Physics Tension: A sign is hanging from 3 ropes with tension T1=320.51N, @1=61.9*, @2=37.1*

[Amelinator]

So far, I've found the X and Y components of 61.9 deg. I'm not sure where to go from here to find tension 2.

 

[The Highlander]

View attachment 37194
So far, I've found the X and Y components of 61.9 deg. I'm not sure where to go from here to find tension 2.

Hi (again) @Amelinator,

You seem to be posting rather a lot of Physics questions in here. You do know this is a Maths forum, don't you? Maybe you would be better off posting your questions in a forum devoted to Physics itself?

I happen to have taught both Maths and Physics (at HS level) for thirty years and there are some others in here who have extensive expertise in Physics too but I'm beginning to be concerned that you're just getting us to do all your Physics homework for you!

Though this question does (again) seem to be from some kind of online test?
Are you doing only a (completely) online course in Physics?
Do you not have any face to face teaching time?

We can offer you assistance on the questions you post but there's no substitute for proper teaching of a subject. If there's something you don't understand or know how to tackle then you should really ask a teacher or tutor to explain it to you in detail rather than just getting us to guide you to the solution.
I'm afraid you may not get everything you really need to progress in the subject area from the assistance offered in a forum like this.

However, the problem you are having with this question is because you haven't done something that is very important with many, if not most, Physics problems involving forces!

In addition to your sketch of the problem (that I have replicated here because (IMNSHO) it is better supplied as a picture rather than the PDF file you uploaded)...

​

...you need to draw a Free Body Diagram (FBD) to 'enhance' your understanding of the situation and provide the necessary insight to solve the problem given.

Your drawing simply replicates the picture that the question already provided but the FBD analyses that situation and shows you how to proceed.

Here is a FBD of a similar situation to the one you have been given...

​

You know that the system is in equilibrium (ie: the sign is stationary) so all the forces must be in balance.

You have been able to calculate the forces acting in the x- & y- directions due to the tension in the left rope but, since the forces in the x- & y- directions must balance then the force in the x-direction due to the right rope must be equal (and opposite) to that produced by the left rope.

Now you know the force in the x-direction due to the right rope, you can calculate the tension in that rope and, thence, the force in the y-direction due to that rope's tension.

Thus you now know all the upward (y-direction) forces acting on the sign and can therefore calculate its mass assuming whatever value you've been told to use for the gravitational field strength (usually 9.81 ms^-2 or 10 ms^-2).

Please now draw your own FBD and calculate the required answers then come back and show us a picture of your work.
Please don't just come back and say you put the right answers in online and they were marked correct (at your eighth attempt!).

Hope that helps.

 

[Amelinator]

Hi (again) @Amelinator,

You seem to be posting rather a lot of Physics questions in here. You do know this is a Maths forum, don't you? Maybe you would be better off posting your questions in a forum devoted to Physics itself?

I happen to have taught both Maths and Physics (at HS level) for thirty years and there are some others in here who have extensive expertise in Physics too but I'm beginning to be concerned that you're just getting us to do all your Physics homework for you!

Though this question does (again) seem to be from some kind of online test?
Are you doing only a (completely) online course in Physics?
Do you not have any face to face teaching time?

We can offer you assistance on the questions you post but there's no substitute for proper teaching of a subject. If there's something you don't understand or know how to tackle then you should really ask a teacher or tutor to explain it to you in detail rather than just getting us to guide you to the solution.
I'm afraid you may not get everything you really need to progress in the subject area from the assistance offered in a forum like this.

However, the problem you are having with this question is because you haven't done something that is very important with many, if not most, Physics problems involving forces!

In addition to your sketch of the problem (that I have replicated here because (IMNSHO) it is better supplied as a picture rather than the PDF file you uploaded)...

View attachment 37196​

...you need to draw a Free Body Diagram (FBD) to 'enhance' your understanding of the situation and provide the necessary insight to solve the problem given.

Your drawing simply replicates the picture that the question already provided but the FBD analyses that situation and shows you how to proceed.

Here is a FBD of a similar situation to the one you have been given...

