Trucks carrying bowling balls
Tom and Jack each own identical trucks, on which they each carry an equal number of bowling balls with equal weights. Tom keeps the bowling balls loose so they move around on the truck, while Jack has them tightly secured.
If they travel the same route with lots of bumps, pits, and stops, then whose truck will consume less fuel?
Details and Assumptions:
- Both the drivers are equally skilled.
- Air drag and other factors that may affect the fuel efficiency of the trucks are also exactly the same for both the trucks.
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9 solutions
Given that bowling balls have very low rolling resistance, the energy required for them to move around is pretty tiny. A sneeze could move a few. Even if they were constantly rolling back and forth, I cannot imagine very much energy would be wasted on a flatbed truck surface.
On the other hand, every time Tom's truck hit a bump. the balls would fly a little bit in the air. Bowling balls being heavy, this takes energy, which is also transferred from the truck. Since each bump will transfer some amount of vertical force to each truck - lets see what can happen. In Jack's truck, the balls themselves are tamped down, so every bump causes the entire mass of truck plus all the balls to jump up, and Jack has to work harder at maintaining the same speed (or take each bump slower). In Tom's case, the truck jumps a little less and the balls jump a little more, making it easier for him to maintain the same speed over bumps with less effort than Jack. This is because the loose balls dissipate the vertical force far more efficiently - allowing a few balls to jump while the truck as a whole remains relatively level.
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It is not rolling, but collisions, that lose most of the energy. Collisions do waste a lot of energy.
The impulse gained by the trucks when they hit a bump is same for both trucks. What can we say about the heights by which the centers of mass of the trucks rise? What happens in Tom's truck when the balls land back on the truck?
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Actually, collisions between highly elastic balls such as bowling balls will waste negligible energy. Collisions waste energy only if inelastic, else they merely transfer.
Balls landing back to not transfer any new energy other than what they gained in going up. The reason a loose mass will waste less (maybe) is that the only real loss is when the balls move vertically. There, individual balls jumping is much more likely to be efficient the whole solid mass jumping. Remember, we are talking wastage; without wastage the vertical jump of 1 ball will merely be 10x that of ten balls etc. However, if the balls are loose, the truck chassis is likely to jump less and the balls a lot more which is probably more efficient that the whole tightly lashed mass of balls and truck jumping. In a perfect world (vacuum etc) the two would be the same (since the vertical impulse should be the same). Total momentum will be the same, but in Tom's case the balls would jump more (say x) and the truck body a little less (say y) while in the second the whole mass will jump a bit more than x and less than y to keep the same momentum. However, in the real world, there are probably far more mechanical losses in moving a large mass - friction in the suspension, air resistance, flex in the body of the truck etc - than in moving a number of unencumbered, highly elastic bowling balls.
Not to mention that the longer the balls are in the air, the more efficient the first truck. If the road is very bad and the balls spend (say) 10% of the time in the air, then 10% of the time Tom's truck is not loaded and thus using less power moving horizontally.
Collision, friction between the balls, rolling resistance, these are likely to be miniscule for bowling balls. Replace with, say, tennis balls or basketballs or balls of hay and the situation will be different.
So two potential benefits: 1. Balls are easier to propel vertically if loose, than the truck body plus the balls as a whole 2. While the balls are in the air, the truck uses less fuel
When the truck goes over a bump, and bowling balls are in the air, wouldn't the truck be temporarily more efficient ? It just seems that there are too many variables in this environment ? Perhaps an actual study would've been nice, but that will never happen.
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The bowling balls are very heavy, isn't the time they spend in the air very little? What if when the balls land back on the truck?
The key word is "heat". If the balls and the walls of the truck were perfectly elastic then all the energy used to move the balls around in the bed would be returned and the total energy used by the truck would be the same. Since nothing is "perfectly elastic" there will be some small amount of heat produced, which must come from the engine.
Shouldn't the secondary energy come from the gravitational potential energy of the truck and the balls before they fall into a pit?
The origin of the potential energy prior to the truck falling into a pit is also from the fuel. Gravity, being a force, is not a source of energy.
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Potetial Energy of a truck falling into a pit comes from the fuel? What if the truck with no engine or fuel was parked on a slight incline caused by frost upheaval on the edge of the pit, the brakes give out letting the truck to roll into the pit? Potential energy didn't come from any fuel. Just a hypothetical scenario. The potential energy is always in the truck until a force (in this case gravity) acts upon it and turns it into kinetic energy, The "kinetic" energy of the truck in your example came form the fuel acting on the pistons transfered through the rest of the engine components and drive train to the potential energy of the truck turning it into the original kinetic energy pushing the truck into the pit. Since the wheels are no longer in contact with the ground the fuel is no longer acting on the trucks potential energy. Gravity takes over as the force acting on the trucks potential energy keeping the truck moving.
