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From: siegman@sierra.Stanford.EDU (Anthony E. Siegman)
Newsgroups: sci.electronics,sci.physics
Subject: Re: Re^2: HV Cap Fun!
Message-ID: <148@sierra.stanford.edu>
Date: 2 Jun 89 22:41:47 GMT
References: <4924@m2c.M2C.ORG> <3806@mit-amt> <20772@quacky.mips.COM> <166@mother.dde.uucp> <147@sierra.stanford.edu> <2329@quanta.eng.ohio-state.edu>
Sender: siegman@sierra.STANFORD.EDU (Anthony E. Siegman)
Reply-To: siegman@sierra.UUCP (Anthony E. Siegman)
Organization: Stanford University
Lines: 10

There's a mechanical analog to the switched-capacitor "where did half
the energy go" problem.  A slow conveyor belt rolls past a loading
chute which dumps dirt or coal or something on the belt at a fixed
rate dm/dt (m=mass of dirt dumped).  The dirt is instantaneously
accelerated to the belt's steady velocity v as it hits the belt's
surface.  Force required to keep pulling the belt (no friction) = f =
dp/dt where dp = dm v = momentum added to the mass dm.  Work done in
time dt = f dx = dm v^^2 (using dx = v dt).  But kinetic energy added
to (or carried by) the dirt is only (1/2) dm v^^2.  Where's the other
half?