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

[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

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?

 

[HallsofIvy]

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.

 

[Moose100]

So how do you get 34 degrees?

 

[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.

 

[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.

 

[Moose100]

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.

Ahh that's 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.

 

[CWatters]

Ahh that's 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.

As Hallsofivy said in post #2...

Essentially, what you did is set up a coordinate system where the "x- axis" was along the 80 N force.

I did that more explicitly when I checked your answer... I made this drawing...

 

[Moose100]

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

 

[CWatters]

Then you draw a new one with the resultant.

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

 

[Moose100]

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

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.