Will These Vehicles Run? Modern Mechanix, 1932.

HEREâ€™S a real brain tickler for puzzle fansâ€”study the drawings above, figure out whether the lead balls and the water motor will move the vehicles or not (and why), send in your less than 300 word letter giving your reasons, and you may be rewarded with a check for \$10. Somebodyâ€™s bound to win that \$10 check; it might just as well be you. There are no hidden tricks in these drawings. All you need is an understanding of natural laws. In addition to the \$10 award for the best tetter, all other letters published will be paid for at regular space rates. Keep your letter under 300 words, and be sure to mail it before May 15, 1932. Address letters to the Freak Vehicle Editor, Modern Mechanics and Inventions, 529 S. Seventh St., Minneapolis, Minn. Donâ€™t fail to tell why the vehicles will or will not run. Here is the problem: A vehicle carries a number of heavy lead balls, on its roof, which fall off the end of a trough and strike a second trough, mounted at a 45 degree angle at the rear of the car. Will the falling of the balls make the vehicle move? The second vehicle is similar to the first, except that water is used instead of lead balls. The water is pumped against the trough by a motor, is retrieved in a funnel after it has passed down the trough, and is used over again. Will the water power move this vehicle?

Ok makers, post up your comments and solutions – since Modern Mechanix won’t be sending you a check for \$10, I’ll send you a Maker’s Notebook for the best answer.

## 74 thoughts on “Will these vehicles run? A puzzle from the past”

1. Timm Murray says:

The first will work, though probably very slowly (depending on the weight of the balls, weight of the vehicle, and the coefficeint of friction on the axels). The lead balls leave the system, and so impart an equal and opposite reaction. However, I have the feeling that any real truck will have too much friction on the axels for it to actually move.

The second can’t work at all. Strictly speaking, it’s not a propetual motion machine because energy is being taken from the water pump (presumably from an electric motor or gas engine). However, since the water is collected back to the pump, the force of the water going towards the back is counteracted equally by the water being returned. It could work if you simply shot the water out instead of returning it, but here again, you’d need to be shooting the water out fast to overcome friction.

2. Dave Turner says:

Timm – I don’t think that the first one will work either. I see what you’re saying about the weight of the truck, but did you take in to account that the weight of the truck also includes the lead balls? At some point the release of the ball might generate enough energy to move the truck, but how many of the balls have to be gone first?

3. DU says:

m*v must be constant.

In the first example, let’s assume the feeder trough is tipped a little more so they fall off (I think that’s what they are trying to say, but it’s not clear). At t = 0, the entire mass of the truck + balls multiplied by the velocity (0) is 0. At t = 1, one ball has fallen off and is rolling backwards. The mass of that ball times it’s velocity is some number, say -M. (Negative because it’s moving leftwards.) But the total momentum has to be constant, which was zero. Therefore the momentum of the truck has to be M. That M is the mass of the truck + the remaining balls multiplied by the velocity of the truck. Divide M by the mass to get the velocity.

In the second example, the water is being sprayed out the back. That’s a rocket which clearly should work the same as the truck + ball example. The problem is, the net velocity of the water is 0 because of the pipe underneath. It comes out the nozzle and has some velocity -M as before, but the water underneath has +M, which ensures that momentum is conserved without the truck having to move.

4. malweth.myopenid.com says:

The “trick” to these is in understanding different types energy. The first machine does not generate its own power, but has kinetic energy stored as potential by the high masses. This energy is lost through motion and the corresponding work (force x total displacement) will move the car forward.

The second machine generates energy with an engine (combustion). The difference is that this energy is used to create motion of water. The water’s motion flows in two directions, one toward the back of the truck and the other toward the front (cycling back into the pump). This closed system means that no work is being done (total displacement is zero) and the vehicle will not move.

5. IdanBeck says:

I don’t think that the water jet car would work at all but I think that the lead ball one may move slightly.

