Adding Vectors: How to Find the Resultant with 3 Given Force Vectors

[suki86]

Need help adding vectors --please help

Homework Statement

i have 3 force vectors i want to add to get the resultant.
vector a mag=1.31N and is 51.34deg to the x-axis (Quad 1)
vector b mag= 1.31N and is 51.34deg to the x-axis (Quad 4)
vector c mag = .719N and is along the pos y axis

how do you add these for resultant?
ive learned this before but forgot how to add them, --isnt there a simple way to get the one resultant vector?
thanks for any help!

Homework Equations

The Attempt at a Solution

 

[suki86]

also, the forces are from point charges, so no gravity

 

[Dick]

Split them all into x and y components and then add the components to get the components of the sum.

 

[suki86]

thanks for the reply.

ok but isn't there a faster way to get the resultant rather than breaking them apart then putting back together again?

 

[suki86]

Fxa = 1.31N * cos 51.34deg = .818353N
Fxb = 1.31N * cos 51.34deg = .818353N
Fxc...... = 0 (because force is along the y-axis)

Fya = 1.31N * sin 51.34deg = 1.0229N
Fyb = 1.31 * sin51.34deg = 1.0229N
Fyc = .719N = .719N (because along the y-axis)

 

[suki86]

ok so, I broke them down into x and y components. just need help adding them now?
thanks!

 

[=CIA= h1tman]

I'm pretty sure you have to use basic trig functions to find the lengths. Then, add them together.

 

[Dick]

Ok, so now add all of the x's and all of the y's. That gives you the x and y components of the total force T. Do you need to get the total magnitude and direction of T? Do you know how to do that?

 

[suki86]

yeah total magnitude is what i want.
So Fx = 1.636706
Fy = 2.7648

ho do i add them? thanks

 

[Dick]

Good so far. You don't 'add' them. The vector is (Fx,Fy). The magnitude is sqrt(Fx^2+Fy^2), the angle is arctan(Fy/Fx). It's the opposite of splitting into components, you are 'recombining' the components.

 

[suki86]

oh duh. this is just pythagarus isn't it? i mean x and y components mean i just get the hypotenuse and that's how you "add" them right>?
so, sq rt Fx^2 + Fy^2 = resultant vector

 

[suki86]

i mean the MAGNITUDE of the vector at least.

 

[Dick]

Yes. You are on the right track.