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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

1752.0. "The penguin and the igloo" by IOSG::CARLIN (Dick Carlin IOSG, Reading, England) Sat May 22 1993 16:19

    Help
    
    My honour is at stake. This is from my son's homework. I've had a quick
    look but can't do it, although it seems pretty easy.
    
    A mass m sits on a smooth hemisphere, radius r. It starts to slide
    down. At what point (and velocity) does it leave the surface?
    
    Dick
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1752.1AUSSIE::GARSONnouveau pauvreSun May 23 1993 04:403
    re .0
    
    Sounds like you need some PHYSICS to answer this.
1752.2Differential equationIOSG::CARLINDick Carlin IOSG, Reading, EnglandSun May 23 1993 08:0010
    Derek, you're right, it is physics. But I soon got to the point where 
    the angle swept by the body satisfies the differential equation (wrt 
    time):
    
         y'' = c * sin(y)    y(0) = 0, y'(0) = 0
    
    which I suppose is still physics though. Differential equations are so 
    messy, give me number theory any day.
    
    Dick
1752.32nd tryIOSG::CARLINDick Carlin IOSG, Reading, EnglandMon May 24 1993 09:1942
1752.4CSC32::D_DERAMODan D'Eramo, Customer Support CenterMon May 24 1993 19:229
        Computing y(t) is neat.  If the object starts at the top of
        the hemisphere with 0 kinetic energy, then it stays there
        forever.  If instead it starts at cos(y) = 2/3 with the exact
        amount of kinetic energy directed upwards to get back to the
        top with 0 kinetic energy left, then it takes forever to
        actually get to the top, although it does approach arbitrarily
        closely (going more and more slowly) as t -> oo.
        
        Dan