————-
Energy must be conserved and what this car does is it accumulates potential energy through the placement of the lead balls above the ramp which will receive the impact. This difference in height will give each one of the balls a potential energy of LeadBallMass*GravitationalAcceleration*Delta(BallHeight – RampImpactHeight). So this apparatus will actually produce a certain acceleration and force on the car. However, this force will only be applied at a certain percentage dependent on the angle of the ramp. Since some of the force will be applied in an effort to push it into the ground the other portion will be applied to the car to push it forward. The resultant force that is applied to the car forward should be F*(sine(theta)) where theta is the angle of the ramp in reference to the vertical plane. While at this point we would need to look at the velocity of the ball it is more important to think of the force which will be constant since F = ma. Before any momentum can really be transferred the ForceBallImpact needs to be greater than the opposing static friction of getting the axles to start rotating which would depend on the apparatus of the car etc. If the force is in fact greater then the car will inch forward by the certain velocity CarVelocity = BallMass*BallVelocity / Car*Mass but will be slowed down by the kinetic friction of the axles. I think it would be important to release the balls in such a way that the car never comes to a halt since that initial static energy “blip” is wasteful and while the axles continues to move it will never need to be dealt with again. Another issue, however, with this design is that the mass of the car differs drastically with each ball that is released making it much harder to start then it is to keep going not to mention the difficulty of storing so many heavy balls. But the overall answer here is, it will at least move if the axles aren’t terrible and the angle of the ramp is realistic.

Waterjet Car
————

This car will not move. Everybit of the energy imparted onto the apparatus of the car by having the water spray against the ramp is recovered by it’s re-splashing against the collector bin and the motor sucking it back up. This goes, as well, for the water jet spraying down. Energy must be conserved and for this car to actually move it would break this rule. For every action that the water takes there is an opposite reaction at some point in the chain of water flow. The energy that motor consumes, however, is lost as heat due to the movement of the water and likely noise. If this car does move at all it would be forward and backwards in an equal amount which would just result in a kind of shake.

To make this design work you couple employ the use of momentum and have a tank of water which would then spurt out the water much like a rocket. If the force of the water spraying out (pressure) can be enough to push the car over the static friction threshold you could get the car to move.

Neat question!
Idan

6. Nick says:

The first car won’t probably roll, but the balls rolling down will at least generate a force against the car. If the wheels and drive system were frictionless, I will move.

The second car won’t work because the transfer of momentum stays within the system, there’s no net momentum on the car and no locomotion.

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.

8. malweth.myopenid.com says:

The “trick” to these is in understanding different types of energy. In the first machine, kinetic energy is stored in the raised masses. This acts as an engine and the displacement of high masses generates force. This force is toward the back of the truck (at a <45 degree angle) and may be enough to drive the truck forward. This process is inefficient because the work done by each lead ball is counteracted by the mass of the truck (including remaining lead balls).

The second machine generates energy using a combustion engine. This drives a pump that forces water out the back. This water is collected, however, and returned to the pump. The force of water might've been enough to create motion in the truck, but the force is downward. Furthermore, the force of water downward hits the truck as its being collected, cancelling out any possible effect.

9. Mike says:

The most important things in physics are the conservation laws, from which everything else is derived. In these two cases, we must consider the conservation of momentum.

Since there are no “hidden” energy sources (i.e.- fuel being burned, batteries being discharged, etc), the only way for these vehicles to go forwards is if something else goes backwards, so that momentum is conserved.

So, take Vehicle #1:

We’ll start by assuming that the vehicle is at rest (so the total momentum is zero), and we’ll draw a square box around it. Now, the vehicle starts dropping the lead balls off of the back. The balls roll backwards, (and assuming they don’t experience too much friction when they hit the ground), and out of the box. This gives us one momentum vector (from the mass flow of the balls) pointing backwards. Now, since the total initial momentum was zero, the total momentum must forever remain zero, and we must have another momentum vector, equal in magnitude to the first, pointing forward, in order to cancel out the momentum of the balls. This second momentum vector has to come from the vehicle, as there’s nothing else to consider, and so Vehicle #1 moves forward.

