# Homework Help: Three rescuers pulling horizontally on a safety net to keep it taut

1. Feb 21, 2013

### 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 dont know how to solve for the force but I have an angle of 37 degrees.
as a model but I do not know where they get the numbers like -120 N and -150 N.

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2. Feb 21, 2013

### haruspex

Re: Three rescuers pulling horizontally on a safety net to keep it tau

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?

3. Feb 21, 2013

### Sneakatone

Re: Three rescuers pulling horizontally on a safety net to keep it tau

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

4. Feb 21, 2013

### haruspex

Re: Three rescuers pulling horizontally on a safety net to keep it tau

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?

5. Feb 21, 2013

### Sneakatone

Re: Three rescuers pulling horizontally on a safety net to keep it tau

I do not

6. Feb 21, 2013

### haruspex

Re: Three rescuers pulling horizontally on a safety net to keep it tau

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

Last edited: Feb 21, 2013
7. Feb 21, 2013

### Sneakatone

Re: Three rescuers pulling horizontally on a safety net to keep it tau

this is how I see it, its probaly not right

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8. Feb 21, 2013

### Sneakatone

Re: Three rescuers pulling horizontally on a safety net to keep it tau

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

9. Feb 21, 2013

### Sneakatone

Re: Three rescuers pulling horizontally on a safety net to keep it tau

I tried using angle ratios like (31/37)295 with all the combinations but I dont know if that s right either.

10. Feb 21, 2013

### haruspex

Re: Three rescuers pulling horizontally on a safety net to keep it tau

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 RN, say.
- add up all the due E components for a due E result to get RE, say.
- the magnitude of the resultant force is √(RN2+RE2); its direction is atan(RN/RE). 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.

11. Feb 21, 2013

### Sneakatone

Re: Three rescuers pulling horizontally on a safety net to keep it tau

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

12. Feb 21, 2013

### haruspex

Re: Three rescuers pulling horizontally on a safety net to keep it tau

I used "RN" 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?

13. Feb 21, 2013

### Sneakatone

Re: Three rescuers pulling horizontally on a safety net to keep it tau

the angle going E would 37 or unknown.

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

14. Feb 21, 2013

### Sneakatone

Re: Three rescuers pulling horizontally on a safety net to keep it tau

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

15. Feb 21, 2013

### haruspex

Re: Three rescuers pulling horizontally on a safety net to keep it tau

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

16. Feb 22, 2013

### Sneakatone

Re: Three rescuers pulling horizontally on a safety net to keep it tau

250cos(31)=214.29

17. Feb 22, 2013

### haruspex

Re: Three rescuers pulling horizontally on a safety net to keep it tau

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

18. Feb 22, 2013

### Sneakatone

Re: Three rescuers pulling horizontally on a safety net to keep it tau

It is answering the E component.

19. Feb 22, 2013

### haruspex

Re: Three rescuers pulling horizontally on a safety net to keep it tau

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.

20. Feb 22, 2013

### Sneakatone

Re: Three rescuers pulling horizontally on a safety net to keep it tau

1. south east
2. component meaning 31 degrees?

21. Feb 22, 2013

### haruspex

Re: Three rescuers pulling horizontally on a safety net to keep it tau

"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.

22. Feb 22, 2013

### Sneakatone

Re: Three rescuers pulling horizontally on a safety net to keep it tau

would it be 149 degrees going east?

23. Feb 22, 2013

### haruspex

Re: Three rescuers pulling horizontally on a safety net to keep it tau

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?