# Why use 0 degrees for one of two forces acting at an angle?

1. Feb 19, 2015

### Moose100

1. Two forces, 80N and 100N, acting at an angle of 60deg with each other, pull on an object. a) what single force would replace the two forces?

r^2=(x^2 + y^2)^2 , sinΘ, cosΘ

3. The attempt at a solution
I actually got the correct answer by using an angle of 0 degrees for 80N and 60 degrees for 100N finding the x and y sums and using the pythagorean theorem.

156N at 34°

I am the victim of a lucky guess. I have no idea why I was actually to use 0 degrees instead of another value. What is the definitive reason behind why it worked?

Last edited by a moderator: Feb 19, 2015
2. Feb 19, 2015

### HallsofIvy

Staff Emeritus
Because the difference between the values is all that is important. You could have use 20 degrees and 80 degrees instead and got the same answer (of course, the angle for the resultant force would be 34+ 20= 54 degrees). Essentially, what you did is set up a coordinate system where the "x- axis" was alog the 80 N force.

3. Feb 19, 2015

### Moose100

So how do you get 34 degrees?

4. Feb 20, 2015

### CWatters

Are you familiar with the head-to-tail method of adding vectors? Do the drawing and then it's basic trig to get the 34 degree angle.

5. Feb 20, 2015

### CWatters

PS: 26 degrees is also a valid answer.

You should specify which vector the angle is measured from. Eg The resultant is 34 degrees from the 80N vector or 26 degrees from the 100N vector.

6. Feb 20, 2015

### Moose100

Ahh thats right I was just thinking about that the answer does say 34 from the 80N vector. How do I KNOW that or find that out? Sorry.

7. Feb 21, 2015

### CWatters

As Hallsofivy said in post #2...

8. Feb 21, 2015

### Moose100

Ahhh so basically I didn't use the parallelogram method. Those figures are lifesavers.
Then you draw a new one with the resultant.

Last edited: Feb 21, 2015
9. Feb 21, 2015

### CWatters

Actually I used the same drawing. You can calculate R using Pythagoras or trig..

R*Cos(33.7) = 130
R = 130/Cos(33.7) = 156N

10. Feb 21, 2015

### Moose100

Ok. I was referring to those dotted lines. Also the fact that I always trip up when I don't draw the x an y sums.