Moving without the application of an external force

[iyerk0]

Hi,
I am new poster on this forum. Apologies if you have already answered a similar problem before. let me get to the point straightaway.


Now consider one example: Take a shopping cart and sit in it. Now jerk your body in any manner you require. The goal is to create a net motion forward. Can you sit in the cart and move it say 1 meter forward by giving the appropriate jerks? remember that you cannot push against the ground or a wall. Your arms and legs are totally inside the shopping cart and not touching any external surfaces.

My contention is that this is quite possible. My friend is equally convinced that it is impossible? Who is right ? (and why?)
For this problem i think we need to consider the ideal case (where there is no friction involved) and the real world case (where there is friction is involved).
I am quite convinced that if i take a walmart shopping cart moving my self forward by simply jerking my body (while not contacting any external surface) is quite do able. I have a theory for this, but i will wait for your answers so as not to bias you in any way.
Thanks again and i hope to get some illuminating answers.

 

[ice109]

lol why don't you just do it?

 

[Doc Al]

I am quite convinced that if i take a walmart shopping cart moving my self forward by simply jerking my body (while not contacting any external surface) is quite do able.

Realize that you are in contact with the floor, which can exert a horizontal force on the cart.

In the absence of any external forces (put the cart on a frictionless surface), the motion of the center of mass of "you+cart" will remain unchanged. If you start at rest, you'll stay at rest.

 

[iyerk0]

Realize that you are in contact with the floor, which can exert a horizontal force on the cart.

No i am not ! That is why i stated that i sit in the cart and keep my arms and legs inside without contacting any external surface.

 

[pardesi]

since there is no external force the c.m can't move though the basket may

 

[momentum_waves]

No i am not ! That is why i stated that i sit in the cart and keep my arms and legs inside without contacting any external surface.

Does your cart plummet towards the centre of the earth? If not, then - why not? Think through all the force transfers from your body, through the cart frame & so forth.

 

[smallphi]

The force that will move the cart is not the force between your body and the cart which is an internal force for the system but the reaction force from the floor in response to your jerks. That reaction force is part friction part normal force because the ground and the wheels of the cart are not absolutely rigid bodies and can deform slightly, away from horizontal, to push the cart horizontally.

If you and the cart are on very slippery ice that is absolutely rigid (doesn't deform at all but always remains strictly horizontal surface) there can't be any horizontal reaction force. If you jerk forward, the cart will go backwards and the system's center of mass won't move. You won't be able to move the center of mass any distance in that situation.

 

[iyerk0]

since there is no external force the c.m can't move though the basket may

well which case does this apply to ? the frictionless case or the frictional case? or both?

 

[ice109]

how come kicking your feet on a swing increases your angular velocity then?

 

[smallphi]

There is an external force with horizontal component acting at the point where the swing is hanged. That force responds to your kicks and increases your swinging.

 

[pardesi]

well which case does this apply to ? the frictionless case or the frictional case? or both?

ofcourse the frictionless case .as smallphi said the parts get deformed and the normal force just doesn't pass through the C.g.

 

[iyerk0]

There is an external force with horizontal component acting at the point where the swing is hanged. That force responds to your kicks and increases your swinging.

are you imagining that a person standing on the ground pushing the swing? (since you mentioned external force)
Do you know that for increasing the amplitude of the swing a person sitting on the swing can do so without even touching his feet to the ground?

 

[smallphi]

If your system is man+swing the only external force to increase the swinging is the force acting on the swing from the pivot.

If your system is only the man, then the only external force to increase its swinging is the tension force of the 'string' of the swing.

 

[bullshark01]

Shopping Cart filled with tennis balls.

I have a variant of the problem being discussed here. Imagine a shopping cart filled with tennis balls and yourself also sitting in it. Can you move forward by throwing the tennis balls out of the cart ,in the opposite direction?

 

[smallphi]

yes you can, that is the principle of the rockets, the tennis balls play the role of the fuel ejected backwards

 

[iyerk0]

Does your cart plummet towards the centre of the earth? If not, then - why not? Think through all the force transfers from your body, through the cart frame & so forth.

no the cart does not move towards the center of the earth. It is resting on a simple planar surface and cart is subject to gravitational force. The only variables to play around with are whether it is a friction free surface or a frictional surface. Of course you may consider bending, warping etc of the shopping cart for getting an explanation. But i consider those factors unimportant.

