If I’m running or walking and pushing a stroller, I can keep my hands on it and push using a constant force, or sometimes I give it a little shove and then catch up, shove and catch up etc.
Does one or the other use less energy? My guess is that since I’m moving the same object the same distance, it’s the same amount. Am I wrong, and is one of these methods more efficient?
Just my guess but I’d vote for constant pressure as most efficient. Mainly because you are using a much less complex system to do it.
With a constant push your upper body is effectively locked in place.
With a push-follow method your upper body is flexing and contracting. Any inefficiency in your upper body movements are added to the inefficiencies of your gait which is present in both situations.
Of course “most efficient” is based purely on mechanical systems. Your body as a complex system may fatigue easier if you restrict your upper body movements so I’m at a loss as to which method would actually cause less fatigue.
There’s more air drag on the stroller with the shove method.
If you wait for the stroller to stop altogether, then you would have to expend greater energy to overcome the static friction instead of kinetic friction.
When you shove it you accelerate it faster, so slightly more energy is used to cover the same distance. I’d imagine your hands also have to move a bit to clasp and unclasp, etc.
It could also be restful though, if different muscles are used. In human terms holding a fixed position feels harder than moving the muscles.
If you were headed downhill and it would naturally roll away, then it would use even more energy to speed up your whole body to catch it. Plus, you know, precious cargo and all that.
More air drag when it’s moving faster than the runner, but less when it’s moving slower than the runner (which it has to do for the runner to catch up to it).
It probably nets out to more drag, but it’s not quite that simple.
Either way, you’re doing work against the various dissipative forces (friction, air resistance, etc.). The total work done is equal to the integrated product of the force times the distance. The distance is the same in either case, so the work will depend solely on which has the greater dissipative forces. A sizable chunk of the dissipative forces (such as bearing friction) are approximately independent of speed: These won’t matter. Another chunk (such as wheel deformation) are proportional to speed: I’m pretty sure (but might be mistaken) that these won’t matter, either, because the intervals where you’re going slower than average will be balanced out by the intervals where you’re going faster (assuming you’re maintaining the same average speed in both situations). Finally, there are some dissipative forces (such as air resistance) that are proportional to the square of the speed: For these, the segments where you’re going faster will be more significant than the segments where you’re going slower, and make the irregular speed less efficient. That said, though, at typical stroller speeds, air resistance isn’t very significant at all, and so the difference in efficiency will be slight.
Yes…it actually IS restful. Being able to pump both arms feels like a vacation after pushing that thing with one or the other!
And I do, sometimes, end up having to pick up the pace to catch the thing 
I don’t run on roads or anything, though, so there’s not much danger. It does seriously suck to try to coast a bit for a break and have to sprint instead!
Then it looks like the conclusion is that I’m using the same energy, but being able to relax my arms a bit makes it worth it. Thanks!
Drag scales as the square of velocity. At the same average velocity, the constant velocity will always experience lower drag. It’s pretty simple.
We talking African or European strollers?
What about on a treadmill?
A baby or a coconut?
Well, first assume a spherical stroller. . .
Definitely more efficient to keep both hands on the stroller because when you shove the stroller and it rolls onto the busy road with cars whizzing by you’ll have to sprint to catch it and then expend lots of energy mending your bones that were crushed by that speeding pickup truck.
Although… I suppose if you immediately died from your injuries, you would be conserving energy (not counting the energy moving and prepping your corpse for burial).
I was mostly thinking of inertia, which you don’t mention. If the constant speed is the same in either case, he only needs to accelerate the mass of the stroller once, to the desired speed and then maintain it. If he wants to take it to double the constant speed then he has to apply double the force, and then do so again and again and again. Are you sure that the force which has to be expended to maintain the natural inertia of something against drag and friction is equal to completely wrangling with the stroller itself constantly?
I’m not sure how to parse this paragraph, but to give it a shot:
Moving the stroller at a given speed, friction/air resistance/&c. can be modeled as applying a constant force to the stroller continuously. If you apply exactly that amount of force to the stroller, the stroller will move at that constant speed exactly (and the work done will be force * distance).
If you apply any less force than that to the stroller, it will slow down. If you apply any more force than that to the stroller, the stroller will accelerate. If we model dissipative forces as being constant for all speeds (e.g. stroller with perfectly rigid wheels in a vacuum), it will accelerate forever. It is not simply a “twice the force → twice the speed” rule.
If you instead model the dissipative forces as *increasing *with speed, the stroller, when given enough force to exceed the current dissipative forces, will accelerate until the dissipative forces for the new speed match the additional force.
But…Exercise shouldn’t be efficient, efficient is less effort. To get the most of your exercise you need to focus on doing it as ineffciently as possible. So keep pushing every now and then, and hop on one foot part of the way.
Say that I am a force which wants to act to keep an object which is in motion at the same velocity it is already in motion.
D is a set of forces which want to act to bring the object to a complete stop.
D must expend at least as much energy as is in the object to bring it to a stop as the object actually has. If it is a mass which weighs 10kg and is traveling 1m per second, then my object has a total of 10 joules at its disposal and 10 joules worth of work has to be done in order to bring the object to a standstill.
Now say that it would take D 10 feet to bring the object to a standstill. We can say then that D is expending 1 joule of energy per foot, on average.
In my understanding, the law of inertia says that things don’t like to lose their energy. I don’t need to expend 1 joule of energy every foot to counteract D because I have inertia on my side. To pick a random number, we’ll say that I only have to expend 0.5 joules of work per foot in order to keep the object moving at a constant velocity.
If the object starts at rest, however, then I have the same job to do as D does, except in reverse. I have to expend at least 10 joules to bring the object up to speed. In this case, I don’t have inertia on my side, so if I bring it up to speed over a space of 10 feet, then I also have to match the 10 joules that D attempts to apply in the reverse direction. For the first 10 feet of my trip, I expend 20 joules. For the remaining 90 feet, I expend 45 joules, for a total of 65 joules of work for the 100 foot walk.
If I bring it up to 1 m/s then let it drift to a stop, bring it back up to 1 m/s let it drift to a stop, etc. then my math becomes 20 joules per every 20 feet. Over the course of my trip, I end up expending 100 joules instead of the 65 I could have done.
To put it simply: Constant momentum vs. Shoving would only be equal, in terms of energy exerted, if the time it took to cover the distance was equal, correct?
If shoving the stroller moves it from point A to point B in half the time than maintaining a continuous force, then shoving it in bursts of acceleration would require that much more energy; especially if you were running or jogging to catch up.
What you can’t be sure of is if shoving is getting you to your destination faster or slower than pushing it would.
Mathematically, I think it all works out equivalent. (of course thinking ain’t my strong point after eight beers.)
Practically though, you’re talking about your work. For the body to hold the same position and work only its legs to maintain velocity of travel is, in practice, less work than pushing, releasing, grasping and absorbing the force of velocity differential, then pushing again.