Calculating Tension in a Spider's Web: A Simple Forces Problem

[Heres2hoping]

Homework Statement

A spider builds a web using 4 strands as support.
Strand 1: 21mN [20°E of N]
Strand 2: 16mN [60°E of S]
Strand 3: 18mN [40°W of S]

Determine the force of tension in strand 4 assuming the web is stable.

Homework Equations

r(cosθ) - N/S components
r(sinθ) - E/W components
The pythagoren theorem might be of use along with equations used in simple trig.

The Attempt at a Solution

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North-South components:
Strand 1: 19.7mN [N]
Strand 2: 8mN
Strand 3: 13.7mN

East-West components:
Strand 1: 7.1mN [E]
Strand 2: 13.9mN [E]
Strand 3: 11.6mN [W]

Other than that I've determined that the direction will be in the North-West segment. I'm just having issues determining the total force acted by the 3 given strands. Any pointers would be much appreciated. :)

 

[Heres2hoping]

Strand 2 is 8mN
Strand 3 is 13.7mN

( I'd forgotten the direction )

 

[azizlwl]

Draw a vector diagram.

 

[Heres2hoping]

Draw a vector diagram.

Ok, I'll do that.
But what formula should I use if I wanted to determine the total force and to what degree?

 

[azizlwl]

From there we can get rough idea about magnitude and direction of required force AND we can make calculation base on the drawing.

 

[Heres2hoping]

From there we can get rough idea about magnitude and direction of required force AND we can make calculation base on the drawing.

So, I can assume that the answer is going to be in the north-west segment, right?

 

[azizlwl]

I hope you can show the vector drawing so that we can analyze it.

 

[Heres2hoping]

I hope you can show the vector drawing so that we can analyze it.

I'm not sure how to... Sorry

 

[Heres2hoping]

I'm not sure how to... Sorry

I got it! I think...

 

[azizlwl]

For a stable web, the forces are in equilibrium means total sum of forces equal to zero. A+B+C+D=0
Given vector A,B and C, so you need to find vector D.
So how to add graphicall?
What you have to do is to join(add) the vectors(arrows)
Vector can be moved anywhere as long you do Not rotate or modify size.
So you have to draw another vector diagram with head join to another vector tail.

 

[Heres2hoping]

For a stable web, the forces are in equilibrium means total sum of forces equal to zero. A+B+C+D=0
Given vector A,B and C, so you need to find vector D.
So how to add graphicall?
What you have to do is to join(add) the vectors(arrows)
Vector can be moved anywhere as long you do Not rotate or modify size.
So you have to draw another vector diagram with head join to another vector tail.

do you mean for each individual strand to become its own little triangle (in a sense)? Or more of one big one?

 

[azizlwl]

There are 3 arrows, you label any sequenece as you like as A,B and C.Move B, without size adjustments and rotation, so that tail of B touches head of A. Then move C so that tail of C touches head of B on new position(after adding to A)

 

[Heres2hoping]

There are 3 arrows, you label any sequenece as you like as A,B and C.Move B, without size adjustments and rotation, so that tail of B touches head of A. Then move C so that tail of C touches head of B on new position(after adding to A)

Oh my goodness! It makes so much more sense! Thank you so much! I'm going to go try that out

 

[Heres2hoping]

Oh my goodness! It makes so much more sense! Thank you so much! I'm going to go try that out

Ok, so where do I go from there? I don't have the angles of the new triangle, so do I need to figure them out?

 

[azizlwl]

Hope you can show the vectors addition diagram.
Then we can discuss adding vectors algebraically.

 

[Heres2hoping]

Ok, so where do I go from there? I don't have the angles of the new triangle, so do I need to figure them out?

Actually, I think I'll try to figure out the rest tomorrow. I understand the problem more than I had, so thank you for your time :)

 

[Heres2hoping]

Hope you can show the vectors addition diagram.
Then we can discuss adding vectors algebraically.

im having problems ioading the picture, so maybe I'll try again tomorrow (it's really late for me)thank you for you help :)