 

[iyerk0]

If your system is man+swing the only external force to increase the swinging is the force acting on the swing from the pivot.

Well if the pivot is providing the force (and somehow not the person sitting in the swing) then the following should happen: Consider the empty swing, since the pivot is providing the force, the swing should start swinging all by itself !

 

[smallphi]

no the cart does not move towards the center of the earth. It is resting on a simple planar surface and cart is subject to gravitational force. The only variables to play around with are whether it is a friction free surface or a frictional surface. Of course you may consider bending, warping etc of the shopping cart for getting an explanation. But i consider those factors unimportant.

If the friction between the wheels of the cart and the ground is always non-slipping, that force serves to produce the necessary angular acceleration of the wheels when the axis of the wheels is accelerated in a given direction by your jerks so that the wheels continue not to slip. You can calculate for a give acceleration of the wheel axis, what is the necessary frictional force. I bet is is pretty small to explain the resulting acceleration of the heavy system of cart+man.

I think in most cases the bending of the ground and wheels away from horizontal is the main factor. It gives an opportunity for the big normal reaction force from the floor to have a horizontal component and accelerate the system.

 

[smallphi]

Well if the pivot is providing the force (and somehow not the person sitting in the swing) then the following should happen: Consider the empty swing, since the pivot is providing the force, the swing should start swinging all by itself !

The pivot is providing EXCESS force, in response to your jerks. That EXCESS increases the swinging.

If there is nobody in the swing, there won't be an excess force and the swing will either continue swinging by itself (if it was swinging already) or just hang vertically.

 

[iyerk0]

The pivot is providing EXCESS force, in response to your jerks. That EXCESS increases the swinging.

By using the term EXCESS you do realize you are violating Newton's third law of motion don't you? (every action has an EQUAL and opposite reaction)

 

[esalihm]

No i am not ! That is why i stated that i sit in the cart and keep my arms and legs inside without contacting any external surface.

I think he meant that the cart is

 

[ice109]

the swing problem has nothing to do with forces, it has to do with conservation of momentum

 

[rcgldr]

how come kicking your feet on a swing increases your angular velocity then?

The external forces in this case are gravity, and supporting bar's ability to resist various amounts of tension in the chains. It's a combination of timing properply, the movment of the center of mass up and down as well as back and forth, so that net work is done, increasing energy. Once a moderate swing is established "up and down" movement is sufficient. Move outwards from the supporting bar at the end of the swing there the movement versus the pull of gravity is small, and there's almost no centripal force involved. Move inwards towards the supporting bar at the lower part of the swing, when the movement versus pull of gravity and centripital force is higher and you do more work for a net gain in energy.

As an example, this video of a guy on flying rings going from a moderate swing to bar level in 3 swings, then doing a quadruple back flip.

quad.wmv

Regarding the cart it's because there's a small amount of resistance to horizontal movment, allowing smooth acceleration of the center of mass and then overcome by sufficient jerk of the center of mass.

 

[iyerk0]

the swing problem has nothing to do with forces, it has to do with conservation of momentum

Looking from the momentum point of view as well we consider the following to happen. Sit on a swing and start from a motionless state. Now i know that it is possible for a person sitting in the swing to gradually start increasing the amplitude of the swing without pushing against the ground or an external object. Once the amplitude has increased by a significant amount, one can see that that the momentum is greater at this point that when you started off with the motionless swing. However since i never pushed against an external object (like the ground or a wall etc) there was no input of external force.

Thus we have acheived an increase in momentum without application of external force i.e. the momentum of a closed system is not conserved !
Does this mean that Newton's second law is not conserved? !

Before anybody thinks i am forwarding a new crackpot theory, let me tell you that i believe Newton's second law holds. But there exists a subtlety which is being missed.

 

[smallphi]

By using the term EXCESS you do realize you are violating Newton's third law of motion don't you? (every action has an EQUAL and opposite reaction)

Yeah but the action and reaction act on DIFFERENT bodies so they can accelerate them.

Ther 3rd law of Newton is not a proof that nothing can ever move cause each action has equal reaction that will cancel it out.

 

[rcgldr]

it is possible for a person sitting in the swing to gradually start increasing the amplitude of the swing without pushing against the ground or an external object.

