# Specify force magnitude and angle

See picture.

## The Attempt at a Solution

I tried drawing a parallelogram, but it didn't help, so I'm stuck. I'd need an idea in the right direction, if possible.

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See picture.

## The Attempt at a Solution

I've decomposed F1 into F1x F1y and F1z..
F1x = 150 * sqrt 3
F1y = 150
F1z =150 * sqrt 2[

Now I'm stuck../QUOTE]

gneill
Mentor
I'm not seeing how you've accomplished your decomposition of F1. The magnitude of the vector comprised by those components would be about 367 N, which is larger than the given magnitude of F1. So you might want to re-think your method (whatever that was...).

The diagram is very helpful because it gives you the angles between F1 and each of the coordinate axes. This should make finding the projections of F1 on each of the axes easy to find.

SteamKing
Staff Emeritus
Homework Helper

See picture.

## The Attempt at a Solution

I tried drawing a parallelogram, but it didn't help, so I'm stuck. I'd need an idea in the right direction, if possible.
I don't know what sort of parallelogram you drew, but this is a 3-D kinda problem.

I don't know what sort of parallelogram you drew, but this is a 3-D kinda problem.
yes, I was going to draw a parallelepiped to see if it could help me.

I'm not seeing how you've accomplished your decomposition of F1. The magnitude of the vector comprised by those components would be about 367 N, which is larger than the given magnitude of F1. So you might want to re-think your method (whatever that was...).

The diagram is very helpful because it gives you the angles between F1 and each of the coordinate axes. This should make finding the projections of F1 on each of the axes easy to find.
F1z = cos 60 * 300N = 150N
F1x = cos 45 * 300N = 150*sqrt2 N
F1y = cos 60 * 300N = 150 N

Would this be correct?
I'm confused about the next step..

gneill
Mentor
F1z = cos 60 * 300N = 150N
F1x = cos 45 * 300N = 150*sqrt2 N
F1y = cos 60 * 300N = 150 N

Would this be correct?
For the Z component the angle was not 60 degrees. What does the diagram show it to be? Do you expect the Z-compoennt to be less than or greater than zero?

Check your value for cosine 45 degrees. A cosine should not be > 1.*

* EDIT: Oops. I didn't process the fact that the 300 N was divided by two giving 150 N, so the cosine being ##\sqrt{2} / 2## is satisfied! Sorry about that!
I'm confused about the next step..
You'll want to write a vector equation that expresses your desired result. Fix your F1 vector first though.

Last edited:
mtjc1x
For the Z component the angle was not 60 degrees. What does the diagram show it to be? Do you expect the Z-compoennt to be less than or greater than zero?

Check your value for cosine 45 degrees. A cosine should not be > 1.

You'll want to write a vector equation that expresses your desired result. Fix your F1 vector first though.
F1z = cos 120 * 300N = -0.5 * 300N = -150N (but how does that make sense?)

cos 45 = (√2)/2
so F1x = 300 N * cos 45 = 150 N * √2 = 150√2 N

F1y = cos 60 * 300N = 150 N

Is this right now?

gneill
Mentor
F1z = cos 120 * 300N = -0.5 * 300N = -150N (but how does that make sense?)

cos 45 = (√2)/2
so F1x = 300 N * cos 45 = 150 N * √2 = 150√2 N

F1y = cos 60 * 300N = 150 N

Is this right now?
Yes, that looks right. The z-component is negative because the vector F1 is directed below the x-y plane.

mtjc1x
Yes, that looks right. The z-component is negative because the vector F1 is directed below the x-y plane.
so the idea with F2 would be to cancel out the F1z and F1x and amplify F1y by 650N?
So I need a
F2z = 150 N
F2x = -150√2 N
F2z = 650 N

Am I going in the right direction?

gneill
Mentor
Yes, but sort out your component subscripts. You've listed F2z twice. It would help if you put them in standard order, too: x, y, z. Otherwise, I think you're there.

mtjc1x
Yes, but sort out your component subscripts. You've listed F2z twice. It would help if you put them in standard order, too: x, y, z. Otherwise, I think you're there.
F2x = -150√2 N
F2y = 650 N
F2z = 150 N

How do I calculate F2?

SteamKing
Staff Emeritus
Homework Helper
F2x = -150√2 N
F2y = 650 N
F2z = 150 N

How do I calculate F2?
You don't know how to calculate the magnitude from the three force components?

F2x = -150√2 N
F2y = 650 N
F2z = 150 N

How do I calculate F2?
F2 = √((-150√2)^2 + 150^2 + 650^2) = 700 N

To calculate the angles of F2 I used:

cos x = (F2x/F2) = (-150√2 N / 700 N) ---> x = 72.36°
cos y = (F2y/F2) = (650N / 700 N) ---> y = 21.79°
cos z = (F2z/F2) = (150N / 700 N) ---> z = 77.63°

Correct?

F2 = √((-150√2)^2 + 150^2 + 650^2) = 700 N

To calculate the angles of F2 I used:

cos x = (F2x/F2) = (-150√2 N / 700 N) ---> x = 72.36°
cos y = (F2y/F2) = (650N / 700 N) ---> y = 21.79°
cos z = (F2z/F2) = (150N / 700 N) ---> z = 77.63°

Correct?
Sorry, messed up x:
cos x = (F2x/F2) = (-150√2 N / 700 N) ---> x = 107.64