# How is this child able to move their crib while standing inside of it?

I was scrolling Instagram and saw this Reel which at first was normal but when I started to think how the child was able to move then I got confused. The video shows a child standing inside of a crib and repeatedly bouncing their body against the rail of the crib, which causes the crib to move.

Here is the logic behind the confusion:

The center of mass of any system if initially at rest will move only if there is an external force acting on the system.

In this case the child is applying a force on the bed in the forward direction by hitting it continuously so friction should be acting on it in the backward direction but if that's the case then they should move in the backward direction and not forward.

Can someone give an explanation for this kind of motion of the child?

# Edit :-

As per the comment I am adding the screenshots of the child and the crib initially and how it ended up after some time (though it will not tell how the child make this happen)

• Why would you think the child and the bed would both move backwards? Commented Jan 30, 2023 at 16:48
• For those of us who do not wish to use Instagram... Could you please provide either a screenshot, or a diagram?# Commented Jan 31, 2023 at 9:46
• This question (and top answer) have an XKCD vibe to it. Commented Jan 31, 2023 at 16:04
• Try it yourself... sit in a chair and keep your feet off the ground (either in the air, curled up on the chair, or otherwise around the chair legs). Then wiggle around and try to move the chair. It's not that difficult... how are you doing it? Commented Feb 2, 2023 at 3:47

The kid moves their crib by expertly exploiting the difference between static and kinetic friction.

Initially they pull themselves towards the bars relatively slowly, or more crucially with a relatively small acceleration. The force on them required for this acceleration comes from the crib. They pull the crib to the right and, by Newton's 3rd law, the crib pulls them to the left. The key thing is that the force they apply on the crib is small enough that the force of static friction between the floor and the crib is large enough to keep the crib in place, so the crib does not move to the left during this stage.

Then the kid collides with the bars. Their speed to the left decreases quickly, which means, for a short time, they have a large acceleration to the right. For this to happen there has to a be a large force on them to the right. This comes from the bars of the crib but it means that the kid simultaneously applies a large force on the crib to the left. This force on the crib is now large enough to overcome the static between the crib and the floor and it begins to slide to the left. When sliding, the coefficient of friction between the floor and the crib is less than when it's not sliding which helps the crib move a bit farther left before coming to rest.

Now the kid pushes the bars away to the left keeping the crib moving to the left. After that the kid pulls themselves towards the bars again but, not with enough force to cause the crib to slide to the right.

Since there is a force of friction between the crib and the floor, the crib can not be considered an isolated system. The whole floor/room/building/Earth is now part of the system so considering the centre of mass is not that useful.

• It helped me visualize this by imagining a more exaggerated scenario where the baby runs at the walls of the crib, jumps, and slams against it. Commented Jan 31, 2023 at 1:49
• @Ankit: You don't need the whole crib setup to see problems with that approach. Consider a person walking forwards: The only "external" force on them is static friction in the opposite direction. So no, you can't just take the baby and the crib as your system, at least not unless you're prepared to model the transfer of momentum between your system and the Earth. When you account for that, you see additional forces between the system and the Earth, arising from Newton's third law. Commented Jan 31, 2023 at 4:58
• @Ankit Don't try to lawyer yourself through physics - it's only going to cause pain and suffering. It's not about twisting words, it's about understanding the models, their applications and limitations. "We can take any combination of bodies as our systems" is not a free action; and just because you pick a combination of bodies and call it a "system" doesn't mean you can ignore the rest of the world. Every model has its limitations, and you can't use that model if you don't understand those. You're doing the equivalent of throwing random numbers at a wall and assuming the pattern is useful. Commented Jan 31, 2023 at 8:37
• @Ankit: So I think I can take the baby and the crib as my system If you take the only the baby and crib as your system and ignore everything else, how can you show that the system moves across the floor? Commented Jan 31, 2023 at 21:28
• @Ankit You can pick any system you like. You can take the baby and the crib as the system, but you have to consider the system is not isolated and there is an external force acting on the system (which is friction). The friction force goes all over the place during this maneuver and doesn't automatically balance itself out. You would have to analyze it properly, not just handwave it away. Commented Feb 1, 2023 at 18:47

There is an external force. When the child runs inside the crib, the bottom of the crib pushes against their foot; foot and crib are engaged via static friction. In turn, the crib itself is similarly engaged to the floor via friction. So there is a force acting between the floor and the foot, through the crib. This force accelerates the child's body, which can then strike the wall of the crib, transferring some of its momentum to it. In a free-body diagram of the crib and child, this would appear as an external force.

What we have to explain is how an external force acting on the crib move the individual inside it via their foot, given that the crib doesn't move (at that point), and neither does their foot? The answer is that it doesn't. The friction is preventing the backwards movement of the crib when the child begins to fall.

We need to explain walking.

How does your generate an external force when you walk? Walking begins with falling. You lean slightly forward, disrupting your balance, and begin to fall. At the same time, you lift a foot, and extend that leg; the fall accelerates. Eventually, the free foot is planted in order to prevent a complete fall; and the center of gravity vaults over that leg.

In the absence of friction, the resting foot would slide backwards and the body's center of gravity would fall straight down. Because there is friction, the resting foot stays planted, and acts as a pivot; a force is generated between the foot and ground which deflects the center of gravity to fall in the walking direction rather than straight down. In a free-body diagram of the person, this would appear as the external force which generates displaced movement,.

The rest of the walk is just a sequence of controlled falls, with a supply of energy to counteract losses.

Thus, back to the crib. If there were no friction between the crib and floor, (but the usual friction between foot and crib), what would happen when the child starts to move is that the crib would move in the opposite direction. Then when the child bumps agains the crib wall, that movement would stop. There would be net displacement of the crib, but the center of mass of the crib-child system wouldn't go anywhere.

You're right that this would not work in space. However the crib is attached to the floor via static friction. When the crib is bumped, the floorboards are pushed in the opposite direction, which is eventually transferred to the house/earth.

• Also the baby can be foiled by attaching well-oiled casters to the crib. Commented Jan 31, 2023 at 21:30
• @A.I.Breveleri: I'm aware we're delving into off topic pedantry here, but the fact that the crib is against the wall initially means that the baby is able to push off against the wall (I don't mean physically touching the wall, I mean by doing the same thing they're doing now), and once the crib has been set in motion, the well-oiled casters make them glide right over. The well-oiled casters would only foil the baby's attempts if the crib had ample clearing all around it to account for any crib movement that the baby is able to create from inside of the crib. Commented Feb 1, 2023 at 1:02
• @Flater: I agree. Indeed pushing off from the wall is possible either in space or on casters. Commented Feb 1, 2023 at 3:28
• The floorboards are pushed in the opposite direction during the run-up, not during the bump. Commented Feb 1, 2023 at 17:30
• @A.I.Breveleri yes, well-oiled casters are a good way to foil this odious behaviour. May I suggest also sloping the floor in the opposite direction? Bonus points for any crocodile moats or nuclear mines you can include in your strategy against these aberrations. Commented Feb 2, 2023 at 12:38