As I just posted, the person is pushing against the swing itself, which increses the tension in the chains, and is resisted by the supporting bar, which deflects only a small amount in response to a change in tension, and gravity is an external force to this system.

The increase in energy occurs because net work is done. The center of mass of the person is initially moved in a circular pattern, timed so that net work is done versus gravity initially and so that angular momentum is preserved, and then versus both gravity and the centrepital force provided by the supporting bar once the swing height is sufficient enough. Standing on a swing is much more effective since the center of mass can be moved more.

If you want an example of "movement" without an external force, a rocket in space is potential example, except that what really happens is that the rocket expells part of it's mass (burnt fuel) at high velocity so that the expelled mass moves away in one direction while the rocket moves in the other direction.

 

[Doc Al]

the swing problem has nothing to do with forces, it has to do with conservation of momentum

But we are obviously talking about changing the momentum by pumping the swing. And that requires forces.

Thus we have acheived an increase in momentum without application of external force i.e. the momentum of a closed system is not conserved !
Does this mean that Newton's second law is not conserved? !

Of course there are external forces acting on the swing. The swing attaches to a pivot (as smallphi stated) which in turn is supported by a frame (and the earth). Since the swing is not isolated, Newton's 2nd law is safe.

Before anybody thinks i am forwarding a new crackpot theory, let me tell you that i believe Newton's second law holds.

But you thought you could move your cart without an external force?

But there exists a subtlety which is being missed.

Actually, there is a bit of subtlety about swing pumping and resonance. I recall a spate of AJP papers on the topic some years ago.

 

[ice109]

But we are obviously talking about changing the momentum by pumping the swing. And that requires forces.


Of course there are external forces acting on the swing. The swing attaches to a pivot (as smallphi stated) which in turn is supported by a frame (and the earth). Since the swing is not isolated, Newton's 2nd law is safe.


But you thought you could move your cart without an external force?

Actually, there is a bit of subtely about swing pumping and resonance. I recall a spate of AJP papers on the topic some years ago.

link please...

 

[iyerk0]

Yeah but the action and reaction act on DIFFERENT bodies so they can accelerate them.

Yes you are right that action and reaction act on different bodies. But remember that man+swing act as a SINGLE body. So when man applies force to swing, then swing responds with equal and opposite force back to man and the forces are statically balanced since they are conected to each other. Hence the man sitting on a swing cannot push the swing in a certain direction while still sitting in it as per your explanation.
Thanks all for being so enthusiatic though!
I am still formulating my own explanation and will put it here once i can make it coherent.

 

[rcgldr]

man+swing act as a SINGLE body.

Two "bodies" involved here. One is the support bar that virtually doesn't move and provides a resitive reaction to any veritcal or horizontal force applied to the bar. The other is the person and swing, and the two "bodies" are connected via chains.

While sitting on a swing a person can lean and push or pull on the chain. The center of mass of the person and swing initially just moves upwards, but the tension between the now non-vertical component of the chains and the non-moving bar now provide a horizontal component of tension, which now results in some movement of the person and swing. This creates the initial movement. After that it's a matter of timing as to when to push/pull the chains and raise/lower center of mass with respect to the supporting bar.

 

[smallphi]

Here is my explanation of the swing problem. Let our system is the man only, without the swing. The only two external forces acting on the man are gravity and the pull of the string of the swing.

Think of what you do intuitively when you want to swing faster. You lower your body to as close to horizontal as possible when the swing is going towards the lowest point (assuming you are facing the lowest point) and again straighten it vertical when the swing passes the lowest point and is going up. You keep your body vertical for half a period till the swing returns to the original position and then you 'pump' again.

Considering the torques of the external forces around the pivot of the swing, only gravity has a torque. By laying horizontal when the swing is going towards its lowest point, you put your center of mass further from the vertical position of the swing increasing the shoulder of the gravity force around the pivot thus adding EXTRA torque of gravity in excess of the usual torque when your body is vertical. That extra torque creates the extra angular acceleration that swings you faster. After you pass the lowest point of the swinging you have to raise your body vertical, otherwise you will have a DEFICIENCY of gravity torque with respect to vertical body position.

