xmPuzzle 008 Disastrous Spin

Slide28

A biology teacher and a physics teacher (of similar mass) took the chair swing ride at the amusement park. The bio teacher chose an outer chair (B) while the physics teacher chose an inner chair (A). Unfortunately, the motor went berserk, and the ride reached an unreasonably high speed. A cable snapped and a teacher went projectile. Which one?

Full explanation at xmphysics.wordpress.com/008

THIS IS A WORK OF FICTION. NAMES, CHARACTERS, BUSINESSES, PLACES, EVENTS, LOCALES, AND INCIDENTS ARE EITHER THE PRODUCTS OF THE AUTHOR’S IMAGINATION OR USED IN A FICTITIOUS MANNER. ANY RESEMBLANCE TO ACTUAL PERSONS, LIVING OR DEAD, OR ACTUAL EVENTS IS PURELY COINCIDENTAL.

Answer:

The bio teacher went projectile (tangentially btw).

The bio teacher chose an outside chair, the bike accident still fresh in the memory presumably. Alas, at the SAME ANGULAR VELOCITY, the outer path with the larger radius of turn requires a larger centripetal force. (Think Fc=mrω2) The tension (the horizontal component, to be specific) in the cable, which provides the required centripetal force, is thus always larger for the outer chair than the inner chair. Logically, the outer cable should snap first.

P.S. It is misleading to think Fc=mv2/r because the two motions do not have the same linear speed v.

 

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