Three rescuers pulling horizontally on a safety net to keep it taut

[Sneakatone]

Three rescuers are pulling horizontally on a safety net to keep it taut. One pulls northward with a force of 295n; the second pulls in a direction 31 degrees south of west wit ha force of 250N. In which direction and with what force must the third pull to keep the net stationary?

I don't know how to solve for the force but I have an angle of 37 degrees.
I tried to use http://answers.yahoo.com/question/index?qid=20100208080145AAFCZ4V
as a model but I do not know where they get the numbers like -120 N and -150 N.

 

[haruspex]

37 degrees which way from what compass direction? Pls post your working.
In the example, they take the given forces, as vectors, and resolve them into components in the NS and EW directions. Do you know how to do that?

 

[Sneakatone]

37 degrees south of east. there wasn't really a real strategy to it I just added 6 to 31 to get 37.

 

[haruspex]

37 degrees south of east. there wasn't really a real strategy to it I just added 6 to 31 to get 37.

I won't ask where the 6 came from.
Do you know how to resolve forces into orthogonal components, and use those in statics equations?

 

[Sneakatone]

I do not

 

[haruspex]

I do not

Then I don't understand how you are expected to solve a question like this. Have you not been taught anything related?
OK, so given a force F magnitude F at angle θ north of east (I choose that reference because anticlockwise from the positive x-axis is a standard way of specifying directions in maths), you can 'resolve' it into two forces. There are any number of choices for the directions in which to resolve it, but standard would be N and E. The component in the E direction has magnitude F cos θ, and that due n has magnitude F sin θ.
If everything is in equilibrium (i.e. no acceleration), the sum of components of forces in the EW direction is 0. Similarly in the NS direction.
So:
- create unknowns for the magnitude and direction for the third force
- resolve each of the three forces into NS and EW components
- write out the statics equation for each of NS, EW

 

[Sneakatone]

this is how I see it, its probably not right

 

[Sneakatone]

would equations like t=w/sin(theta) be relavent?

 

[Sneakatone]

I tried using angle ratios like (31/37)295 with all the combinations but I don't know if that s right either.

 

[haruspex]

this is how I see it, its probably not right

In the drawing, you've written 25N instead of 250N for the second force.
You don't make it clear which angle is 31 degrees. You've no basis for marking any angle as being 37 degrees.
This is how you resolve a force (or one way, at least):
- find the angle, θ, the force makes to due East, measured anticlockwise. For a force due N, that's 90 degrees, due W 180 degrees, etc. Depending onwhat you use to calculate sines and cosines, you may need to convert to radians.
- if the force has magnitude F, it resolves into F*cos(θ) due E and F*sin(θ) due N. Be careful with signs here.
When you've done that:
- add up all the due N components for a due N result to get R_N, say.
- add up all the due E components for a due E result to get R_E, say.
- the magnitude of the resultant force is √(R_N²+R_E²); its direction is atan(R_N/R_E). You may need to convert the angle back from radians to degrees. Taking an arctan cannot distinguish directions that differ by 180 degrees, so you'll need to think about which of the two answers it is.

 

[Sneakatone]

for RN I did 250cos(31) and had 214 but how do you get RE without and angle?

 

[haruspex]

for RN I did 250cos(31) and had 214 but how do you get RE without and angle?

I used "R_N" to refer to the total for the N components of all three forces.
For the 250N force, the direction is 31 degrees S of W. What angle is that measuring anticlockwise from due E?
I said to take the sine of the angle for the N component, the cosine for the E component.
So what are the N and E components of the 250N force?

 

[Sneakatone]

the angle going E would 37 or unknown.

the components for 250, N=295 N , E=unknown

 

[Sneakatone]

295sin(90)=295
250sin(31)=128

 

[haruspex]

295sin(90)=295

That's the N component of the 295. What's the E component?

250sin(31)=128

I said to measure all angles anticlockwise from due E. The 31 degrees is given as S of W. What is that anticlockwise from E?
Again, you need two components from it, the cosine for the E component and the sine for the N component.

 

[Sneakatone]

250cos(31)=214.29

 

[haruspex]

250cos(31)=214.29

That is undeniably true, but which question is it answering?

 

[Sneakatone]

It is answering the E component.

 

[haruspex]

It will help speed things up if you answer each question in sequence. Try at least the first two now, and we can progress to the others later. But please do not skip any.
1. What is the direction of the 250N force, measured as an angle anticlockwise from due E?
2. What, therefore, is the Eastward component of the 250N force? Be careful with the sign.
2. What is the E component of the 295N force?
3. What is the sum of the E components?
4. What is the E component of the force the third rescuer needs to provide?

5. What is the N component of the 250N force?
6. What is the N component of the 295N force?
7. What is the sum of the N components?
8. What is the N component of the force the third rescuer needs to provide?

9. What is the magnitude of the force the third rescuer needs to provide?
10. What is the direction, as an angle anticlockwise from due E, of the force the third rescuer needs to provide? You'll need to be careful with this one.

 

[Sneakatone]

1. south east
2. component meaning 31 degrees?

 

[haruspex]

1. south east
2. component meaning 31 degrees?

"south east" is not an angle. The answer is some number of degrees, and it's not 31. The force is at an angle 31 degrees anticlockwise from W, so how many degrees is it anticlockwise from E?
A component of a force is a force, not an angle. If a force has magnitude F and acts at an angle θ anticlockwise from E then it has a component force magnitude F cos θ due E and a component F sin θ due N.
Given that, please try those two again.

 

[Sneakatone]

would it be 149 degrees going east?

 

[haruspex]

would it be 149 degrees going east?

No. Have you drawn yourself a picture? With E to the right and W to the left, 31 degrees S of W will be down and to the left, yes?, 31 degrees 'below' due W. So, starting due E and running around anticlockwise, how many degrees do you go through to reach 31 degrees S of W?