Vehicle #2:

We’ll do the same thing for vehicle #2. First assume it’s at rest, and draw a box around it. Once we turn on the pump… nothing happens. Well, sure, the pump starts moving the water, but none of the water leaves the box that we’ve drawn. So then there’s no extra momentum vector from the water, and the vehicle can’t move because then momentum wouldn’t be conserved.

A further note is that the force of the water pushing on the plate at the back of the vehicle is canceled out by the force of the water then pushing on the turn in the pipe directly below the reclamation funnel. :-)

—–

Conservation laws — they’re not optional.

10. Timm Murray says:

Dave–No, the weight of the remaining balls won’t stop it from moving (if we’re ignoring friction). It does mean that the first ball to fall out the back will push it a lot slower than the last ball. It’s equivalent to a rocket which must push its own fuel in addition to the regular cargo.

Once you add in friction, the first ball may not provide enough force to overcome that friction, but the last ball might.

11. Sam Whitehall says:

Firstly, I’d like to point out that I’m only a 16 year old about to sit his first Mechanics A-Level next year… but I have a few ideas.

Firstly, I’d like to say that I modelled the device using the game… I mean erm, “physics modelling software”, Incredibots in two different ways.

The first method was using a “sliding joint” to push the balls off the roof, but the inertia of the heavy balls would push back against the slider (which is affixed to the car) and this would cause the motion.

I also tried another configuration where the ball feeder was at an angle. The car moved again, which maybe implies that the friction between the balls and the car helped.

Of course the friction, lack of air resistance etc. in the software is unrealistic, but I guess it shows that this kind of thing works theoretically; given heavy enough balls with enough friction.

The model can be found here: http://incredibots.com/?robotID=gesiwuj4947f285e06bf0.99143634

Thankyou for a great magazine and a great blog :)

12. Fredex says:

Vehicle two doesn’t work because the water is circulating in a closed system. There is no transfer of momentum between the vehicle and its environment which would make it move.

Vehicle one doesn’t work because the EPA would never allow that much lead in the exhaust. The physics of the vehicle work, however.

13. Chris says:

I am an engineer. The first car moves (slowly). The second does not.

One easy way to look at this is to draw an imaginary “box” around the entire vehicle (an engineer would call this a “control volume”). The center of mass of this box can never move unless you exert a force from _outside_ the box.

When you roll a ball off the back of the first car, make your box bigger in order to still contain the ball. In that case, you have a small amount of mass moving backwards, so in order to keep the center of mass of the _box_ stationary, you’ll have to move everything else in the box forwards slightly.

In the second example, you have equal amounts of water moving forward and back, so nothing else inside the box has to move.

14. Tim says:

Conservation of momentum says that the momentum of a closed system must be constant. This is very intuitive – if you are in space, or on very slippery ice, (or on frictionless wheels), then it is impossible to change your velocity without throwing/catching anything.

In this case the closed system is the car and balls (or water). The initial momentum of this system is zero, so it must remain zero forever. As the wheels clearly have momentum going left when they roll off, the car must be given an opposite momentum going right, so that the whole system (which still includes the balls) has zero momentum. Thus the car moves (slowly).

For the second case, the water never leaves the car so the cars total momentum cannot change from zero. It doesn’t move. Thinking about it intuitively, if you put the pump & water in a box, and then put that on the car, how could it possibly make it move?

15. Dave says:

If truck #1 is going to work, the weight of the truck needs to be very close (and preferably lighter) than the weight of my balls.

Giant Black Balls for the WIN!

16. jeffcarr.info says:

The first truck will actually move quite quickly if you turn the wheel…

You can plainly see from the shadow that the sun is fairly low and barely to the left of the truck. However, the shadow on the right of the truck is long, so it’s obviously on a fairly steep slope going down to the right. Simply turn the wheel right and it should roll right down.

