xmPuzzle 009: Disastrous Swing

Slide29

The physics teacher cracked a joke, which the biology teacher find not the least funny. The biology teacher grabbed a rope to tarzan-swing across to have a word with the physics teacher. The rope can only withstand a tension of 1000 N. The bio teacher weighs 1000 N. The physics teacher weighs 700 N. One teacher had to take MC the next day. Which one?

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 had to take MC the next day.

If a mass is hanging at rest on a rope, the rope only needs make sure that the net force on the mass is zero. So the tension in the rope will be 1000 N to support the weight of 1000 N.

However, if a mass is swung on a rope, in order to constrain the mass into circular motion, the rope must make sure the mass experiences a net force of mv2/r in the centripetal direction. In fact, at the bottom of the swing, we have Tmg = mv2/r. The tension is in fact T = mg + mv2/r. So the tension in the rope will be more than the weight of 1000 N. Logically, the rope must snap.

 

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