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Yes. The potential Energy of a truck falling into a pit does comes from the fuel. In your example of a truck with no engine or fuel, some other type of energy source has placed the truck at a higher elevation so that potential energy can be stored and then released upon falling into a pit. For example, the truck had engine and fuel at some point, and after going to a higher elevation, the engine was removed. In any case, gravity is not a source of energy, and it is just a force.
How significant do you think would the difference in fuel consumption of the two trucks be?
Yes this shows that there is more work done by Tom's truck's engine, but not that the fuel used is less. So while the engines may have the same fuel efficiency for all levels of speed or torque, when accelerating rapidly, Jack's load will be lighter (as the balls slide to the back), and the load will only be greater after an initial period of acceleration. So Jack has a lighter load when the engine is very inefficient, and a heavy load only when the engine is more efficient. My guess is that this could easily outweigh any secondary motion mechanics.
While energy lost on breaking introduces a whole new kind of ball game.
So another way of explaining it is while Tom's engine is accelerating the balls go to the back of the truck = do not get carried as far as Jack's balls. While Tom's balls advance only while he is breaking - when the engine and fuel are not in use.
Now the loose balls roll to the back and get energy imparted into them by the back of the truck box on acceleration. On deceleration the balls roll forward and return some of the energy when the hit the front of the box. Would they not?
Whether they are allowed to move or not, the energy that causes the secondary motion is still generated. If they are covered by the tarp, then the energy is simply absorbed by the tarp. If we assume that the engine is equally efficient through all speeds, and that the tarp has no impact on aerodynamics, then I see no argument for either truck using more or less gas than the other.
I disagree with this assessment. Bowling balls are designed for elastic collisions. A perfect elastic collisions use no energy. The walls of the are also approximately elastic in low velocity collisions. The threshold velocity depends on materials. Also, 'rolling resistance' is not a fiction, the energy going into rotating a ball can be retrieved by using the rotation.
The above would not matter (because nothing is perfect and there is always some dissipative forces) if there wasn't a competing effect. The competing effect is when there is a minimum or maximum in the acceleration curve (and the balls are still rolling) the balls do not attain the same velocity as the truck. Hence the truck effectively weights less. The truck dissipates a lot of energy.
So which effect wins? Can't say. It depends on too many incalculables. But the use of 'bowling balls' indicates an elastic collision approximation, so I went that way.
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I see what you are saying. If the acceleration of the truck changes direction quickly, then the truck with loose balls will consume less energy. But it will have more collisions and rolling.
(Rolling resistance refers to the fact that since a ball is never a perfect sphere, any rolling ball comes to a halt due to friction, and this energy cannot be retrieved back.)
It can be difficult to decide between the two factors. The balls would be colliding and rolling around most of the time, and the acceleration of the truck wouldn't reverse direction as often over a long trip. There can't be a big difference between the velocities of the truck and the balls, because they both travel the same distance in the almost the same amount of time.
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Remember, bowling balls are designed to ver highly elastic and have very very low rolling resistance
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@Sankarson Banerjee – Also remember they said there were lots of stops. Any energy loss during a stop will be taken by the breaks not fuel consumption. Acceleration on pickups with weight in the back is relatively slow. This gives next to no impact against fuel consumption and gives the balls more time to not be moving with the truck which also equals less fuel consumption. This is not including the better traction had on the rear wheels upon the balls hitting the bed of the truck. More traction means better fuel economy. In this case when it is needed most, coming off a bump.
Solved this while drunk (right now), chose Tom as I've misread "which truck consumes MORE energy" 😂
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Actually makes sense, as energy is needed to make the balks move around in the truck. Lesson learned: don't drink and solve Brilliant problems ☝️
I would think the bowling balls would fall off allowing Tom to require less energy to go farther.
This question should be a Basic one instead.
What are you guts thinking it will be Tom. The tailgates are down and Tom will lose his load thus he will get better mileage. Duh
I was dumb, I voted tom thinking it asked which consumes more fuel...
Relevant wiki: Conservation of Mechanical Energy
Tom's truck has to translate the balls just as Jack's truck does, but it also has to excite all of the additional "vibrational modes" associated with the loose balls, which takes more energy. Analogously, a 230-pound man with considerable excess fat stores probably burns more energy walking / jogging than a 230-pound lean (muscular) man does.
