How Do You Calculate Vector Components in Physics?

[physics(L)10]

Homework Statement

A 10kg mass has a force pointing in the east direction and another force pointing in the south direction 45 degrees from the east force |F1|=12 Nt, |F2|=19 Nt

a)total force vector?
b)mag of total force
c)direction of total force

Homework Equations

F=F1 + F2

The Attempt at a Solution

a) The only thing that's confusing me really is what to do with the degrees. I'm guessing to find the total force vector you would do 12(cos theta, sin theta) + 19(cos theta,sin theta). I'm just having trouble deciphering which degree to use. As a guess, I would think its cos1,sin0,cos45,sin-45 respectively.

b)Once you find this vector, you add the squares of the two numbers and then take the sqrt of the total. I'm pretty sure this is correct.

c)I'm thinking the direction is asking for the degrees, so you would have to take the inverse of tan y/x.


I'm okay with b&c I think. I just need help on how to find the degrees

 

[Doc Al]

I suggest that you find the components using the angle each vector makes with your +x axis. Use east as your +x axis. Hint: Use the trig functions to get the magnitudes of the components, then add the correct signs.

 

[physics(L)10]

So you're saying I'm wrong?

 

[jegues]

I'm guessing to find the total force vector you would do 12(cos theta, sin theta) + 19(cos theta,sin theta). I'm just having trouble deciphering which degree to use.

Assign your x and y axes respectively, break the vectors down into component form, add them and compute your total force vector.

Find the magnitude of this vector.

If you want to find the direction let's remember the properties of a vector. A vector contains a magnitude and a direction, the answer for part c should be masked within the answer in part a.

 

[physics(L)10]

Ahhh I see, I think I got it. It should be 12(cos1,sin0) + 19 (cos315,sin315) ?

 

[jegues]

12(cos1,sin0)

This is wrong.

I think you're overcomplicating this... If you assigned your positive x and y axes to east and north respectively, without using the unit circle you can simply imagine what the components of your forces would look like.

The twelve Newtons is traveling in solely in the x directly so that force only has one component and that is 12N in the positive x direction.

The nineteen Newtons is traveling 45 degrees south, so down diagonally towards the bottom right.

Simply assign the angle of 45 degrees to each component and adjust the sign by intution... 19Sin45 gives a positive value, but we are going DOWN and to the RIGHT so we need a negative infront of that, Y component: -19sin45, and the X component: 19cos45, can you see why I didn't need to add a negative to that one?

 

[physics(L)10]

I'm thinking of the CAST system here to understand you and it worked. Can I use this in other cases too? So the answer would be then, 12 + 19(cos45,-sin45)?]

Edit: I used CAST because if you changed those values you still get .707 and -.707

 

[jegues]

CAST is something teachers throw to students for memorization of a simple coordinate system.

Don't memorize, understanding what you're actually doing is much more powerful.

 

[physics(L)10]

Yeah I kinda have a problem, I have to like memorize it to understand it lol. I'm right though right?

 

[jegues]

I'm right though right?

Don't worry about whether you're right or not, try and grasp what you're actually doing and you will know if you're right.