Physics Problem! Runaway train boxcar?

Question

A periodic sinuous track is installed on an uniform plane slope, such that it intersects the straight fall line at regular intervals. A boxcar with wheels rolls without friction down this track, so that if left to itself it will gain speed as it descends due to gravity alone. Is it possible to build a mechanical apparatus wholly inside the boxcar, containing its own energy source, that will counteract this freefall, so that the boxcar can maintain speeds not exceeding some maximum? No use of jets or propellers or magnets interacting with the world outside the boxcar is allowed, this is a purely Newtonian problem, the apparatus must be totally enclosed inside the boxcar. Assume that the wheel design guarantees that the boxcar will never derail, like a roller coaster car. Also assume that the boxcar is able to dissipate heat energy from its descent, which is necessary in order to maintain average speed.

Since it's the 21st century, you're allowed to use computer control.

Right, because then a brake would make the boxcar NOT rolling down frictionlessly. Brakes are excluded.

The axles of the boxcar is to turn freely and without friction or force. Any tampering with the axles is out.

Answer 1

I think Dan's argument is essentially correct.

One minor technicality; for a mass-spring-damper system to work implies that the *center of mass* of the boxcar is not strictly confined to the path of the track. The C.M. must be able to "drift", or "slew" somewhat to the left and to the right of the centerline.

If you decompose the forces on the boxcar into "tangential" and "normal" components, with respect to the path of the track, then the work done on the boxcar is:

W = ∫T d{s} + ∫N d{s}.

Since no brakes or friction against the track are allowed, the tangential contribution to work is zero. However, since the C.M. is able to undergo a displacement {s} to the left or the right of the track, and since,(due to the damper system,) the Normal force can be said to always *oppose* this displacement, clearly the normal forces can be said to be "nonconservative."

i.e. ∫N d{s} ≠ 0.

In other words, instead of braking, using the wheels or axles, the boxcar's center of mass is "braking" against the *sides* of the track.

One could argue here that, technically, friction actually still does exist, at least according to the frame of reference of the boxcar's C.M.

~W.O.M.B.A.T.

Answer 2

darn, now what??
some sort of inertial divice but i dont see anything working. interesting question but when you are my age, there arent many brain cells left that arent already being used to just to maintain life so . . . . . sorry, nothing coming to mind

there are train cars that have generators mounted on the axle, now taht you have a source of electricity you can install electric brakes, computer controlled or more conventional controls that use magnetic sensors on the axles that measure pulses and convert that to speed.
I hope this helps
another solution might be a wind powered generator on the roof, as the car builds up speed, there will be a source of electiricty to control the braking system.
or pnuematic, you can install an air compressor on an axle that could be used to operate hydraulic or air brakes

I guess this is assuming you can use wheel or axle mounted energy generators and braking systems.
if not, then i gotta do some more thinking.

Answer 3

The one thought I have is a mass/spring/damper system, such that the changes in velocity due to the sinusoidal motion result in energy being sucked out of the system as heat in the damper, it is non trivial to see that this can actually dump sufficient energy from any given combination of slope and sine amplitude to actually maintain constant average velocity. Clearly the rato of sprung to unsprung mass will also be of critical importance.

If we know the maximum velocity and know the period of the sine curve, it may be possible to make the mass/spring system resonant at the appropriate frequency?

Regards, Dan.

Answer 4

One thing for sure; your device WON'T need an energy source. Its task is to dissipate the potential energy of the car as heat, but your restrictions seem to prevent a simple brake from being a valid method.
GFL..............