The Answer Is Forty-Two — Many Mechanics Problems, Only One Answer

The answer is 42, actually 42 minutes, but what was the question? There are, in fact, a number of physics questions, not at first glance closely related to one another, to which 42 minutes (or perhaps 84 minutes) is the answer. This paper was prompted by one such question, a Figuring Physics item in a recent issue of this journal,¹ which called for a description of the motion of a block released on a flat frictionless plate tangent to the Earth's surface. The correct answer given in Figuring Physics was that "the block will oscillate to and fro,"² but I was disappointed to see that the time of oscillation was not called for. So let us refine the question: "For small-amplitude oscillations, how long does it take for the block to travel from one extreme to the other, i.e., what is the half-period of the motion?" This is the question (actually just one of the questions) to which the answer is 42 minutes, as we can readily calculate. Those who are familiar with The Hitchhiker's Guide to the Galaxy [Douglas Adams (Harmony Books, New York, 1979)] will understand why I chose to ask initially for the half period (42 min) rather than asking the more obvious question, "What is the period?"³

Contents

• BODY OF ARTICLE
• Grazing Satellites and Earth Tunnels
• A Very Long Pendulum
• Summary
• Acknowledgments
• REFERENCES
• About the Author
• FIGURES