Physics - Force and Interactions

[dummy123]

Hello again,

the problem is this:
"Two dogs pull horizontally on ropes attaches to a post; the angle between the ropes is 60.0 degrees. If dog A exerts a force of 270 N and dog B exerts a force of 300 N, find the magnitude of the resultant force and the angle it makes with dog A's rope."

I can't really visualize what this is saying. I tried this like this: the post is at the origin O, one going straight right horizontal, the other going slightly above it, making a 60 degree separation (a right-angled triangle)
then, I calculate
270 sin 60 = 234 N
300 tan 60 = 468 N

I use arcsin 234/468
= 30 degrees

and the resultant force R = sqrt ( 523^2 + 468^2)
= 523 N.

The answer in the back is
31.7 degrees and 494 N.

I think my problem is in the diagram I'm making. I just can't figure out how to draw this. It obviously can't be a right-angled triangle if 60+31 = 91 degrees.

AHhhh help

 

[dummy123]

I did it a second time. This time I separated each force into its vector components:
(still working this like a right-angled triangle)

Ax = 270 cos 60 = 135 N
Ay = 270 sin 60 = 234 N

Bx = 300 cos 0 = 300 N
By = 300 sin 0 = 0N

Rx = Ax + Bx = 435 N
Ry = 234 N

R = sqrt (Rx^2 + Ry^2)
= sqrt ( 435^2 + 234 ^2)
= 494N
And that is the answer in the back of the book

BUT

when I do arctan Ry/Rx
= arctan 234/435
I get 28 degrees.
The answer is 31.7 degrees.

 

[skeeter]

let rope A be aligned with the x-axis

$$R_x = 270 + 300 \cos(60)$$
$$R_y = 300 \sin(60)$$

 

[dummy123]

let rope A be aligned with the x-axis

$$R_x = 270 + 300 \cos(60)$$
$$R_y = 300 \sin(60)$$

I thought I was. Apparently I am not as familiar with them as I believed.

 

[skeeter]

I thought I was. Apparently I am not as familiar with them as I believed.

a sketch always helps

 

[dummy123]

a sketch always helps

Yup. I sketched.
And that's how I got to the answer I came to.

What's the sketch that I SHOULD have made?

 

[skeeter]

 

[Deleted member 4993]

Yup. I sketched.
And that's how I got to the answer I came to.

What's the sketch that I SHOULD have made?

Force Resultant Diagram as shown above.

 

[jaimerguiza]

Hello,

Why should I let rope A be in the x-axis, and not rope B?

Thanks

 

[Deleted member 4993]

Hello,

Why should I let rope A be in the x-axis, and not rope B?

Thanks

Okay, please show us your calculations - including a diagram - for that situation (where rope B is along the X-axis).....................edited

 

[Dr.Peterson]

Why should I let rope A be in the x-axis, and not rope B?

In general, when you want to know "Why should I do this rather than that?", the thing to do is to try doing "that" and see what you learn. You may learn that it makes no difference, and is just an arbitrary choice; or you may learn why you were taught to do "this". Either way, you will have learned something far more effectively than just being told.

In this case, it will probably be the latter; since what you are to find is related to A, setting up a system that will most naturally yield that angle makes sense. But the other way probably won't be much harder.

 

[skeeter]

Hello,

Why should I let rope A be in the x-axis, and not rope B?

Thanks

The problem asks for the magnitude & direction of the resultant force relative to rope A … aligning rope A with the x-axis makes that task easier to calculate.