17. Tony says:

Clearly neither of these will work. In the first case, there’s nothing to push the balls off, and if it was a ramp, there’s no obvious mechanism to hold them in place while loading. The solution here, is to add steampunk style galsses to the driver, (although we can’t see him so maybe he already has them on), then, use an arduino to activate a solenoid which will release the lead balls. Of course this needs to be wireless so lets put an XBee transceiver on the Arduino and make the control end be integrated into the driver’s clothing so that he can not only control the lead balls, but also emit sequences of beeps and noise, as to entertain himself while he is flying down the road. While we are at it, lets make it sustainable by powering the electronics with a solar panel. Then lets stick some throwies all over it so that you can be seen. Lastly, we need to knit a cover for the entire thing. And give it a big happy face.

The second one won’t work because of zero net momentum transfer as others have pointed out. Not even an Arduino can make this one work!

18. Theodore Minick says:

The only way I can beat the other posters is to actually estimate the speed at which the first vehicle will move, since we all agree the second one has no chance of going anywhere.

A 1-foot sphere has a volume of approximately .524 cubic feet.

That gives each Lead ball (at the top of the chute, before it starts to fall, approximately 1500 foot-pounds of potential energy. (1484, to be a little more exact)

That energy will be pushing against almost 10000 lbs of dead weight. (I count about 20 lead balls, not counting the two on the way down, plus 1 ton of steel, rubber and meat in the truck, for a total approx. weight of 9420 lbs.)

Assuming a one-ball-per-second drop rate, this gives the truck about 2.698 horsepower, and a power-to-weight ratio of 0.00028643119089. Obviously, as the balls drop, this ratio will improve. But getting started will be a royal pain. Even ignoring friction, I’d be surprised if it got over 5mph before running out of balls.

19. Gabriel says:

Both of these problems are, in effect, simple newtonian models. They each model a system; the first is an open system, the second a closed system. Because of Newton’s first law of motion, we know that an object at rest will remain at rest unless acted on by an outside force.

In the case of the truck dropping lead balls, we have an open system. The lead balls are leaving the system, imparting energy to it as they leave. In this case, and if the energy is sufficient to overcome losses from friction, the ball dropping car will move. But fairly slowly; the lead balls appear to be roughly ten inches (this is me guessing :)), and as such have a mass of around 73kg (~160.5lbs). The truck probably has a mass of around 1000-1500 kg. So, each ball dropping will apply a relatively tiny amount of energy to it (two body collision), with most of the energy going to the ball flying away from the back of the truck.

So yes, for the first case, the truck could move, if friction could be overcome.

In the second case, where the truck has a water nozzle firing against a plate, no, it will not move. This is the case because all the energy is being kept in the system. The water jet is being captured and retained; therefore, the energy is not leaving the system. It is a closed system. The water jet pushes water out of the nozzle, and this pushes against the truck. But, the capture plate absorbs all the energy from the water accelerated out of the jet. All the energy of the water leaving is captured again and balances out the energy from the nozzle.

So no, for the second case, the truck will not be moved.

20. Sebastian Rietig says:

Of course will both cars move, all you need is a hillside ;)

21. thomtzvi.myopenid.com says:

The problem with the first is that it is depending on something to push the balls over the edge of the pipe, this is gravity as far as I can see. Immediately you notice that the pipe using gravity to release the balls is horizontal meaning that, if the truck if on a flat surface, which most roads are, the balls would not have anything pushing them over the edge to move the car.

The water truck would also be rendered imobile as the water would not have an incredilbe amount of force to not only move the axle but also to push on it instead of simply moving around it.

22. Trevor says:

Both work theoretically (no friction)- but very badly.

truck 1 works for the reason everyone else has explained.

truck 2 works because the system is not closed.

First, because the drawing shows that the water is not fully contained. Some of the water being sprayed could easily escape towards the rear of the vehicle providing a minuscule amount of force on the vehicle. It wouldn’t provide enough force to over come friction.

Second, even if fully contained, there is a gravitational force affecting the system, so it is not a closed system.
The liquid traveling down the slide is transferring force (part of the force from gravitational acceleration of the liquid) to the truck.

23. Mark says:

When you first look at them, the first will generate a force, but probably not enough to move the truck. So I say if the truck is light enough it will work, but probably not.

