1. In one of my previous answers I had pointed out that understanding vectors would be useful in physics.
Now in this problem, you should first recognize that you need the ANGLE of the sag before you can proceed.
To do that it would help you to draw a diagram. If you did that....
....
are you finished.
Now what's tan(theta) from your triangle. You should have found it to be tan inverse of 0.4/20 which would give you 1.146 degrees, a very small angle of sag indeed.
Now once you have the angle you have to realize that the tension in the cable prevents the traffic light from falling. The horizontal components cancel and you'll be left with only the vertical components for the two sides of the cables on either side of the traffic light.
Resolving them you should have
2T sin(1.146) = weight = 20(9.8)
giving you a value for the tension as
T = 4900 N
Did you solve it or are you simply copying the answers down. It's important for you to try and solve it once again yourself to see if you can recall the principles and made the connections to apply it in a new situation later.
2. Have you ever tried to break an egg by squeezing it along the long end? In fact it is a popular physics demonstration to let the students take an egg and put it into a paper cylinder and drop it from the roof of a building. Guess what...? The egg does not break. If you're mum wouldn't mind a possible mess, why don't you try to sqeeze an egg by keeping it between your two palms and try to smash it. It shouldn't break unless you cheat by applying a force along the smaller side. I had some frustrated students do this when they didn't succeed by applying a very large force along the long side.
The reason for this is the strength of "arches". Have you observed how tall building including the ancient Roman ones and even stone bridges were built with arches? The strength of these structures is the distribution of the force on them. The arch helps to transmit a sideward force downwards along the ground and it is not possible to force something along the grond easily. Of course you can apply a very very large force and surely expect the ground to give way, but under normal cicrumstances the ground is firm.
Similarly the glass tube and glass bulbs don't shatter even when you remove the air from the tube although the air is pushing it from all sides. You should however be careful because sometimes when the glass is blown to its shape, some parts of it may not be as strong as the other and accidentally it may shatter. It's always safer to have some grill around the tube to prevent this shattering if you're trying out some experiments with it.
3. The answer to this question is not as simple as it used to be. Earlier one could have explained a few gyroscopic principles and told you that the stability is on account of the gyroscopic forces that come into the fore. A recent article in the American Journal of Physics -- July 2000 -- Volume 68, Issue 7, pp. 654-659, says it is quite the contrary. Unfortunately I do not have access to this journal and have to pay for it, whereas I would have read it for free back home. If you have access to a good library where they have back issues of AJoP, it's worth a read.
In any case I'm providing you a useful list of references which may at least help you understand the issues involved before you read the more recent article.
How Bicycles Work
When on a bicycle, why can you stay upright only when moving?
For more on how bicycles work, check out How Things Work - Bicycles
If you are unable to see the URL's I sent you by clicking on links above, then copy and paste the full URL links provided above into your browser.
http://www.howstuffworks.com/bicycle.htm
http://www.madsci.org/posts/archives/mar97/859224069.Ph.r.ht
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http://rabi.phys.virginia.edu/HTW/bicycles.html