Equilibrium In Two Dimensions Help

[Evie]

Hi, I have been trying to attempt this problem for quite some time and I would be very gracious if anyone could help me out.

A clothes-line is attached to two fixed ends which are 10.0m apart. A pully of mass 40.0 kg hangs freely in the middle of the line. The sag at the centre is .20 m. Find the tension in each half of the clothes line.

Marking is as follows (I figure it might give a guidline as of what I need to do)

-1 mark for steps 1 and 2
Step 1: Select the object to be studied
(This is the pulley)
Step 2: Draw a free body diagram
(I have no problem doing this although I cannot do it on the computer)
Step 3: Choose a set of x and y axes for each of the objects being analyzed and resolve the free body diagram into components that point along these axes
*This is where I get into trouble*
Step 4: Set up the equations in such a way that the sum of the x components of the forces is zero, and the sum of the y components is also equal to zero.
(I know where the x and y components are and such but I am having difficulty making an equation and solving it because there is no angle written or told of and I have no idea how to solve for it otherwise.
Step 5: Solve the equations for the unknown quantities you are looking for.
(I really have no idea how to do this without knowing the previous 2 steps)

I hope someone knows how to do this cause I am really stumped. Anyways could you also explain how to show magnitude and distance with this type of problem? I have looked this up on the internet and I was thinking of renting a grade 12 40S textbook from my local library. By the way this is a grade 12 level physics course.
Thank you.

 

[Pyrrhus]

This is a classic problem. In order to obtain the angles, you have to notice you have a triangle with base 10m and height 0.2 m, with some trigonometry you should be able to obtain the angles. You should be able to form the equations from your FBD.

 

[Evie]

See, that is where I come into trouble.. I am very bad at math and have like tried to do this question over and over again for about 5 hours now. That is what I thought but the rope isn't 20 metres long it is 10 metres long.. I understand how to get Fg.. (The third tension force) But the other two I can't get at all..
Fg=mg
Fg=(40.0)(-9.8)
Fg=-392
I got the equations set up and then I came to some real difficulties.
For the x components:
-T1cos Pheta + T2cosPheta = 0
For the y components
T2cos Pheta + T1cos Pheta - Fg = 0
(Note: T1 and T2 are labels for both sides of the clothes line)
From here I am confused about how to do the geometry and work out the equation because the math part is really confusing me

 

[Pyrrhus]

What i was saying is that if you draw a straight line connecting both supports, and then draw straight lines from each support to the pulley, and finally draw a straight line from the pulley to the line (it should be perpendicular to this line) connecting the supports, you'll see your triangle.

 

[Evie]

The total length of the clothes line is 10 metres... You said earlier in another post something about 20 metres. I get what you mean about the triangles and i know how to do that. But I am confused about how to get the angle.. and then once i have the angle i am unsure of how to solve for the forces... It is mostly because I do not understand the math.

 

[Pyrrhus]

The total length of the clothes line is 10 metres... You said earlier in another post something about 20 metres. I get what you mean about the triangles and i know how to do that. But I am confused about how to get the angle.. and then once i have the angle i am unsure of how to solve for the forces... It is mostly because I do not understand the math.

Remember the trigonometric relation tangent, look it up.

Yea about the 20 meters, i meant 10, base 10 meters and height 0.2 meters. Fixed it in my other replies.

 

[andrevdh]

A right angle triangle is formed by going from one of the fixed ends to the point where the pulley is hanging. Then up to halfway between the two fixed ends. Then back to the starting point - the fixed end where you started. The base and perpendicular of this right angled triangle is known from the trigonometry. Can you calculate the angle of the triangle next to the point where the pulley is?