Steel girder?

Question

A boom of mass m supports a steel girder of weight W hanging from its end (see figure below). One end of the boom is hinged at the floor; a cable attached to the other end of the boom and pulls horizontally on it. The boom makes an angle (theta) with the horizontal.
For (theta) = 0, does T approach zero or infinity?
For (theta) = 90, does T approach one or zero?

http://i116.photobucket.com/albums/o23/dead10252006/6.gif

Answer 1

This will aid you in picturing how T will behave when the angle theta is 0 and 90. Imagine the weight of the steel girder + W as being one resultant force, F.

Then tan(theta)=F/T
T=F/tan(theta)

when theta approaches 0, tan(theta) =0.
It's because the opposite is a very very tiny
length almost equal to 0. The adjacent side
remains the same. tan0=almost 0/adjacent side=0.

Now when theta approaches 90, tan(theta)=infinity.
It's because now the adjacent side is almost
equal to 0 while the opposite side remains the
same. tan90=opposite side/almost 0=infinity.

Now go back to our equation T=F/tan(theta)

When tan(theta)= 0 ,
T=F/0=infinity.

When tan(theta)=infinity,
T=F/infinity=0

If you do it this way, you don't have to memorize
anything, or if you forget what you memorized
you can still resort to this type of analysis.

Answer 2

T approaches infinity as theta approaches zero
T = zero when theta = 90