Given the concurrent forces, Determine the resultant

[hiineko]

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

Please help thankyou guys!

 

[BvU]

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

 

[hiineko]

Help pls thankyouuuu

 

[SammyS]

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

Not right.

Please follow the suggestion of BvU.

Show your work.

 

[hiineko]

Not right.

Please follow the suggestion of BvU.

Show your work.

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

 

[SammyS]

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?

 

[hiineko]

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]

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?

 

[hiineko]

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

 

[hiineko]

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]

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.

They are already given.

 

[hiineko]

They are already given.

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

 

[SammyS]

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

Yes

 

[hiineko]

Yes

F3 = 14 N toward the negative z-axis what about this? Can you please translate this to me

 

[SammyS]

F3 = 14 N toward the negative z-axis what about this? Can you please translate this to me

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

 

[hiineko]

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

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

 

[SammyS]

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

How about 180° ?

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

 

[hiineko]

How about 180° ?

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]

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 .

 

[hiineko]

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]

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

Yes, -14 Newtons.

 

[hiineko]

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]

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.

 

[hiineko]

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?

 

[SammyS]

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

That sentence is kind of garbled, but I gather that you have gotten the answer.

I hope you understand it.