Forces and sitting on a chair with wheels

• Anisotropic Galaxy

Anisotropic Galaxy

So I am a person sitting on a chair that has wheels. Now, the question is - can I push the chair when I am sitting on the chair and have nothing to push against? [other than the chair]

Whenever i try to push against the chair, friction with the ground seems to pull it back. According to Newton's 3rd Law, each force produces an equal and opposite force. So as I push against the chair, the equal and opposite force acts on the me + chair system to move it back. But part of the force is friction against the me + chair system, and part of it is the chair against me. So I refrain from moving and the net effect is that the chair and I go in the direction of where i push, but with some recoil. This logic probably applies to cars as well [since the engines have nothing to push against, other than the car itself]

Note that I have no contact whatsoever with the floor.

I'm not sure I understand - if you are sitting on a chair, where, exactly are you applying this force? If you are not applying it against an object not on the chair, there are no forces (besides weight) present between the wheels and the ground. Since the wheels are not driven, an external force on a wheeled chair is resisted by only the chair's mass and the rolling resistance of the wheels (due to the bumpiness of the floor and the friction in the axle bearing).

A car engine applies a force against the ground via the static friction between the ground and the wheels.

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Now, the question is - can I push the chair when I am sitting on the chair and have nothing to push against? [other than the chair]

This is a misleading question, because you do have something to push against (the ground). Sure, if there was just you and a chair out in space, you wouldn't be able to take the chair in your choice of direction.

But on the ground.. if you bounce up in the chair (making the situation a little like above) you can push on the chair to make it go one way, and your body goes the other. Then, when you press back into the seat (increasing friction with the ground) you can shift your body back without the chair moving (technically the entire planet moves just imperceptibly, which compensates the total motion of you and your chair).

This positive answer is obvious after playing on a wheely chair, so from you're question I guess you were just confused by the complexities of the real world as compared to the frictionless world used to explain basic physics concepts. Likewise, by turning the tyres, a car's engine does push against the road (and hence the road pushes the car, which makes the car accelerate).

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Okay, so I'm assuming that I have no contact with the ground whatsoever (and can only apply force against the chair, which in turn, applies force against the ground).

Should the FBD look somewhat like this? I'm assuming that the analogy between my muscle power and the engine applies.

<----
Me on chair

-->
Chair on me

-->
Chair on ground

<--
Ground on chair

So the net effect of the chair + me direction is in the direction that I am "pushing" the chair

Are the dashes representative of the maginitude of the force? If so you need to make a correction, is the force you put on the chair larger than the force the chair puts on you?

<----
Me on chair

-->
Chair on me

What happened to Newton's 3rd?

Okay, so I'm assuming that I have no contact with the ground whatsoever (and can only apply force against the chair, which in turn, applies force against the ground).

Should the FBD look somewhat like this?
<----
Me on chair

-->
Chair on me

-->
Chair on ground

<--
Ground on chair

So the net effect of the chair + me direction is in the direction that I am "pushing" the chair
Simple logic should be all that is required to see that this is flawed. What if you put a scale between your hand and the chair? How many different forces would it measure? If there is only one point of contact, there can be only one force and in a fbd, it can be expressed as a force and its equal and opposite reaction.

Clearly, if you are not pushing on something off of the chair, you can be applying no pushing force to the ground.
I'm assuming that the analogy between my muscle power and the engine applies.
Why would it? You are not applying a force to the ground in any way and you are not turning the wheels with your hand. The only way it would apply is if you reach down and turn the wheels with your hand.

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Okay, sorry, my folk physics isn't that good.

<----
Me on chair

---->
Chair on me

<--
Chair on ground

-->
Ground on chair

Net motion of chair: <--

The net effect, then, is that the chair moves forward (since friction by ground on chair must strictly be equal to or less than the force I push on the chair).

Okay, sorry, my folk physics isn't that good.

<----
Me on chair

---->
Chair on me
Gooooood...
<--
Chair on ground

-->
Ground on chair
Where do these forces come from? If "Me on chair" + "Chair on me" = 0 (and it must), there is no force left to push on the floor.

But I know that when I play with a wheely chair, that the chair moves [and that there is acceleration]. cesiumfrog said that I can press back into the chair without the chair moving, so this enables me + the chair to move.

If "Me on chair" + "Chair on me" = 0 (and it must), there is no force left to push on the floor.
Huh? Where are you getting this from?

It sounds like you're arguing that since an engine exerts a force a stopped car's axle (and the axle exerts an equal and opposite force on the engine) there's "no force left" for the wheels to exert across the road (and cars can't work).. which is absurd.

Despite that, A.G., I think any single free body diagram will be insufficient since the crux is to alternate between 1) having forces mainly just on the person and chair (so that the chair does accelerate left across the ground, in an opposite direction to the person's acceleration, with little force upon the ground) and 2) with forces also conducted strongly to the ground (to prevent the person falling off the chair he must now be accelerated left, and to prevent the chair moving right back to where it all started: the chair must push the ground right so that friction can oppose the other force acting on the chair). -- But on average, there is little force at all (technically some between the chair and ground, and less between the heavier person and chair, so the net force on each the chair and person corresponds with their average net acceleration).

