Finding Resultant Vector: A=220g@0°, B=100g@110°, C=160g@260° | Homework Help

[faunalove22]

Homework Statement

We are given three components: Component A has a magnitude of 220g at 0 degrees, Component B has a magnitude of 100g at 110 degrees, and Component C has a magnitude of 160g at 260 degrees.

We are supposed to find the resultant vector. HELP! :)

Homework Equations

The Attempt at a Solution

So I started off by drawing a free body diagram with all the components. For Component B I made a right triange using the vertical Y access. For Component C I also made a right triangle using the vertical access.

Am I doing this correctly, or should I be using the horizontal access to make the right triangle? Does this even matter? I keep getting different answers. I am very confused. Any help to solve would be great!

 

[rock.freak667]

The Attempt at a Solution

So I started off by drawing a free body diagram with all the components. For Component B I made a right triange using the vertical Y access. For Component C I also made a right triangle using the vertical access.

I think you meant to type 'axis'.

but yes, you need to split each vector into horizontal and vertical components (remember to take direction into account, e.g. all vectors point left are negative)

Find the resultant horizontal and vertical vectors. Post your work if you can.

 

[faunalove22]

Thats a bit emarrasing, yes axis. That will remind me to proof read :? .

So in my drawing, I have a free body diagram that includes the three forces. I created right triangles with the two forces that both have x and y components.

F1= 220g, 0 degrees
F2= 100g, 110 degrees
F3= 160g, 260 degrees

So, I sum the forces in the x direction:

NetForce_x= F1-F2cos110degrees-F3cos80degrees
= 220-100cos110degrees-160cos80degrees === 226

Then I sum the forces in the y direction:

NetForce_y= F2sin110degrees-160sin80degrees === -64

Then:
226²-64²=46980 ==> Then take the square root which equals 217 g.

To get the angle I take the inverse tangent and divide the net force of y by the net force of x = -16

So my answer is 217g at -16 degrees

I don't think this is the right answer. ?

 

[vela]

Recheck your calculation for the x-component. Your method is correct, but your numerical answer doesn't match what I get.

EDIT:

Oh, I see your mistake. You subtracted 100 cos (110 degrees). If you use the full angle, you always add, so you should have either +100 cos (110 degrees) or -100 cos(70 degrees) (if you draw the right triangle relative to the x-axis).

 

[faunalove22]

Thank you!