Again at first look, the second one makes no sense. It’s a closed system, or maybe a slight loss of water which generates little to no force.

However, if the axle were to work like a water wheel, like at a mill, some force could be generated. If there was no gear system though, in the direction of the water traveling, the truck would only move in reverse. And of course, the force of the water on the wheel would have to generate enough force to actually move the truck, so you run into the same problem as the first truck.

24. Sam H says:

The second vehicle could move very well if the flow was pulsed instead of continuous.

Chances are it would just be a rocking motion, but it would at least move.

I believe the first vehicle would move, but the second one would not. Neither is particularly practical, but that’s not really the question.

With the first, as a ball falls and lands on the ramp, the ramp pushes back with a force; however, because the ramp is angled 45 degrees, that force, normal to the surface of the ramp, is decreased and diverted. As a result, due to basic kinematics, the ball would exert an equivalent force in the opposite direction. Because the weight of the vehicle is larger than that of the ball (and it would have to be at first regardless of the actual mass of the vehicle, considering the remaining balls), it would start *very* slowly and gain a little acceleration in the regular loss of mass, in much the same way a rocket engine maintains jerk during a burn. Not at all efficient, but it would certainly move.

With the second, quite simply the reason it will not work is that all the forces involved balance each other out. While there is certainly a large amount of force from the water exerted on the ramp in much the same manner as the balls in the previous hypothetical construct, there is a necessary force in bringing that same volume of water back to the pump in the opposite direction. Due to the nature of fluids, both the top and the bottom flows would have to be moving at the same rate, thus canceling out any possibly useful work that way. Gravitational effects dealt with on the down-flow would also be canceled by the flow opposite, going up the pipe. In short, I really hope that guy in the second picture has his Flintstone’s feet on.

26. cyenobite2 says:

Thanks to Sam for introducing me to what looks to be a great time wasting website! (incredibots.com) +1

Tony = Win! For incorporating every make article in the solution :)

27. Chris Pitzer says:

It’s simple to understand if you reduce the two car designs to geometric figures.

The first can be thought of as a line. As a ball bearing leaves the car rolling backwards, the car will have an equal force pushing it forwards. If the ball leaves the car fast enough, this force *might* even have the power to overcome the car’s friction and move it forward a small distance. So, yes – in theory the first car will move.

The second can be compared to a loop. Every gallon of water that is pumped down and flows to the back of the car (pushing it forward) is then pumped back the the front of the car (pulling it backward). Since the loop is closed, every gallon of water will push the car forward and pull it backward equally, and there will be a net force of 0 exerted on the car. Thus, it cannot move.

28. The big three says:

Both trucks are part of our continuing effort to improve our fuel efficiency and keep the american economy from collapsing.

Please send 50 billion in bailout money.

KThanxBai

Long story short, the balls work, the water doesn’t.

To put it more meaningfully: the first vehicle is basically a rocket with a reaction mass that’s lent its kinetic energy via gravitational potential energy.

The second is a version of that rocket with the exhaust port capped.

And just as encasing a bottle rocket in iron will make a rocket that (at best) doesn’t go anywhere, recapturing the water prevents its energy from generating any thrust.

30. Steve Poling says:

The first car is essentially the same as a rocket car with lead balls expelled instead of exhaust gases, operating according to Newton’s 3rd Law of motion. The second car with its jet of water would operate similarly EXCEPT for the redirection of the water forward to be pumped back into the tank.

The thoughtful reader may have heard of the Emdrive (http://en.wikipedia.org/wiki/EmDrive) which some claim is essentially the same as the water car. It remains to be seen whether the relativistic effects cited by the inventor make a difference.

31. Apis says:

There are obviously a lot of very talented makers that understand how this works and who’s already given very elegant solutions to this problem. But I would like to make an attempt to explain this in terms of Newton’s laws of motion. :)

The first car work on the same principles as a rocket, jet engine or ion-thruster. All which are a type of reaction engine. If we know of the laws of motion, discovered by Isaac Newton, we can explain how this works.

