Coplanar system or Convergant forces?

[Kris_At_N]

Homework Statement

I cant find the exact answer.

Relevant Equations

##\sum_{x=i}^\infty x_i##
##\sum_{y=i}^\infty y_i##

The problem is that. Answer of reaction in the rods are as follow :
R1 = 19,3 kN
R2 = 19,3 kN
The image in the post shows the angles that are given in the task.

The equations that i get from my Free-body diagram are :
##\sum_{x=i}^\infty x_i## ; ## R1\cos45 - N2\cos30 - R2\cos15 = 0 ##
##\sum_{y=i}^\infty y_i## ; ## R1\sin45 + N2\sin30 + R2\sin15 - N1 = 0##

 

[Steve4Physics]

Hi @Kris_At_N. Welcome to PF.

Have you read the rules? If not take a look at https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

In particular, Rule 3 requires you to “Reproduce the problem statement accurately”. You haven't done this. You need to tell us the original problem exactly as set, word-for-word and with all diagrams.

There seems to be a lot of other missing information too, for example:

- there is no free-body diagram (though you refer to one);

- the 4 forces (##R_1, R_2, N_1## and ##N_2##) in your equations aren’t defined; what about the tension in the rope? forces should be marked on a free body diagram then it will probably be clear what each force is;

- how is each rod is attached to the wall on the left; is it by hinge?

- ‘G’ is shown in the diagram but no value is given.

Without all the information (even if you think some is not relevant) it is very difficult to provide help.

 

[berkeman]

In particular, Rule 3 requires you to “Reproduce the problem statement accurately”. You haven't done this. You need to tell us the original problem exactly as set, word-for-word and with all diagrams.

There seems to be a lot of other missing information too, for example:

- there is no free-body diagram (though you refer to one);

A bit more info -- This new user originally posted this thread start with an unreadable sideways image of his work and a PDF document with the problem statement in some Slavic language. We deleted that thread start and asked that they repost and type their math into the forum instead. So at least to their credit, in this repost of their thread they are trying to type some of their math into the forum, which is a step in the right direction.

Hopefully they return tomorrow and clarify things a bit, but in the mean time here are the PDF of the problem statement (sorry, I could not copy the text, so I could not use Google Translate) and a cleaned-up version of their handwritten work from the original thread start:

 

[Kris_At_N]

Moderater's note: threads with identical questions have been merged.

The problem is that. Answer of reaction in the rods are as follow :
R1(Reaction in 1) = 19,3 kN
R2(Reaction in 2) = 19,3 kN
The image in the post shows the angles that are given in the task.
Where N2 is reaction in the rope
Where N1 is G(Gravity)
The equations that i get from my Free-body diagram are :
##\sum_{i=0}^\infty x_i = 0## ; R1\cos45 - N2\cos30 - R2\cos15 = 0
##\sum_{i=0}^\infty y_i = 0## ; R1\sin45 +N2\sin30 +R2\sin15 - N1 = 0
I can't find the exact answer from the book.
The free body diagram is shown.

 

[Kris_At_N]

## R1\cos45 - N2\cos30 - R2\cos15 = 0 ##
## R1\sin45 +N2\sin30 +R2\sin15 - N1 = 0 ##

 

[haruspex]

## R1\cos45 - N2\cos30 - R2\cos15 = 0 ##
## R1\sin45 +N2\sin30 +R2\sin15 - N1 = 0 ##

Two of your trig functions are wrong.
There is also a sign error.

What is the (very simple) relationship between N1 and N2?

 

[Steve4Physics]

... but in the mean time here are the PDF of the problem statement (sorry, I could not copy the text, so I could not use Google Translate) ...

Out of curiosity I tried this:
1. Converted the pdf to jpg using https://www.freeconvert.com/pdf-to-jpg.
2. Translated the introductory text with Google Translate using the 'Images' option with the jpg file. (There is no other useful text in the document other than the introductory text.)

But Google didn't state the original language.

 

[Kris_At_N]

The language is russian. Yes that are the tasks for solving. I can't find the exact answer. Can someone to show the solution? I tried many times.

 

[Kris_At_N]

Two of your trig functions are wrong.
There is also a sign error.

What is the (very simple) relationship between N1 and N2?

I think that in this case N1=N2.

 

[Steve4Physics]

Hi @Kris_At_N.

I think this question is best solved using the idea of ‘concurrent forces’ (forces whose lines of action intersect at the same point).

##F_1## = compressive force in rod 1.
##F_2## = tensile force in rod 2.
It seems that you are required to find ##F_1## and ##F_2##.

Since G = 10kN, the tension in the rope is 10kN. By symmetry, the overall force, ##F_3##, due to the 2 sections of rope around the pulley, has magnitude ##2 \times 10 \cos(15^o) ~ kN##. And ##F_3## acts through point B, directed at ##15^o## to the vertical.

##F_1, F_2## and ##F_3## are balanced at point B. One way to proceed is to draw the force-triangle for these 3 concurrent forces and use the sine rule.

 

[Kris_At_N]

Hi @Kris_At_N.

I think this question is best solved using the idea of ‘concurrent forces’ (forces whose lines of action intersect at the same point).

##F_1## = compressive force in rod 1.
##F_2## = tensile force in rod 2.
It seems that you are required to find ##F_1## and ##F_2##.

Since G = 10kN, the tension in the rope is 10kN. By symmetry, the overall force, ##F_3##, due to the 2 sections of rope around the pulley, has magnitude ##2 \times 10 \cos(15^o) ~ kN##. And ##F_3## acts through point B, directed at ##15^o## to the vertical.

##F_1, F_2## and ##F_3## are balanced at point B. One way to proceed is to draw the force-triangle for these 3 concurrent forces and use the sine rule.

Thank you!

 

[Lnewqban]

It seems to be a symmetry problem.
If the line bisecting angle α is perpendicular to the line bisecting the angle formed between both tensions of the string (30°), the internal efforts of rods 1 and 2 must be equal (R1=R2) regardless the angles formed between the wall and each rod.

 

[Steve4Physics]

It seems to be a symmetry problem.
If the line bisecting angle α is perpendicular to the line bisecting the angle formed between both tensions of the string (30°), the internal efforts of rods 1 and 2 must be equal (R1=R2) regardless the angles formed between the wall and each rod.

In fact it's even more symmetrical than that - the 3 forces (as defined in Post #11) form an equilateral force triangle!

 

[haruspex]

I think that in this case N1=N2.

yes.
What about the other two points I raised?
To check whether you have the right trig function (cos or sin) it helps to consider a special case. What if that angle were 0 (or 90°)? Would the function I chose give the right result?