Brain Teaser Challenge
by Butch Shadwell
Brain Teaser Challenge Solution - December 2007 Butch Shadwell
From my discussion with Uncle Gary concerning an electric toothbrush I got the following problem. “…can you tell me the maximum power output I can get from a 1.5 volt battery with an internal resistance of .1 ohms?”
One of the fun things I get to do once in a while is demonstrate to EE students that the maximum power transfer occurs when the load impedance matches the source impedance. You can use the second derivative of the power equation (with respect to the load resistance) to find the max point, and voila. I don’t have room here for the math but you can take my word for it.
The way I would solve this one is to simply double the source resistance and calculate the current from a 1.5 volt supply. Then P=I^2R. Making the substitution we get 5.625 watts. But I bet you already knew that.
Brain Teaser Challenge – January 2008 Butch Shadwell
The year was 2108 and Zorg was considering his New Year’s resolution. Like every one of his past 40 New Years, he was spending far too much time thinking about a resolution that had virtually zero probability of being kept. But he thought, “Every new year is a chance to start over. I could become the person I’ve always wanted to be this time, if I would just commit myself to that end.” Of course this wasn’t the first time for this thought either. He had wondered what had held him back all of those times in the past when he had tried and failed to keep that promise to himself. Was he just too lazy or was there actually a reason why he could not allow himself to succeed? Oh well.
As the smoke cleared around his overheated brain, the answer came to him. This year he would complete his work on the new improbability drive for space propulsion. When he had set it aside last year he was stuck trying to lift his prototype contraption into the test stand to measure the output. It weighs 2000 pounds but Zorg is only able to pull with 100 pounds of force. If he uses a block and tackle system (multi-wheeled pulleys) and he pulls on the rope end coming down from the upper block, what is the minimum number of wheels each block needs (upper and lower) in order for him to be able to lift his device into position? The other end of the rope is fastened to the bottom of the upper block. Also, assume zero friction from the pulleys. This could be a little tricky for some.
What happens if we terminate the far end of the rope on the lower block instead of the upper one? Have fun.
Reply to Butch Shadwell at b.shadwell@ieee.org (email), 904-223-4510 (fax), 904-223-4465 (v), 3308 Queen Palm Dr., Jacksonville, FL 32250-2328. (http://www.shadtechserv.com) The names of correct respondents may be mentioned in the solution column.
