Simple physics Q - pushing a stroller.

[Snarky_Kong]

@cmyk

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?

No. Shoving would take more energy. Drag doesn’t increase linearly with velocity; the extra energy used when you were going faster than average is larger than the energy you save when going slower than average.

[TokyoBayer]

@Sage_Rat

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.

Uuumm. Can you please link to somewhere which will back this? Admittedly, it’s been a couple scores of years since I took engineering, but from my distant memory, this is absurd.

The applicable equation is:

F=ma

where
F is force
m is mass
a is acceleration

The forces which is slowing the stroller down are supplying a constant negative acceleration to the stroller. It takes a constant positive acceleration in order to maintain a constant speed.

Look at it like this where F = F1 + F2 where you supply F1 in a positive direction and D is the net forces in the negative direction.

F=ma
a=F/m
a=(F1+F2)/m

For the net acceleration to be zero, then F1 must equal F2 but be in the opposite direction. F2=-F1
a=(F1-F1)/m
a=0/m

The OP is asking if it makes a difference between pushing at a constant speed, which would just counter the resistant force F1=-F2 or to let the resistant force take over F1=0, then accelerate by supplying a force F1>F2.

There actually isn’t a really easy way to calculate this to great precision but it can be assumed that unless there were greater wind resistance or other factors which caused nonlinear acceleration.

For example, if you look at water skiing, the boat requires greater force to get up on a plane both for it and to drag the skier out of the water. Once on their respective planes, it takes less energy to maintain the plane (less water resistance) than to slow down and get more of the objects into the water.

Likewise pushing a baby stroller over ice may have additional factors which could not be neglected, in addition to any added danger to the baby or risk of divorce from the mother.

[TokyoBayer]

@kyogi

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.

Except that you aren’t keeping your arms locked. You’re constantly pushing, relaxing, absorbing the differential, just on less of a scale.

[cmyk]

@Snarky_Kong

No. Shoving would take more energy. Drag doesn’t increase linearly with velocity; the extra energy used when you were going faster than average is larger than the energy you save when going slower than average.

You’re right of course, as you wouldn’t be pushing a stroller in a vacuum. Nonetheless, I agree that shoving is more of an energy drain than pushing steadily (despite the drag factor).

If we could distill the essential problem, by setting the stroller on, say the moon, with a flat, paved surface, would the only factor that would add to the energy between the two methods be distance over time?

The inherent nature of a person applying a force would be far more chaotic when shoving off, catching up, shoving again, etc. There’s no way they’d be able to control the vector of force as accurately in the direction of motion as they could by walking and pushing.

Our arms act as natural shock absorbers, but shoving the stroller would introduce forces that would push the stroller down a bit to keep the acceleration from forcing the stroller into popping a wheelie, or even flipping backwards due to a higher center of gravity—so I have to assume there’s some energy wasted there too which you wouldn’t have if you were in constant control at steady acceleration.