View attachment 37197​

You know that the system is in equilibrium (ie: the sign is stationary) so all the forces must be in balance.

You have been able to calculate the forces acting in the x- & y- directions due to the tension in the left rope but, since the forces in the x- & y- directions must balance then the force in the x-direction due to the right rope must be equal (and opposite) to that produced by the left rope.

Now you know the force in the x-direction due to the right rope, you can calculate the tension in that rope and, thence, the force in the y-direction due to that rope's tension.

Thus you now know all the upward (y-direction) forces acting on the sign and can therefore calculate its mass assuming whatever value you've been told to use for the gravitational field strength (usually 9.81 ms^-2 or 10 ms^-2).

Please now draw your own FBD and calculate the required answers then come back and show us a picture of your work.
Please don't just come back and say you put the right answers in online and they were marked correct (at your eighth attempt!).

Hope that helps.

Sadly, my physics class is completely online and emailing the professor and asking for help doesn't really help, as he just restates the question. I have been asking about the homework questions that I'm not sure how to do, not asking for solutions for tests. I will come back with my FBD shortly!

 

[Amelinator]

Hi (again) @Amelinator,

You seem to be posting rather a lot of Physics questions in here. You do know this is a Maths forum, don't you? Maybe you would be better off posting your questions in a forum devoted to Physics itself?

I happen to have taught both Maths and Physics (at HS level) for thirty years and there are some others in here who have extensive expertise in Physics too but I'm beginning to be concerned that you're just getting us to do all your Physics homework for you!

Though this question does (again) seem to be from some kind of online test?
Are you doing only a (completely) online course in Physics?
Do you not have any face to face teaching time?

We can offer you assistance on the questions you post but there's no substitute for proper teaching of a subject. If there's something you don't understand or know how to tackle then you should really ask a teacher or tutor to explain it to you in detail rather than just getting us to guide you to the solution.
I'm afraid you may not get everything you really need to progress in the subject area from the assistance offered in a forum like this.

However, the problem you are having with this question is because you haven't done something that is very important with many, if not most, Physics problems involving forces!

In addition to your sketch of the problem (that I have replicated here because (IMNSHO) it is better supplied as a picture rather than the PDF file you uploaded)...

View attachment 37196​

...you need to draw a Free Body Diagram (FBD) to 'enhance' your understanding of the situation and provide the necessary insight to solve the problem given.

Your drawing simply replicates the picture that the question already provided but the FBD analyses that situation and shows you how to proceed.

Here is a FBD of a similar situation to the one you have been given...

View attachment 37197​

You know that the system is in equilibrium (ie: the sign is stationary) so all the forces must be in balance.

You have been able to calculate the forces acting in the x- & y- directions due to the tension in the left rope but, since the forces in the x- & y- directions must balance then the force in the x-direction due to the right rope must be equal (and opposite) to that produced by the left rope.

Now you know the force in the x-direction due to the right rope, you can calculate the tension in that rope and, thence, the force in the y-direction due to that rope's tension.

Thus you now know all the upward (y-direction) forces acting on the sign and can therefore calculate its mass assuming whatever value you've been told to use for the gravitational field strength (usually 9.81 ms^-2 or 10 ms^-2).

Please now draw your own FBD and calculate the required answers then come back and show us a picture of your work.
Please don't just come back and say you put the right answers in online and they were marked correct (at your eighth attempt!).

Hope that helps.

Ok, so I've drawn my FBD. I can see what to do for the next steps! The next thing I will do is use the Fnet=ma equation for the x component of T2.

Again, I'm sorry that I am seeking advice on this forum, as I just thought physics was applied math. I will relocate to a different forum, as my content area is not meant to be posted here.

 

[Amelinator]

Ok, so I've drawn my FBD. I can see what to do for the next steps! The next thing I will do is use the Fnet=ma equation for the x component of T2.

Again, I'm sorry that I am seeking advice on this forum, as I just thought physics was applied math. I will relocate to a different forum, as my content area is not meant to be posted here.

Is this correct? T2= 189.3 N

 

[blamocur]

Is this correct? T2= 189.3 N

Looks correct to me.