I voted for Tom's truck.. why? Did you see the picture? Tom's bowling balls will fall out of the truck which will lightened up Tom's load. That would save a lot of gas than Jack's.. So whoever think that the answer to this question is correct for Jack... is absolutely WRONG!
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I answered before there was a picture
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The picture is just to show the bowling bowls, obviously, when they drive their trucks they will close the rear doors.
tu keep the rolling in a fixed position we have tu give more energy than when freee
Actually, there is little evidence that a 230-lb fat person uses more energy jogging than a 230-lb muscular man. Really heavy muscular men burn up massive amounts of calories doing anything, and eat correspondingly as much. A muscular man can probably outrun a fat man of the same weight, but thats because of a poor metabolism (not burning enough calories). Its like comparing a 1930s wheezer to a modern Ferrari of the same weight.
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Yes, but that's basal metabolism. I'm not interested in that. I'm talking about the energy used in locomotion.
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fat man struggle not because they're burning more calories but because their lungs and muscles and heart are weaker. Indeed, they usually burn fewer calories for the same exercise, making slimming down that much harder. Take, for instance, an exercise machine where you're pulling a light weight repeatedly (like a rowing machine). No "fat vibration" or body weight involved, but you can be sure the fat guy will tire out far before the fit guy. Its not because he's burning more calories, but because his lung capacity is lower, his muscles are poorer are getting rid of lactic acid buildup, heartbeat faster than the fit guy.
Fit people, like Ferraris, have great output but not great efficiency. Indeed, the reason for people to get fat is that their bodies prioritise efficiency over output and store the difference. Muscle burns a lot of calories, and the bigger the muscle the more it burns, even for the same work. Again, not unlike a car engine - the bigger the engine, the less efficient it is.
I don't know about this, but it seems to me that any force(s) that might lead to vibration or movement of the balls would be exerted on the balls irrespective of whether they are tied down or not. The way I see it is that the fact that the untethered balls move does not mean more energy has been applied to them or that more fuel has been used to move them. It just means that a restraint has has overcome whatever might have caused them to move.
Yes, effectively more direction changes for the loose balls = more energy needed.
- possibly a more visible/intuitive demonstration of this - it is likely to provoke more wheelspin and lateral slip due to the weight leaving the trick at times, crashing down at others, slamming into the sides and generally shifting the centre of gravity.
That said, I didn't answer at all due to the statement: "Air drag and other factors that may affect the fuel efficiency of the trucks are also exactly the same for both the trucks."
The balls (in pick-up trucks as pictured) being secured/covered will affect the drag , meaning some properties of the balls might be excluded using that language (possibly really down to the images showing covered and uncovered pick-ups - if there were enclosed vans, I wouldn't have questioned it). So the statement, combined with the images might imply there's a very specific "non other" effect, the questioner is considering, leaving room for anything else to be thrown out...
Even though muscle mass is much denser than fat mass, muscle mass also burns more calories to perform the same work (say walk). The lean 230 lbs man will burn more calories than the "fat" one.
The bed of Tom's truck will be dented and littered with chips of bowling balls. That kinetic energy came from the fuel tank.
The difference will be minimal. Is there experimental data out there?
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I would also like to know how significant is the energy loss because of this.
Yes, but don't forget that the rope also 'absorbs' some energy. It stretches and contracts, generates heat, and some fibers may break (otherwise ropes would last forever). You would need to compare the dents and chips to the stretching/contraction/fiber breaking of the rope, and that's not too evident.
You are assuming that they would dent, but there is the slight possibility of that just not happening. What is the answer then?
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Even if there are no dents, there would be more collisions between the balls and the wall, and energy would be lost at each impact.
What about the time the balls spent aloft after each bump. Reducing the load that the truck must bear?
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Since the states of both the trucks are same before and after the bump, the impulse gained by both the trucks is the same. Where do the balls get the energy to jump up against gravity? What happens in Tom's truck when the balls land back on the truck?
Just consider turns. When the Tom's truck turns, the centrifugal force will act on loose balls carrying them to the side of the truck opposite from the acceleration direction. That will cause centar of mass to shift to the outer side of the truck, making it harder for truck to turn and requiring more fuel.
what about the added weight of the device used to secure the bowling balls? ;)
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Hahaha, oh I totally forgot about it. That changes everything ;)
Details and Assumptions: ... other factors that may affect the fuel efficiency of the trucks are also exactly the same for both the trucks.
Implies that both trucks carry the same weight.
centrifugal force
Centrifugal force, Inertia, or just 'the reaction to centripetal force'? The cause of many an argument.
