Simple phisics riddle? Bicyclist on a freight train

[Cloxxki]

Hi all,

Sorry if I'm all over the place here.

I was reading http://www.evert.de/eft301e.htm and although I'd felt it as a bike rider, now I understand this more deeply from the scientific side. Great website BTW, browse it. On a side note from my real Q further below, I envision human transport capsule networks in major cities. You get abord on boardwalk level, or high up an office building. To get to the other side of town, get on the appropriate capsule. It will use gravity to get to high speed train speeds (low resistance environment provided, of course), and cruise deep under town (really deep), an turn upward near the target, to come to a full rest after having expended hardly any energy. Mono rail network, eat your heart out! At its greatest depth, the majority of the trip's distance would be covered. Mass is cour friend now, it helps overcome air friction. Permanent Maglev for "wheels", of course. Long, heavy capsules will be most efficient at such speeds. From one side of Gathan City to the other in maybe a minute or 2, powered by gravity? No elevators needed, just directly from the penthouse of Gotham Tower to top floor of City Hall, bypassing traffic and elevators.

Anyway, working towards ideas to try and beat gravity, I came up with this little riddle:

Rider on his/her bike, total m=100kg
Riding over a rather tall flatform
No air
No wheel weight
Freight train, going 10m/s, flat top, same height as platform.

Freight train passes. Rider speeds up to 10m/s, and hops on the train, at no effort at all.
Ek Rider+bike = 1/2 * m * v² = 5kJ

Rider enjoys the train ride, but wants more speed. He gets back on his bike, and does the +10m/s acceleration again. Now doing 20m/s. Ek=20kJ now.

Now, where does the extra 10kJ come from? Did the spring from 10m/s (0 on the train) to 20/ms (10 on the train) this time expend 15kJ from the rider's muscles?
Or, did the train push him along, 10kJ worth? Did the rider effective slow down the train some? That seems most logical, but doesn't make it clear.
How would the second acceleration have felt, in a noo air enviroment, with recovered legs? I'm a bike racer myself, but find it hard to make the distiction between kinetic energy and wind resistance.

What I'm trying to find, is a way to utilize optimal speed vs. time vs. height relationship, where a weight can do more work, per time unit, than when just sitting on a wheel or pendumum. Even when released from 90 degree (level with the ground I mean), a pendulum is slower (11%) to the bottom than a free falling weight, although it did also cover some good initial horizontal ground there. Even if that buys us nothing. If a gravity machine will ever exist, I sense we'll have to milk that 11% in lost time somehow. This is of course for a weight doing no useful work at all, I want to learn to understand energy flow when weight do perform work coming down, at the cost of their own energy.
I keep coming back to wondering how Abeling supposedly "did" it. It seems he found excess energy on the uphill side of his wheel, in part from taking the inside line slong the axle. With a start-up velocity, I can imagine inverted freefall would have it's traits.

Thanks for any helpful comments.

J

[spoondini]

The extra 10 m/s was supplied by the train.  And to some degree the bicycle worked against the train, it's just so small compared to theoverall momentum of the train that it can be deemed negligible.  Every time I walk with the earths rotation I slow it down, but because the net effect is so small in relation to the earths momentum, it doesn't really matter. It's all relative. Kind of like the moving walkways in the airport.

[sm0ky2]

what if we had a wheel, spinning at 50 RPM.
on top of this wheel is mounted a second motor, and a smaller wheel.
this second wheel also spins at 50 RPM,
but with the lower wheel already spinning, the second wheel is spinning relative to a stationalry observer, at 100RPM.

how much energy can be recovered from the second wheel, compared to what it took to spin it?

[d3adp00l]

are the two wheels coupled? if so how? this makes a big difference.

If the axles are coupled but the wheel is bearinged then there would be no transfer of energy(with friction free bearings)

The fact is the two wheels only store the energy put in them, how its transfered is pointless.

how much energy do I have if I am shot at 100m/s from the front of a train traveling 100m/s? where did the energy come from? simple first the train, second the shot. I hit with 200m/s worth of energy, and the train would move back or experience resistance from the shot.

This is basic newtonian physics guys.

[Cloxxki]

Thanks for the responses so far!

So, for now I'll accept that the train gave 10kJ (not 10m/s, the rider also gave his input)

Now, let's repeat for air airplane. Someone walking jogging from the toilet to the front row.
Plane : 300m/s
Static passenger : 100kg
jogger : 5m/s
Ek passenger sitting: 4.5MJ
Ek passenger jogging forward : 4.625MJ
Jogger on ground : 1.25kJ
Difference sitting and joging passenger : 125kJ
Factor 100! And the jogger doesn't know the difference.
Yet, the pilot may wonder why his engine are working so hard. without increase in air speed.

Very interesting that Ek is apparently ramping up this way. And that it seems so hard to observe it in everyday life with muscle power.
Let's take the wonderful sport of Javelin. Who plays/played? When jogging along (not doing a maximum distance attampt), is the javelin heavier to accelerate relative to your body? At least with a javelin, we can conveniently much consider air drag close to zero.
I'll take it further. Perhaps the arm doesn't notice anything (being attached to the torso), but the legs DO? Perhaps a javelin is relatively too light to notice it this way.

Any thought welcome!

J