Given the concurrent forces, Determine the resultant

  • Thread starter hiineko
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  • #1
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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!
 

Answers and Replies

  • #2
BvU
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Write all three as ## \ \ a \; {\bf \hat\imath} + b\; {\bf \hat \jmath} + c\;{ \hat k}\ \ ## and add up the components.
Make a sketch.
 
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  • #3
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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
 
  • #4
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Help pls thankyouuuu
 
  • #5
SammyS
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hmmm I'll get the magnitude of it?
I got 14.9666
Not right.

Please follow the suggestion of BvU.

Show your work.
 
  • #6
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Not right.

Please follow the suggestion of BvU.

Show your work.
Can you please guide me in understanding f3 and f4? Thankyou!!
 
  • #7
SammyS
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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?
 
  • #8
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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
CA3ZgMS.png
????
 
  • #9
SammyS
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Soooooo I'll just
CA3ZgMS.png
????
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
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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
 
  • #11
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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.
 
  • #12
SammyS
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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.
 
  • #13
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They are already given.
So you mean to say
i = x component
j = y component
k = z component
???
 
  • #14
SammyS
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So you mean to say
i = x component
j = y component
k = z component
???
Yes
 
  • #15
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Yes
F3 = 14 N toward the negative z-axis what about this? Can you please translate this to me
 
  • #16
SammyS
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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.
 
  • #17
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What would be your interpretation of 5N to the West?, for example.
I say it as 5N 0 degrees from the x-axis
 
  • #18
SammyS
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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.
 
  • #19
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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
 
  • #20
SammyS
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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 .
 
  • #21
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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?
 
  • #22
SammyS
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So you mean to say that F3 has x-component of 0, y-component of 0, z-component of -14?
Yes, -14 Newtons.
 
  • #23
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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?
 
  • #24
SammyS
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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.
 
  • #25
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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?
 

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