1. The first law is the law of inertia:
“A body continues to maintain its state of rest or of uniform motion unless acted upon by an external unbalanced force.”
2. The first law is actually a special case of the more general second law:
“The net force on an object is equal to the mass of the object multiplied by its acceleration.”
3. And at last there is the third law which gives the name to this type of engine:
“To every action there is an equal and opposite reaction.”

***
In the first car, when a ball falls down from the roof, gravitation accelerates the ball towards the ground (second law). A steel trough on the car changes the balls direction so that it moves backwards away from the car.

But in order to change the direction of movement the car must have exerted a force on the ball (first law) pushing it backwards! At the same time the ball exert a force on the car of equal magnitude and in the opposite direction (third law) pushing the car forwards!

Would it be effective? no, and it is easy to convince yourself of this. In order to lift an object to a higher place we need to use some energy to counteract gravity. When we let the balls fall down again gravity converts some of the energy we used to kinetic energy (as the balls pick up speed).

So the energy that push the car forward is on the same magnitude as the one needed to put the balls up on the roof. If you compare that to the energy needed to push the car forward you realize you wont get very far. Not only that, half of the kinetic energy is actually wasted on the balls still having some speed when they fly off in the opposite direction behind our car.

***
The second car is actually very similar to the first. We can think of the water molecules in the pipes as small lead balls. The engine is used to push the ball upwards giving it potential energy. It then falls down again, hitting the trough like in the first car. This time however, the ball is caught again by the car. That means the car must exert a force on the ball to stop it (first law). In order to stop it, the force must be equal but opposite in direction to the fore that was used to propel the ball backwards to begin with. At the same time the ball exerts a force on the car of equal magnitude and in the opposite direction (third law) pushing the car backwards again. So the push forward is counteracted by a push backwards when the ball is caught again. The net effect is that the car stand still.

32. Peter says:

Place either vehicle on an inclined plane and the weight of either system will move them so both move. On a flat plane, conservation of momentum will move the 1st [mv=(m-m_b)v]. The second one will not move because the forces sum to zero so no movement [F=MA].

33. Brandon says:

Actually, I don’t believe that either system would work. The water jet truck is obvious, a closed system that cannot impart any forward momentum to the truck due to the dispersion / collection relationship. The ball truck, I believe *would* work, but would require an outside force to get it started, in other words, the balls don’t look to me like they would roll themselves off the top of the truck. Furthermore, I seriously doubt that rolling only one ball off the top of the truck would start it in motion. From the looks of the diagram, the trough looks to be level for the most part. If that is the case, the truck would not only have to overcome enough friction to move itself, but also move forward quickly enough to overcome the friction of the next ball in the trough (greater surface area due to curvature) to force it off the drop. I say that neither will move in the *real* world.

34. Apis says:

Actually I kind of presumed the roof is tilted to allow the balls to fall of. If you can adjust the tilt you even have a way to adjust the power (e.g. “throttle”).

Even if you can’t, if the friction is small enough, there is no force acting on the balls when the car accelerate forward (or very small). Thus the balls would stand still relative to the ground (Newton’s first law). Relative to the car they would move back off the roof and thus power the car. In principle it would work. Giving everything the right dimensions and making sure friction is low enough that it will work efficiently is what engineers are for. :)

35. bfos7215 says:

Myth Busters!

36. JM says:

I think the second car will move (ignoring rolling resistance, etc).
If instead of a ramp it had a turbine in some way connected to the wheels, it would move. Turbine blades deflecting the water transfers some of the kinetic energy from it.
Now think of the ramp as a single blade. By slowing the water and changing it’s direction theres a force applied on the ramp.It might not be that big, but it is there.

37. JM says:

I think the second car will move (ignoring rolling resistance, etc).
If instead of a ramp it had a turbine in some way connected to the wheels, it would move. Turbine blades deflecting the water transfers some of the kinetic energy from it.
Now think of the ramp as a single blade. By slowing the water and changing it’s direction theres a force applied on the ramp.It might not be that big, but it is there.