Your first drawing is slightly misleading because the 61.9 degrees angle looks smaller than 45 degrees.

 

[The Highlander]

I'm sorry that I am seeking advice on this forum, as I just thought physics was applied math. I will relocate to a different forum, as my content area is not meant to be posted here.

Please don't think that I am trying to chase you away! You are welcome to post your problems in this forum and there is always likely to be someone with the Physics expertise around to address your queries.
And, as you say, Physics is, indeed, largely (though not all) 'Applied Mathematics', so even if there are no Physics 'experts' about one of the other helpers is bound to be able to offer advice on how to approach any numerical problems you have.

Ok, so I've drawn my FBD. I can see what to do for the next steps! The next thing I will do is use the Fnet=ma equation for the x component of T2.

I am fairly sure that what I've highlighted above (in red) was just a 'slip of the pen' and you meant to write that F = ma would be used to get the mass of the sign.

However, I'm afraid your "FBD" is far from acceptable. I gave you an example of how a FBD ought to look earlier; it should show all the forces in the system and (ideally) in their (approximately) correct orientation and with lengths (roughly, at least) representative of their magnitude. You could almost have just copied the example I gave you for this problem but yours doesn't really do any of those things.


Here is my FBD of the situation described in you question... (→)

Note how all the forces extant are shown (including those that are the x- & y- components of the tensions in the ropes) and I've drawn T₁ and T₂ in the right directions and with appropriate lengths.

The easiest way to do that is to start with x- & y- axes and draw a line (at the correct angle) for T₁. You can then draw its x- & y- components (using a pencilled-in rectangle enclosing the line or even just 'by eye').

Next you would draw T_2x the same length as T_1x but in the opposite direction (ie: to the right), then a vertical pencil line at the end of T_2x will allow you to draw T₂ at the correct angle, and, finally T_2y at the same 'height' as T₂.

You then just make T₃ the same length as the lengths of T_1y and T_2y added together but in the downward direction.


Basically you are just going through the same steps as you would when making your calculations. Once you have successfully constructed your FBD (with an accuracy at least approaching mine), you are then ready to write out your calculations to get the answers that the question requires of you.

Is this correct? T2= 189.3 N

Your final answer there is correct (as rounded to 1 decimal place) though I get a different answer (from the "189.27N" in your picture) due to a rounding error you have made at some intermediate stage. You should only ever round your results at a final answer; the more you use values that you have rounded in subsequent calculations, the greater the final error will be at the end! Modern calculators allow you to store intermediate results such that, with a bit of judicious sequencing, you don't have to round anything until you reach a final answer (in most situations).

@blamocur also made a valid point about your first sketch being slightly misrepresentative of the situation (because your angles were 'off'), however, (personally) I would accept that drawing because it is (just) a sketch and you have labelled the angle as being "61.9" (though it should have been 61.9°!) even though it looked more like a 45° angle!

Again, it's quite important (in the Physics department) to make even sketches provide a fair representation of conditions and omission of units is, of course, a Cardinal Sin in Physics!

I'm a little disappointed that you haven't come back and shown us your final working and answer(s). We always like to see people come back with their final results because that's how we know that our advice or help has been understood and applied which, in turn, makes us more willing to help those individuals in future. (If an OP can't be bothered to work problem through to the end and show us their efforts, then why should we go to the bother of helping them any further?)

I am fairly confident that you did manage to get the right answers to your problem (or, no doubt, you would have been back asking us why your submissions weren't being accepted by the online system you're using) so I will just go ahead and present the correct working below for the sake of completeness and closure of the thread...

​

Hope that helps.

 

[The Highlander]

NB: I should, of course, have written g as 9.81 ms^-2 but didn't notice this (small) error until after the post was submitted so please just assume that g was meant to be 9.81 ms^-2 and not 9.81 ms (as shown).

I know I rant about including appropriate units in all Physics work but fixing the gif would have involved changing every still that the error appeared in (all 25 of them!) and that would not have been possible to do before the time limit for editing the Post ran out.

There is also a (red) closing bracket missing in the final frames but that 's not as big a worry as the mistake explained above.