Either way, rotational forces on the balls are not in play until the balls come into contact with the side of the truck. Before then, they just wish to continue in a straight line.
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Centrifugal force is an inertial (fictitious) force. Note that inertial forces occur only in systems that accelerate and rotation is one kind of acceleration (change in direction of motion).
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That may be the case, but if the loose balls are in a position of relative rest before the truck enters a turn, I maintain that there is no force or acceleration on the loose balls until they contact the side of the truck. Between a state of relative rest and the moment that they begin accelerating around the turn (upon contacting the side of the truck), they have no change in direction of motion, only the truck does, because the balls are loose.
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@Jonathan Quarrie – It all depends in which reference frame you look! That's the interesting part when you deal with inertial forces. There is no actual force or acceleration on loose balls, but that's when you look in reference frame of independent observer or loose balls themselves. However, we are interested in the reference frame of a truck. In the reference frame of the truck, truck itself is not moving, and when truck starts turning (in the reference frame of the independent observer) loose balls suddenly start accelerating, and grouping in one side of the truck. That is the result of the centrifugal force, that, once again, doesn't actually exist (for independent observer), but exists for the truck which is accelerating.
I did edit my initial comment soon after posting it, which originally only questioning whether you meant Inertia, so my apologies if that was all you were replying to.
The balls on both trucks have identical principal Kinetic Energy, KE, in the directions of the trucks’ travel. The balls on Tom’s truck have additional KE due to their lack of constraints and resulting movement. Their collisions convert their KE to Heat Energy, HE, which is transferred to the atmosphere. Energy cannot be created or destroyed but it can be transformed from one type to another. In this case the HE is supplied by the fuel in Tom’s truck. Therefore Jack’s truck uses less fuel than Tom’s truck.
Yes, energy remains conserved. The energy that is carried by the movement of the balls must be supplied by the truck.
Since Tom's bowling balls are loose, they roll to the back and press against the back of the truck, causing the truck to struggle to move forward, whereas Jack's bowling balls are secure, so they only exert force downwards due to gravity. Because of the extra force going backwards in Tom's truck, his truck will consume more fuel.
When the truck wants to accelerate, the balls will roll to the back and press against the back of the truck and when the truck hits brakes, the balls roll to the front. This way the balls will resist in both stopping as well as in accelerating.
Jack by packing all that tightly made "1 system" whereas Tom kept them loose which makes it a multi system i.e., they all have their own motions sometimes in the direction of truck and sometime opposing it, which will result in more energy to compensate their drag. Hence, more fuel consumption in Tom's truck
I think Jack's truck requires more energy because it is applying the force on all the balls constantly throughout the motion. But as Tom's truck jumps on bumps, the balls also jump but with a horizontal velocity (inertial), so till the time they descend back to the truck bed, the truck applied force on lesser balls. Also, some balls might get fallen off the truck during the journey. ;)
For the moment they are in the air, yes. But the moment they accelerate back to the truck bed and impact, their force increases which balances perfectly with the loss of mass during their air time. But the heat generated from striking the truck bed and each other means that more energy needs to be added to the equation, which can only come from the trucks consumption of fuel.
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I totally agree. When we say that the truck uses less energy while the balls are in air, we should also see that the truck uses more energy when the balls fall back to the truck.
Conservation of energy. Vehicles movement except balls wrangling being equal, there is more energy spent in the internal interaction between balls. That had to come from somewhere, only possible source given the circumstances is from the fuel. Analogy: which requires more energy, moving an ice block for 1km or moving the same amount but keep close to boiling point... Brownian movement needs energy. Another simplified approximation to facilitate explanation... If the trucks had a constant rectilinear movement, the fact that they are in motion would be irrelevant and then the question would be - between a vehicle which sits perfectly still and one which wriggles the balls, which one consumes more fuel... Bit of a no brainer.
The engine produces a given amount of energy, which is shared by the truck and the balls. The freer the balls are the greater energy they will acquire and hence the truck is left with lesser energy.
The loose bowling balls in Tom's truck have two types of movement, one is the primary movement, which is going forward at the speed of the truck. There is another movement, which is when they are tossed around within the semi-trailer. That is called secondary motion in mechanics. Burning of the fuel provide energy for initiating the secondary motion. It also provide energy for all the impacts among balls, between balls and walls, as well as energy to overcome balls' rolling resistances. These all turn into heat that is released to the environment. So Tom's truck consumes more fuel. The balls in Jack's truck, on the other hand, only have the primary motion, so Jack's truck consumes less fuel.