But I know that when I play with a wheely chair, that the chair moves [and that there is acceleration]. cesiumfrog said that I can press back into the chair without the chair moving, so this enables me + the chair to move.
Are you lunging...? Are your feet touching the ground? If you are on the chair and not applying a force to anything off of the chair, you cannot possibly make the chair move.

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Huh? Where are you getting this from?
You know what - you're right. We're missing a force. If you are sitting in a chair and pushing against it (and not falling off), there must be two force/reaction pairs.

I'm envisioning AG kneeling on the chair, facing backwards, and pushing on the back of the chair with his hands. There is a force pair betwen his hands and the back of the chair and another one between his knees and the bottom of the chair (there must be a static friction there, or he'll push himself out of the chair).

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You know what - you're right. We're missing a force. If you are sitting in a chair and pushing against it (and not falling off), there must be two force/reaction pairs.

I'm envisioning AG kneeling on the chair, facing backwards, and pushing on the back of the chair with his hands. There is a force pair betwen his hands and the back of the chair and another one between his knees and the bottom of the chair (there must be a static friction there, or he'll push himself out of the chair).
That seems correct. AG kneels on the chair and pushes back on the chair with his hands. His knees push back on the chair in the opposite direction with equal magnitude of force. Theoretically, the chair does not move at all, with or without friction on the floor.

Maybe what the OP means is if the friction in the wheels resists a change in the center of mass when he leans forwards in the chair, but then suddenly stopping and/or leaning back quickly enough to overcome the friction in the wheels, the chair would move forwards.

If the wheels were frictionless, then it wouldn't matter how the person moves around, as the center of mass of the system would remain motionless.

If the chair were steerable, then a person could shift side to side, shifting the center of mass side to side. By coordinating the shifting so that it's nearly but not quite perpendicular to the wheels the chair could be propelled.

Skateboards can be propelled withough touching the ground via two methods.

From a standstill, a person can exert a torque force and a linear force perpendicular to the wheels. One the center of mass if moving sideways, the skateboard is wheelied and turned into the direction that the center of mass is moving. Actually it's turned a bit past that direction, and the person then leans and twists to the other side, repeating the motion to propel the skateboard. Initially the twisting force is small, just enough to reposition the skateboard while doing a wheely to reposition it for the next cycle.

Once up to speed, the person can just twist back and forth applying a torque force, and steering the skateboard so it's just out of phase with the persons twisting motion to continue propelling the skateboard. Both method would work if the bearings were frictionless, and only require that the wheels have friction with the ground.

A similar method can be used to propel on's self on a single ice skate (figure type skate that turns easiliy).

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So I'm looking at old threads and came across this interesting problem.

So
|
| O
|(a) - |-
|_____/\___
o o

is the diagram. The guy is in the middle, and he tries to push the chair to the left. I see three forces exerted. (a) is the man pushing chair left, the chair edge pushes the man right. Then the man's bottom and the chair have to push each other (b). Man pushes chair right, chair pushes man left. And what if you replace the man with say, a motor? The difference here would be that the motor would probably be a lot more attached to the bottom of the chair than the man would be.

So the question is - is the force in (a) greater than the force in (b) and why? Since if the force in (a) is greater than that in (b), then the chair will experience acceleration to the left, which is apparently what the OP experienced (and yes I have experienced it as well).

EDIT:
I just tried the experiment again. It seems that it's nearly impossible for me to move the chair when I exert a force that is totally horizontal to the chair. But it is possible for me to move the chair if I exert a force at an angle to the chair. In this case, the component parallel to the direction of movement effectively moves the chair. The force exerted on me, of course, is partially in the vertical direction, which then does not factor into the force between my bottom and the bottom of the chair. But a 1D model would predict that this is no different than a horizontal component force. Could it be the effect of torque? (since torque = (distance from axis)*force)? In which case, if I push from a higher point, it will then cause more force. But this torque seems to be applied against the back of the chair (which is somewhat flexible), rather than the axis of the wheels. But can't this torque in turn transfer to the bottom of the chair's wheels, effectively moving the chair?

EDIT2:
But on average, there is little force at all (technically some between the chair and ground, and less between the heavier person and chair, so the net force on each the chair and person corresponds with their average net acceleration).

Perhaps since the equal and opposite force exerted on me affects me less than it affects the chair since I'm more massive than the chair? This will in turn make the force pair between my knees and the chair smaller in magnitude than the force pair between my hands and the back of the chair, resulting in net motion? But then if I were heavier, there would be a larger frictional force between myself and the bottom of the chair. hmm

EDIT3: The core assumption is that the force the back of the chair exerts against me will NOT all be transferred to the force that then comes between my knees and the chair. The reason is that I'm not a completely rigid body, and that some of the force is lost. But what is the force lost to?

EDIT4: I don't have to press against the back of the chair when I want to make it move. But somehow when I don't press against the back of the chair, I then move my legs forward to move it forward (I avoid touching external ojects, I just use the friction between my bottom and the chair). That I have to move my legs forward implies some conservation of angular momentum. Could this be the reason? (since I have to constantly move my legs back and fro?

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