Search Us Circus
3 Ring Boulevard
Barnum, PU 54321
September 1, 1999
Calculus Students
Franklin & Marshall College
Lancaster, PA 17604-3003
Dear Calculus Students:
I am pleased to introduce myself to you. My name is Matilda Majestica, and I am the proud owner of Majestica's Search Us Circus! We are world renown for our amazing acts of bravery and skill. No doubt you have heard of the exploits of Snavely Bravely, our wild animal tamer, who stopped a rhinoceros charge with his bare hands. You have read of the incredible leaps and plunges of Lead Head McCann, our stunt diver--the only human being to dive headfirst from the top of the Smucker's factory into a vat of peanut butter. You have been awed by the immense power of our strong man, Dick Dasterdly, who can lift his weight in lead while dancing the mazurka. And you too have sighed over the grace and beauty of our elegant Electra Walker, our high-wire walker.
And just as you have heard of us, so we have heard of you: particularly of your amazing abilities to understand the intricacies and subtleties of that elusive subject, Calculus. It is because we are both pinnacles of our own arenas that I thought of you when this most disagreeable trouble arose at the Search Us Circus.
You undoubtedly saw the many press releases that came out when we first bought the brilliant titanium wire: the pictures of Electra in her rubber insulating suit (the suit is lovely in itself, and it protects her from the voltage of the wire). The pictures don't do justice to the beauty of her act. She glides along the wire in the dark carrying her pole, which she touches to the wire to electrify her many props. These props light up, or sing out, or spin, and the whole act is one of wonder and amazement.
You may have seen the article about Snavely's accident: he was polishing the wire for Electra when Dick, who didn't see him, plugged it in. Please have no fears for Snavely! Lead Head McCann found him and turned off the power, and with a short hospital stay, Snavely is fully recovered. The show must go on!
But I digress. I am trying to explain our difficulty with the wire so that you can help us. The vendor who sold us this wire has offered to build a giant glass bowl that we could use for a new stunt (picture this: Lead Head McCann dives from the top of a statue of Bill Cosby into a giant bowl of Lime Jello!). But Dick Dastardly tells me that he thinks this vendor cheated us when she sold us the wire, by selling us aluminum instead of selling us pure titanium. If the vendor truly was dishonest, of course we wouldn't want to encourage her by buying even more from her. But on the other hand, the new stunt would be such a draw for our circus, that I'd hate to refuse to buy anything from her if she's honest.
We can't just cut off a piece of the cable to analyze it--we don't want to break such a crucial apparatus for one of our most popular acts. I read in the Encyclopedia Britannica that "Pure titanium is ductile, about half as dense as iron and less than twice as dense as aluminum; it can be polished to a high lustre." This made me think about weighing the cable, but where would we find a scale large enough? But then I looked in a book about Calculus, and there I discovered (which you no doubt already know) that the wire hangs in the form of a catenary, and that the variables for a catenary curve have height, weight, and tension in them. So I got out a tape measure and a spring scale, and measured as much as I could. Here's what I found.
The circus tent holds 650 people, and each person pays $15 for a ticket. The cable hangs between two 75 foot high pillars on the north side of the tent; these pillars stand 200 feet apart from each other. There is 10 feet between the pillars and the ceiling of our arena. In the middle, though, the cable is 50 feet above the ground, because it sags a little. The cable itself is 6 inches in diameter. There is a net which is roughly halfway between the cable and the ground. According to the spring scale, the horizontal tension is 11,219.5 pounds. The voltage running through the wire (when we turn it on) is 110 volts. I can not tell you how much the wire costs because I do not want to give away trade secrets which could give an advantage to our competition. I do know, however, that titanium has a density of 4.507 grams/cubic centimeter, or 281 pounds/cubic foot.
I anticipate your perspective on this interesting problem. In return, may we offer you complementary tickets to our upcoming extravaganza?
Yours most sincerely,
Matilda
Matilda Majestica
Owner, Majestica's Search Us
Circus