# Pushing a kid on a swing

1. Feb 19, 2015

### cragar

My teacher told us to push a kid the highest on a swing, that you want to push on the bottom of the path.
Im not sure why this is the case, obviously you wouldn't want to push against the kid.
But it seems to me that as long as you were pushing on the downward swing it shouldn't matter. Because when you push the kid, you are adding energy to the system. it seems like the energy you add plus the total energy the kid had on the swing would be constant.

2. Feb 19, 2015

### RUber

I would think pushing him on the way up would be better.
You might argue that maximum velocity is reached at the bottom of the path, so if you are adding a push there, any additional speed goes right into the swing height.

3. Feb 19, 2015

### jbriggs444

If you are applying a fixed force for a fixed time, you do the most "work" when that force is applied over the greatest distance. That would be when the child is at maximum velocity.

"Work" in the physics sense is the product of force times distance covered in the direction of that force. This concept of "work" is useful because it turns out that the "work" done on an object is equal to the mechanical energy gained by that object.

This makes a certain amount of sense. If you push on a wall, it does not matter how long or hard you push. You are not adding energy to the wall. But if you push a cart up a hill using a fixed force, the faster it is moving, the more rapidly it is gaining height (and thus potential energy).

4. Feb 19, 2015

### A.T.

That probably assumes that you can apply the same force, for the same time, regardless at which point you push. A rather unrealistic assumption for pushing by hand. More realistic for a rocket powered swing.

5. Feb 20, 2015

### Staff: Mentor

That might be said on the assumption that your "push" is going to be horizontally directed? At any other point on the trajectory, some of your horizontal effort would be wasted. In practice, pushing along with the forward downswing seems best, especially when (through tedium) your effort is probably going to be expended over a distance of just two lazy paces.

While pushing on the forward upward swing may be effective, it's awkward and you're more likely to lose some teeth.

6. Feb 20, 2015

### sophiecentaur

What counts here is the amount of Energy you are introducing during each cycle. The work done during each push will depend upon the force times the distance that the push lasts. The answer to the question is basically 'it depends'. If you have very long arms which are not very strong then the place to push it is when the swing is traveling fast. Short, stronger arms may not be 'matched' to pushing the swing where it is going fastest (it could leave them behind) but could increase the height near the top of the swing with a large force, moving slowly. The long, weaker arms could not exert enough force over a short time, to inject enough energy, if they are used to push at the top of the cycle.
I am assuming, here that the two pushers inject the same amount of energy.
There are many examples where Matching the Input (Impedance) to the output (impedance) of a system can maximise the energy transfer - this is just one of them.

7. Feb 28, 2015

### tech99

For an oscillating system, the sustaining force is always in quadrature to the oscillation. Have a look at a steam engine for instance. With electricity, with a series resonant circuit, for a given current, the voltage across the inductor leads the current by 90 degs, that across the capacitor lags by 90 degrees but that across the loss resistance is in phase with the current. V and I must be in phase for energy to be supplied.

8. Feb 28, 2015

### sophiecentaur

That refers to a sinusoidal driving force. When you push a swing, you are delivering an impulse which occupies only a small portion of one cycle. The optimum time to apply an impulse will depend on the details of the situation.

9. Feb 28, 2015

### Spinnor

I wonder if your teacher ever pushed a child on a swing. I think you can best supply energy to a child by adding energy at one of the end points. See video,

10. Feb 28, 2015

### sophiecentaur

You need to be able to produce a relatively large force to do that but you only need to be able to 'lift' the child + swing, in order to get it as high as you like, all in one go!
You can get away with a much smaller force when the child is travelling horizontally at the bottom.
But the original statement / question doesn't have enough detail to apply to a real situation. The teacher's statement is too vague to be correct.

11. Feb 28, 2015

### Spinnor

Your arms can only move so fast, pushing at the bottom does not make sense to me. Have you ever seen someone do that?

12. Feb 28, 2015

### sophiecentaur

Precisely. You need less force but more speed at the bottom. Our arms are not really matched to that requirement. Otoh, you could not add much Kinetic energy at the top of the cycle if your arms were weak.
That teacher has a lot to answer for, I think. I wonder how many other examples of sloppy thinking are presented to kids all over the world.

13. Feb 28, 2015

### Spinnor

You can add loads of energy at the top where are arms are matched for large forces at low speeds. It does not take many pushes (not at the midpoint) to get a child to the horizontal. I know this from actual experience, as do you if you have children.

14. Mar 5, 2015

### cragar

My teacher said it had to do with F*v dt =work ,F=force , v= velocity dt= time change , same force but with different speed. max speed at the bottom of the path. I tried thinking about it with storing energy in a compressed spring. And using that to push the swing.

15. Mar 6, 2015

### A.T.

Yes, but as already said, this makes the completely unrealistic assumption that you can push with the same force, for the same duration at a higher velocity. This ignores the constraints of human anatomy and is thus of zero practical relevance.

If you had rockets attached to the swing, then yes, you should fire them at max. speed, to get the most energy to the swing out of the same amount of fuel.

Last edited: Mar 6, 2015
16. Mar 8, 2015

### cragar

Ok so if I had rockets attached to it I would fire them at max speed. This seems strange to me if I consider the moving frame with the swing. If I am with the swing it would have zero speed relative to me but if i fired the rocket for the same time, it would seem to add the same energy.
What if instead of a swing we had 2 elevators out in space, one moving at some speed v and another at rest relative to the same point. If we had rockets attached to the elevators and fired them for the same time, it would seem that the same amount of energy was transferred to each elevator. I mean the elevator moving at some speed v, from the rockets point of view you could tell it was moving. seems the same to me. The swing probably has something to do with it accelerating. There is probably something im missing.

17. Mar 8, 2015

### jbriggs444

One way to resolve the conundrum is to realize that energy depends on your choice of frame of reference. The work done by a force can also change depending on your choice of reference frame.

But that is somewhat unsatisfying. It feels like there is something missing. And there is. While the energy work by a force depends on your choice of reference frame, the work done by a third law force pair is invariant. In the case of a rocket, there is a third law force pair. One element of that pair is the force of the exhaust stream on the rocket. What is the other element?

18. Mar 9, 2015

### Jewish_Vulcan

You would have to push at the end of the swing where he PE is highest to have the greatest impact on how high the swing goes. When you push where PE is highest you apply a positive force or negative force depending from where you push. The swing has the most displacement in a continues direction whether positive or negative before changing directions when the PE is highest.

19. Mar 9, 2015

### A.T.

Only if the force and application duration depend on the velocity, like is the case for a human standing on the ground. If force and application duration are fixed, then the above is the worst place to push.

Last edited: Mar 9, 2015