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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

412.0. "flying to work with full cup" by SPRITE::OSMAN () Thu Dec 19 1985 11:17

In note 383, I asked how far away work was, given that the fastest trip
took 2 minutes, accelerating as fast as possible without spilling an open
half-full cubical cup of coffee.

Let's suppose that on another day, you take a FULL cup of coffee in
the car, and you cover it in order to keep it hot and in the cup.

Let's assume you place the cup on a non-slip level surface in the car, such as
the floor, and you align the cup with one of its faces directed forward.

Assuming the cover will remain in place unless the cup tips over,
how long will it take to get to work, again accelerating at the maximum
possible no-mess rate for the whole trip ?

/Eric

T.R	Title	User	Date	Lines
412.1		R2ME2::GILBERT	`Thu Dec 19 1985 18:17`	7
	What do you mean by "tip over"? Is it okay for the cup to be 'balanced', teetering, or are you talking about it falling flat on its side? Also, if you mean flat on its side, then you could accelerate all the way to work, with the cup teetering, let the cup fall to its side while you decelerate to stop on a dime (ouch!), since the force exerted on the coffee at that point makes it 'look' like it's being pushed to the bottom of the cup!
412.2		R2ME2::GILBERT	`Thu Dec 19 1985 18:21`	4
	In fact, with a little skill, you don't need a lid on the cup! Just tip the cup over, and accelerate very very fast, so that the coffee is pushed to the bottom of the cup. And again, you can 'stop on a dime', while flipping the cup over, then upright!
412.3		EXIT26::KUHLMAN	`Fri Dec 20 1985 14:39`	13
	I'm really Eric Osman, SPRITE::OSMAN, not exit26::kuhlman. Your idea sounds entertaining as more complicated cerebral foreplay than I had in mind. Teetering is o.k. as long as the cup doesn't tip over. I'm assuming accelerating all the way, ignoring the problem of stopping when we get there. It occured to me after submitting this problem, that the answer may very well depend on the edge-length l of the cup. If so, I'll gladly accept an answer that's a function of l. /Eric
412.4		SPRITE::OSMAN	`Thu Jan 02 1986 11:05`	7
	It seems to me that the force necessary to topple a teetering cup is virtually zero, while the force necessary to topple a level cup is appreciable. Hence I'd expect the orientation of the cup during the fastest possible acceleration to NOT be teetering, but instead to be level. /Eric