the concurrent forces, Determine the resultant

## Homework Statement

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

## The Attempt at a Solution

I use 10cos37/sin37 for F1
I use 15cos0/sin0 for F2[/B]
But I don't how to use F3
and F4

Related Introductory Physics Homework Help News on Phys.org
BvU
Homework Helper
2019 Award
Write all three as ## \ \ a \; {\bf \hat\imath} + b\; {\bf \hat \jmath} + c\;{ \hat k}\ \ ## and add up the components.
Make a sketch.

hiineko
Write all three as ## \ \ a \; {\bf \hat\imath} + b\; {\bf \hat \jmath} + c\;{ \hat k}\ \ ## and add up the components.
Make a sketch.
hmmm I'll get the magnitude of it?
I got 14.9666

Help pls thankyouuuu

SammyS
Staff Emeritus
Homework Helper
Gold Member
hmmm I'll get the magnitude of it?
I got 14.9666
Not right.

Not right.

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

SammyS
Staff Emeritus
Homework Helper
Gold Member
Can you please guide me in understanding f3 and f4? Thankyou!!
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?

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?
Soooooo I'll just
????

SammyS
Staff Emeritus
Homework Helper
Gold Member
Soooooo I'll just
????
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?

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?
Okay wait

Waiting ...
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.

SammyS
Staff Emeritus
Homework Helper
Gold Member
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.

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

SammyS
Staff Emeritus
Homework Helper
Gold Member
So you mean to say
i = x component
j = y component
k = z component
???
Yes

Yes

SammyS
Staff Emeritus
Homework Helper
Gold Member
What would be your interpretation of 5N to the West?, for example.

What would be your interpretation of 5N to the West?, for example.
I say it as 5N 0 degrees from the x-axis

SammyS
Staff Emeritus
Homework Helper
Gold Member
I say it as 5N 0 degrees from the x-axis

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

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

SammyS
Staff Emeritus
Homework Helper
Gold Member
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
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 .

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

SammyS
Staff Emeritus
Homework Helper
Gold Member
So you mean to say that F3 has x-component of 0, y-component of 0, z-component of -14?
Yes, -14 Newtons.

Yes, -14 Newtons.
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?

SammyS
Staff Emeritus
Homework Helper
Gold Member
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?
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.

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