Winner! Will these vehicles run? A puzzle from the past

Make Pt1471-1
Charles Platt helped pick a winner from our “Will these vehicles run? A puzzle from the past” contest — MAKE reader shabadu please email me to claim your prize, a Maker’s Notebook!

There’s a lot of good stuff here. Most people seemed to get the right answer (so far as I can tell), although they used different paths to reach it. My vote goes to shabadu because he sums it up so succinctly (brevity is always a virtue), he writes clearly, he mentions a couple details that other posters missed, he gets everything right (so far as I can tell), and he adds a note of humor at the end. I regret that he didn’t attempt the calculation regarding the first vehicle that Theodire Minick included, but Minick seems to use some unstated assumptions that bother me. For instance, he assumes that the lead balls have potential energy based on a 4-foot difference, but how did he come up with that number? It has to be a guess, and therefore doesn’t justify his calculation to umpteen significant figures!

I don’t think any of the posters took into account the likely behavior of the balls on the roof. When the vehicle accelerates (assuming it does) the balls in the channel will tend to roll backward relative to the vehicle, because of their inertia. Therefore they will roll off the channel at increasing speed relative to the vehicle, and therefore they will hit the chute lower down, with greater kinetic energy, creating a more powerful forward thrust. On the other hand, their rearward motion will cause them to hit the lower chute at an increasing angle, which will deliver less forward thrust.

Of course the balls will not roll along the upper channel with zero friction, especially if they tend to rub against each other; and the balls in the reservoir over the cab will be significantly constrained. Therefore their mass, in addition to the mass of the vehicle, must be overcome by the forward thrust. However, the aggregate mass will diminish as the number of balls diminishes, and this will enable the vehicle to accelerate faster. Since this is a complex system involving factors such as the friction of lead against lead and the precise contouring of the ball containment system, no precise calculations are possible.

A simple way to look at the first vehicle is to assess the energy which would be required to lift the balls up onto the roof in the first place. This is the most energy that you can get back out of the system by allowing the balls to drop. In practice you will get less, because of frictional losses everywhere in the system.

Another issue which was not addressed is the question of “where the energy goes” in vehicle number two. The motor, after all, is doing work, circulating the water. If that work is not translated into motion, what happens to it? The answer of course is that it is converted to heat by friction between the water and the pipes. I would expect the water to become perceptibly warm as the truck sits there churning the water around and around while going nowhere.

And here’s Shabadu answer…

In the first vehicle, the falling balls will apply a forward force. Just like pool balls bouncing off a bumper, the falling ball will be deflected backward by their impact with the second trough. According to Newton’s third law of motion (“To every action there is an equal and opposite reaction.”) the vehicle will also deflect forward from this same impact. In an ideal system this will move the vehicle forward. However, any deformation of the second trough or the tires, and friction in the axles, and even wind resistance, will very likely overpower any forward force applied by the falling balls.

The second vehicle won’t move at all. The same principle that applied forward force to the first vehicle exists in the second one, so the water hitting the trough does give it a forward force, but since the water is collected it hits the back of the trough/pipe when it turns at the bottom to return to the pump. This impact applies a second force in the opposite direction of the first. In addition, the frictions, deformations, and wind resistance that might completely stop the first vehicle would be even more detrimental in this vehicle because the water will probably have less momentum than the lead balls, which provides less force to be transferred into movement of the vehicle.

On the other hand, the second vehicle does have a better chance of moving after the police arrest the first driver for dropping huge lead balls all over the road.

14 thoughts on “Winner! Will these vehicles run? A puzzle from the past

  1. I like Shabadu answer, but have a concern. I agree that the initial fall of water will impart a force, and that the collection will impart an opposite force. But, since energy will be lost from the first force, the second force can not fully cancel the first. The sum of the forces will be in the direction of motion (even if the car would still probably not be able to overcome wheel friction.)

  2. “Therefore they will roll off the channel at increasing speed relative to the vehicle, and therefore they will hit the chute lower down, with greater kinetic energy, creating a more powerful forward thrust.”

    No this is wrong. If the hit the chute lower down the will be travelling more quickly. More energy will be lost in the collision so they will impart *less* energy to the car. I think you’re forgetting that they push the car *as they roll down the second chute*, not just when they first hit it. If you are talking theoretically (no friction etc.) then it doesn’t matter where it hits the chute. They’ve lost the same amount of potential energy either way so they must have the same kinetic energy.

    “This impact applies a second force in the opposite direction of the first. In addition, the frictions, deformations, and wind resistance that might completely stop the first vehicle would be even more detrimental in this vehicle because the water will probably have less momentum than the lead balls, which provides less force to be transferred into movement of the vehicle.”

    This is extremely misleading. Are you saying that there *is* a chance that the water car could move? Because there isn’t. Not even theoretically (zero friction etc.).

    “But, since energy will be lost from the first force, the second force can not fully cancel the first. The sum of the forces will be in the direction of motion (even if the car would still probably not be able to overcome wheel friction.)”

    No this isn’t true. Temporarily ignoring the pump & pipes (since they probably don’t affect the motion much), you can see that any forward motion generated by the water hitting the trough is cancelled out by backward motion generated when the water hits the bend at the bottom of the trough.

    Intuitively, place the whole water system in a sealed box. Now put it on really slippery ice. There’s no way it can magically start moving is there?

  3. The force of the balls striking the trough just complicates the first example. The car will be pushed forward because the bowling ball ejector is essentially a rocket engine. Bowling balls with mass move backwards; the car must move forwards. For a clearer example, replace the balls with a tank of compressed air and a nozzle. Same effect, smaller items.

    The car would still move if the drop was replaced with a single inclinced trough, or if the entire trough were removed and a person threw the balls backwards.

    The water jet car doesn’t have this property; water moves in a circle.

    Now, I’d really like somebody to tell me if the sailing icecraft with the fan in Barbarella would work or not.

  4. Sort of re-iterating kra’s answer here, but surely the most elegant way to think of this is by considering momentum conservation.

    In the first case, the balls will end up rolling backwards so _something_ has to move forwards to keep the net momentum the same. If the car can roll freely then it will be the car that rolls forward, if the car’s got its handbrake on it’ll be the earth that moves!

    In the second case, the water doesn’t end up with a net backward motion, so nothing else can go forwards.

  5. Yes, the 4-foot drop is a guestimation based on how tall the vehicle looked in the picture, just like the guestimation of the Ball’s Diameter. With no measurements in the photo, I did my best.

    As for the “Umpteen significant digits”, I just copied and pasted what my calculator told me. :) Sorry if I came across as Pedantic. I guess everyone needs their bubble popped once in a while, or they get too full of themselves. :)

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