# Moving without the application of an external force

1. Jun 9, 2007

### 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.

2. Jun 9, 2007

### ice109

lol why don't you just do it?

3. Jun 9, 2007

### Staff: Mentor

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.

4. Jun 9, 2007

### iyerk0

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.

5. Jun 9, 2007

### pardesi

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

6. Jun 9, 2007

### momentum_waves

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.

7. Jun 9, 2007

### 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.

Last edited: Jun 9, 2007
8. Jun 9, 2007

### iyerk0

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

9. Jun 9, 2007

### ice109

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

10. Jun 9, 2007

### 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.

11. Jun 9, 2007

### pardesi

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

12. Jun 9, 2007

### iyerk0

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?

13. Jun 9, 2007

### 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.

14. Jun 9, 2007

### 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?

15. Jun 9, 2007

### smallphi

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

16. Jun 9, 2007

### iyerk0

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 gravitional 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.

17. Jun 9, 2007

### iyerk0

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 !

18. Jun 9, 2007

### smallphi

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.

Last edited: Jun 9, 2007
19. Jun 9, 2007

### smallphi

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

If there is nobody in the swing, there wont be an excess force and the swing will either continue swinging by itself (if it was swinging already) or just hang vertically.

20. Jun 9, 2007

### iyerk0

By using the term EXCESS you do realize you are violating Newton's third law of motion dont you? (every action has an EQUAL and opposite reaction)