Solving a Two-Dog Pulling Problem: Magnitude & Angle of Resultant Force

[spacecadette]

Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is 59.0 degrees. Dog A exerts a force of 254 N and dog B exerts a force of 328 N.


Find the magnitude of the resultant force.
Find the angle the resultant force makes with dog A's rope.


I'm having trouble picturing the diagram in order to solve this problem.
I tried adding the sum of the x components and the y components but I don't know whether to use sin or cos.

I set the equation up as:
Fx = 254N + 328cos59 = 422.9N

Fy = 328sin59 = 281.15

I have a feeling these aren't correct.

 

[Hannisch]

I'd do it the way you've done it. If I draw it I get the exact same expressions for the x- and y-components as you do.

 

[spacecadette]

"I'd do it the way you've done it. If I draw it I get the exact same expressions for the x- and y-components as you do."

It's not giving me the correct answer.

 

[Hannisch]

That is.. very weird.

Perhaps I'm looking at the problem in the wrong way or something. I really don't know.. What's your resultant force?

 

[spacecadette]

I was having trouble finding that as well.

 

[Hannisch]

Oh.. okay. If you have the components it's easy to find the resultant force knowing about superposition and simple geometry.

I'm not sure what to tell you, because according to me your components are correct at least. And I'm not 100% sure where exactly it is that you're stuck, too. (Probably I'm too tired for thinking, it's rather late.)

 

[Doc Al]

I set the equation up as:
Fx = 254N + 328cos59 = 422.9N

Fy = 328sin59 = 281.15

I have a feeling these aren't correct.

Looks good to me. Keep going.

 

[LowlyPion]

I agree. I thought the method of calculating it wasn't symmetrical.

I deleted my post.

 

[Doc Al]

I'll delete mine!

 

[spacecadette]

Now I'm really confused! =(
What do I do?

 

[spacecadette]

OK, so I figured out how to find the resultant force, but how do I find the angle it makes with dog A's rope?

 

[Doc Al]

You have the x and y components of the resultant. Use them to find the tangent of the angle, then the angle.

 

[spacecadette]

I used c^2 =a^2 + b^2 - 2abcostheta to solve for the resultant. How would I solve for the components? I was trying to before and I couldn't seem to get the correct answer.

 

[Doc Al]

I used c^2 =a^2 + b^2 - 2abcostheta to solve for the resultant. How would I solve for the components? I was trying to before and I couldn't seem to get the correct answer.

You found the components in your first post! The resultant is found using F² = F²x + F²y.

(No need for the law of cosines, since you already found the components. You'd use that law if you didn't want to find the components.)