Stan likes music, and likes oldies the best. In his collection of music he has a cassette tape of “The Cassettes 20 Greatest Hits”. The amazing thing about the 20 Greatest Hits, is that each hit is exactly 3 minutes long. This fits perfectly on a 60-minute tape.

Songs 1 – 10 are on Side A, while 11 – 20 are on Side B. When listening to the tape, Stan does one strange thing. He listens to the first 5 songs on side A, then flips it to the other side. He then listens to Side B from that point until the tape ends. How many songs does Stan hear?

• The tape is wrapped around two spools that have identical diameters of 1 cm.
• The spool that is receiving the tape rotates at a constant speed.
• The tape, when located all on one spool, measures 5 cm in diameter.

I confess, I skipped quickly over the three "dots" or bullet points giving conditions about the tape itself.  So I missed the part about constant angular velocity.  How fortuitous that this was conveniently buried in the middle of the 3 bullet points. 

So although I haven't worked through Charlie's solution, I have no doubt that it is correct.  Anyway, I had one thing right:  assumptions were the key.  I assumed it was like the usual tape player.

And yet, ....., I can still resort to a lame technicality.  The second bullet point says:  "The spool that is receiving the tape rotates at a constant speed."  The use of the word speed is generally a scalar not a vector.  It doesn't actually SAY velocity or angular velocity, it says "speed".   Perhaps some may agree with me that the word 'speed' might refer to linear speed of the tape across the tape head.  Sure it also says "rotates", but maybe that is just a qualitative non precise description.          hey, I can try can't I?

One more thing.  If the angular velocity is constant, then perhaps Stan would never listen to his tape at all because the music might sound very bizarre either speeding up or slowing down, worse than a Kazaa download at a bit rate of 32; unless of course he used the same bizarro tape machine to make the recording in the first place.

and that's my story

Posted by Larry on 2004-04-27 19:52:31