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Frozen rich man?

  1. Jan 9, 2007 #1
    1. The problem statement, all variables and given/known data
    Legend has it that a rich man with a bag of gold coins once froze to death when he was stranded on the smooth surface of a frozen lake. If he had not been such a miser how might he have saved his life?

    2. Relevant equations

    3. The attempt at a solution
    Maybe he froze because he was stationary and couldn't move anywhere due to the low friction of the icy ground. Hence froze to death.

    In order to start moving he could have thrown away his coins which would mean he would gained some momentum and would have started travelling in the opposite direction in which he threw his coins due to conservation of momentum. But how would that help? Would a moving person be less likely to accumulate ice? Or does it simply mean that he would have been at a higher temperture due to his movement hence the ice on him will more likely to melt?
  2. jcsd
  3. Jan 9, 2007 #2
    Well, if he was moving he'd eventually reach the shore wouldn't he?
  4. Jan 9, 2007 #3

    Gib Z

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    He could have dug his nails into the ice and dragged himself.

    A moving person, though very slightly, would be less likely to accumulate ice. However I would think that movement would be enough to get him off the lake. If he was desperate, he would have tried his hardest to dig the gold coins into the snow and push.
  5. Jan 9, 2007 #4
    The ice might break hence he could drown.

  6. Jan 9, 2007 #5


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    I think the simple answer is that he could have reached the shore and safety if he had thrown his coins away
  7. Jan 9, 2007 #6


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    Being a miser had nothing to do with it. He was lazy. If he threw the coins one direction, he would move the opposite direction (conservation of momentum). If the ice had so little friction he couldn't move, then there wouldn't be enough friction to stop the man or the coins. The man would reach one shore, while the coins would reach the opposite shore. The man could then walk around the lake to the opposite shore to retrieve his coins.

    (Unless there were people on the shore that might have stolen his coins and he was to cheap to pay one of them to toss him a rope).
  8. Jan 9, 2007 #7
    He could just throw one and get to the shore slowly :biggrin:
  9. Jan 10, 2007 #8
    What I want to know is whether snow accumulates more slowly on a moving person? Or is it the same with the difference being a moving person has a possibilty of saving himself by getting to the shore but the stationary person has no chance, no matter how slow the ice accumulates.
  10. Jan 10, 2007 #9
    Maybe the weigh of the bag of coins made him sink into the ice and get stuck?

    or he couldnt leave his boat without going onto the ice and he was afraid his bag of gold would be too heavy for him to take onto the ice without it breaking
  11. Jan 11, 2007 #10


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    Where does it say anything about snow? You freeze to death because of the amount of time you spend in cold weather. If the snow is accumulating on him, it's because he's already dead or because he's wearing enough insulation that the snow isn't melted when it hits him. The fact that snow accumulates on his hat or coat is just proof that the man isn't losing much body heat.

    If the person had no hat or coat (because he was a miser and refused to spend his money), the snow would melt and carry away body heat and a person remaining stationary certainly would be exposed to more snow even if his exposure was at a slower rate. As far as how much snow he'd be exposed to while moving, I would presume it would be similar to figuring out the best speed to walk while in the rain. In that case, his best bet would throw enough coins that he would move the same direction and speed as the wind.
  12. Jan 11, 2007 #11
    My bad, I made the snowing thing up. The question did say he was frozen to death so at some point liquid would have condensed on him which we can call snow? Although snow may not be falling from the sky in the question.

    The colder he is the more likely he is to accumulate snow on him.

    So you are saying by moving in the direction and speed of the wind, the same amount of snow or rain will be with him and he is unlikely to be caught by anymore new snow or rain. There could be trouble if the direction of snow or rain has a vertical component. He can only move horizontally so in this case his best bet would be to move at the horizontal velocity component of the snow or rain.
  13. Jan 11, 2007 #12


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    The question mentions neither snow or wind. The only sensible assumption is that the ice is a frictionless surface and that is the reason he can't walk to shore.

    Freezing to death has nothing to do with accumulating snow. The unfortunate person dies because it is simply too cold and ultimately organs fail and then death. Once dead the liquid in their bodies will freeze.
  14. Jan 11, 2007 #13
    People are getting into philosophy :p. "Well, if the man was feeling good and on the day his organs were pumping blood and he had an incredibly high blood pressure. Deciding it'd be a good idea, he held his breath and tilted his head around to make blood rush into it. Causing him to move etc." LOL :p.

    Simply; he could have just thrown anything in the opposite direction and he will move due to equal/opposite forces in action.
  15. Jan 11, 2007 #14


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    You live somewhere warm, don't you.

    Generally, freezing to death means he died of hypothermia. In other words, his body temperature dropped too low to sustain life.

    Of course, once he died and chemical reactions in the body ceased completely, he'd lose heat even faster and the fluids in his body would eventually freeze.

    The problem is about conservation of momentum and has nothing to do with whether he has a higher body temperature while moving or not.
  16. Jan 12, 2007 #15
    Yep, I've never seen real snow in my life.

    The question is about conservation of momentum but I did learn many other things from this question.
  17. Jan 12, 2007 #16
    He could have fashioned a set of Ice-Skates by embedding the coins in his shoes and skating across the lake like Torvil & Dean.
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