in this problem we'll talk about hanging traffic light physics what is that so let's say we have a traffic light here and the traffic light is supported by three cables three ropes and we know the angle like this is 25 degree and this is 40 degree and now the maximum the support the any cable can provide is 450 Newton does the maximal the support it can provide and the mass of the traffic light is 40 kilogram now the question is all these cables will be able to support the traffic light or in other words we need to find out what is the tension in each table let's do that so first thing while you solving this problem is to draw the Freebody diagram so what I'm going to do here I'm going to draw the Freebody diagram for this hanging traffic light so here I have the traffic light the weight the weight on the traffic light is always downward so which is given by M G that's the weight all right and the tension in the cable is upward there's the tension that is supporting the the traffic light and these two the weight and this tension are equal and opposite and we'll write down the equation later on so this is the free body diagram for the hanging the traffic light but now he had now indeed we're going to again draw the free body diagram at this point here so the tension here if I just take this point here the tension is the downward at this point the total weight is the mg which is acting downward or we can also say the 1073 if I just look at this weight this cable is upward but at the same time if you look at the ceilings here this table sees also pulling the downward okay so that's the reason we have chosen here the attention t3 is acting downward and the t2 here is a four here in this direction not perfectly upward but at an angle so at this point the tense of t3 is downward the t2 is a after 40 degree and this is a 35 degree as this angle is 40 degree this angle is also 40 degree just because of the in vertically opposite angles and this angle and this angle should also be equal no it is 35 degree and the most of you should be familiar at this point about the resolving a vector into two components or into rectangular components so first thing you have to do it is a resolve this tension t2 in two components the one along the x axis so along the x axis is it has to be t2 cosine 40 degree now you might say how come this is cosine at how do I know that it is a cosine or sine so the simplest way just to look at it close it to the angle closely just remember C and C closer to the angle is cosine so this angle is 40 degree which is the angle so it has to be cosine okay so the cosine component is closer to the angle and this component will be the sine component the same thing t2 or sine of 40 degree here and this way it is t2 sine 40 degree so we'd have resolved t2 now the same thing exactly do the same thing stop the video and write down your own equation now how do you write down the equation this is the t1 and think about this one what this has to be it has to be cosign the reason is this is closer to the angle and this component which is shown where the green is t2 sine 35 degree so we have now a complete picture of the Freebody diagram we know now the direction of all the forces and this is the the total Freebody diagram here and we do not need at this point okay so just just to make you clear you see now at this point that the total weight is downward energy so when I write down this equation here so it's a pretty simple this is the traffic light is not moving here that is incomplete a static equilibrium what does it mean that mean all the total forces has to be equal or in other words the total forces along the x axis has to be equal equal and the total force along the y axis has to be equal or equal and opposite in other words are the total forces along the x axis has to be equal to zero and the total forces along the y axis has to be equal to zero so at this point this force the energy and the 10:33 has to be equal or opposite because these two are in opposite so the magnitude has to be equal so I've written down the equation T 3 is equal to M times Z the mass is given for T and G is 9.8 if you multiply them together you'll get 392 Newton the unit for the tension is the Newton and now the question is how do I write down the equation for this Freebody diagram the first thing you have to look at is the horizontal component or the X component write down the equation along the X component along the X component you have two forces the first force is t2 or sine 40 degree and the other force is t1 or sine 35 degree these two forces and remember these two forces are opposite and the system is not moving at all or the system does not have any acceleration that means this force and this force has to be equal that's exactly what I have eaten here t1 cosine 35 degree is exactly equal to t2 cosine 40 degree and if I solve for t1 what you get is t2 cosine 40 degree divided by cosine 30 finally so pause the video and write down the equation along the y axis how do you write down the equation along y axis look at the all the components along the y axis along y axis you have two components the one is t2 sine 40 40 degree and the other is t2 sine 35 degree so these two components and the other force which is acting downward is the Tipton's and t3 or this is also equal to the weight mg so these are the forces so teeth so how do I write down the equation here the equation that I have written down here is t2 cosines t2 sine 40 degrees plus t1 sine 35 degree my dad here it has to be t1 here let me make this is t1 t1 okay t1 sine 35 degree and t2 sine 40 degree is equal to mg and now mg we already have calculated mg which is 392 deaton so that's what I have written down here so now we have two equation they equated to and equation 3 and we do not know T 1 and T 2 we have two variables and two equations so we're going to solve the two equations now so what I'm going to do and we're plugging the value or the equation of T 1 into this equation here so let's see here T 2 sine 40 degree as it is and now instead of T 1 I'm going to write down T 2 cosine 40 over cosine 35 and then sine 35 degree here and 392 so simply plugging equation 2 into equation 3 and now we're not gonna just by using the calculator sine 40 degrees point 6 4 and then putting all the values and then now once you plug in this value and simplify here you have a point 5 3 and then now the point five three and point six four this is T 2 and this is T 2 so you can add these two numbers together which you get is one point one eight and if you divide 392 divided about one point one eight you get three hundred and thirty-two Newton so you found out the tension in the spring t2 and now if I plug this t2 into this equation we can solve for the t1 and the t1 just plugging this value into this year three hundred thirty two cosine forty degree over cosine 30 35 degree if you solve it you get three hundred ten point five Newton okay and and you can see here and this makes sense too because this angle is a steeper angle so he can imagine this has to be a little stronger or more tense and acting on to this one rather than t1 and that's what we got here t2 is a slightly better than t1 because it is more to a store article that is more tension has to be on the t2 but they but if you look at the numbers here this is 332 and this is 310 and this is 392 Newtons so the maximum support the tension in each spring is the maximum is 392 and the cable can with a stand or can bear up to 450 Newton so there is no problem at all the cable will remain and well the traffic light will remain hanging it won't wait okay because because it is significantly smaller than 450 Newton so that's it and again if you have any questions write down your questions in the comment section below and do not forget to like share & subscribe the channel thank you very much