Hi Bill,
Yes, I've been following the work of Laithewaite for some time. This paper
was one I didn't have, so I appreciate the tip.
Reading the section called "Mass Displacement By Circular Motion" gave me a
couple of ideas. If you look at fig. 7 it shows a mass with centers A1,A2
being moved back and forth as two smaller masses M1,M2 swing back and forth
over an arc. Of course mass A1,A2 will bob back and forth as what
Laithewaite calls 'centrifugal force' pulls it.
So what happens if you put A1,A2 on a rachet so that it can only move in
direction Y?
Obviously the assembly is going to move in direction Y for half of the time
and stop for the other half. Not a very efficient means of transportation
:-) But what happens to the energy stored in the springs while this is
going on?
Suppose the springs are perfect and there is no friction between A1,A2 and
its support---no mechanical losses. Then, the way Laithewaite has the
system moving back and forth without any constraints on its movement, it is
a closed system and it would move back and forth forever, according to the
conservation laws (sorry if I mention a bad word :-)
Now if it is racheted, do the springs lose energy as the assembly moves
forward, even though the actual AMOUNT of movement is half as much? It
seems like they would, somehow, because for part of their arc, the masses
M1,M2 are moving in the same direction as A1,A2 and pulling it along, and
for the rest of their arc, they are moving in the other direction and A1,A2
is resisting their movement because of the rachet stop. But I don't know...
Another way of looking at the same idea without the inconvenient rachet is
this. Picture a heavy pendulum on a short line swinging back and forth. At
the highest point of its arc on either side there is a moment when the bob
is not moving, thus 'centrifugal force' at these points is zero. As the bob
moves to the lowest part of its arc, the 'centrifugal force' increases to a
maximum.
So if you were to plot the 'centrifugal force' on a 360 degree circular
graph all around the pendulum, there would be one maximum point straight
down, decreasing to zero at the top of the swing and then of course zero
all the rest of the way around.
Now take the same pendulum and make it horizontal. Put springs on each side
so that it doesn't need gravity to store the energy of the swing. Put it
with the bob facing forward on a little cart that is constrained so that it
can't move from side to side, only backward and forward. Now get the
pendulum going. All the 'centrifugal force' is in one direction-- forward.
Does the cart move forward along the track? And what happens to the energy
stored in the springs?
I did a little experiment along these lines, and there was no forward
movement, but the bob wasn't heavy enough to develop much centrifugal
force, so I guess the question is still open.
Fred