That explains how gravity creates the extra angular acceleration. What creates the extra horizontal acceleration though? It can't be gravity since it is vertical. The only other external force is the tension in the string of the swing. What happens is that when gravity creates the extra angular acceleration, the extra speed of the swing requires extra centripetal acceleration provided by EXTRA tension in the string with respect to normally swinging without 'pumping'. That extra tension force projected on the horizontal axis creates the extra momentum in horizontal direction, the extra swing.

Where does the energy for extra swinging come from? Your muscles, say the abdominals and flexors, do work against gravity when you raise your body from horizontal to vertical at the lowest point of the swing. So the chemical energy of the muscles converts to potential energy when you raise your body vertical, which converts to kinetic energy of the swing when you lower down your body horizontal. Of course at the end some part of the chemical muscle energy turns into heat.

 

[Mr Virtual]

You will move but only momentarily

Hi iyerk0

My answer to your question is that: Yes the cart will move. But sadly, you are going to find yourself exactly where you started from after a second or so.

If you jerk your body in certain ways e.g. sitting on your feet and pushing the cart with them, the cart will move forwards. However, it will never be able to maintain its new position, because after you have pushed, Newton's law of reaction will push you backwards, and as soon as you touch the cart with your back, the force you were carrying with your backward motion will bring the cart back to its original place. However hard you push, you are going to come back to your original place.
One metre distance is too long mate. Only if you somehow slow down your body's velocity backwards ( you'll have to be a superman to do so ), the cart may have enough time to cover one metre. Atleast you will fulfil your dream of traveling one metre in a shopping cart, even if only for a short while ( that is, before your backward-moving body hits the cart. )

Bye

 

[rcgldr]

Yes the cart will move. But sadly, you are going to find yourself exactly where you started from after a second or so.

This is not taking into account that cart has static rolling resistance (friction in axles, and deformation of the wheels). So the cart can remain motionless while the center of mass is moving as long as the rate of acceleration to establish the initial movement of center of mass doesn't generate enough impulse to overcome the static rolling resistance. Then a large amount of deceleration to stop the center of mass from moving will create enough impulse to start the cart moving, with dynamic rolling resistance coming into play to slow the cart down.

For example, imagine a compressed spring pushing a bowling ball across the bottom of the cart, the spring rate is low enough and/or rollinging resistance high enough that the cart doesn't move when the spring accelerates the bowling ball. However, when the bowling ball bounces off the other side of the cart, the impulse from the sudden deceleration would be enough to start the cart moving, where it would continue to move until it's dynamic rolling resistance stopped the cart. Add a human inside the cart to recompress the spring as the bowling ball returns, and the cart can be moved in steps as far as wanted.

Just a human in the cart moving slowly forwards and quickly backwards could generate the initial forward motion. It's then possible that if the turning reaction of the cart responds at slow enough rate, that a human could twist side to side to generate a torque force to propel the cart (a low dynamic rolling resistance would be required).

 

[iyerk0]

Hi,
As a final followup, i found a good video demonstrating the point i was talking about. I am trying to embed the video here.
http://www.metacafe.com/watch/642856/broken_desk_on_the_daily_buzz/"
or here is the link
http://www.metacafe.com/watch/642856/broken_desk_on_the_daily_buzz/

The relevant part in the first one minute.
Thanks

 

[rewebster]

Now consider one example: Take a shopping cart and sit in it. Now jerk your body in any manner you require. The goal is to create a net motion forward. Can you sit in the cart and move it say 1 meter forward by giving the appropriate jerks? remember that you cannot push against the ground or a wall. Your arms and legs are totally inside the shopping cart and not touching any external surfaces.

My contention is that this is quite possible. My friend is equally convinced that it is impossible? Who is right ? (and why?)
For this problem i think we need to consider the ideal case (where there is no friction involved) and the real world case (where there is friction is involved).
I am quite convinced that if i take a walmart shopping cart moving my self forward by simply jerking my body (while not contacting any external surface) is quite do able. I have a theory for this, but i will wait for your answers so as not to bias you in any way.
Thanks again and i hope to get some illuminating answers.

Sure--IF the 'back' (of the back and forth jerking action of you in the cart in the 'friction involved' scenario) acceleration/movement toward one direction is sufficient and fast enough to overcome all (or some) friction of the wheels-axles and wheels-floor, AND the 'forth' action is slow enough that it DOESN'T overcome any (or much) of the friction. A similar/comparable case is a ratcheting wrench.