Explain what laws of physics were violated in this scenario....

[Davidllerenav]

Homework Statement

From reliable information, once Baron Münchhausen was stuck in a swamp, he pulled himself out of it by the hair. What laws of physics did the baron break? (Find the answer analytically)

Homework Equations

None.

The Attempt at a Solution

Well, I think that he breaks the three laws of Newton. The first one and second one because it says that he pulled himself out by the hair, so he is a applying a force on himself. For an object to move it, an external force must be applied. The inner forces do not cause movement. The third law because it says that every force applied to a body, there is one applied from that body with the same magnitude but different direction. Since he is applying a force to himsel, there would be another force with different direction but same magnitude, since the mass is the same and acceleration too, the sum of both is cero, no $ma$.
I don't know how to express this analytically, I need some help.

 

[Delta2]

Well you are mostly correct on what you saying. To express this more formally, you need to consider the centre of mass (c.o.m) of the body of Baron. We know that for the c.o.m this equation holds
$$\sum F_{external}=m\frac{d^2x_{com}}{dt^2}$$(we arrive at this equation if we combine Newton's 2nd and 3rd law and the mathematical definition of the c.o.m)

So the Right Hand Side of this equation is obviously non zero since Baron moves himself out of the swamp. But the Left Hand Side of the equation is obviously zero.

 

[Davidllerenav]

So the Right Hand Side of this equation is obviously non zero since Baron moves himself out of the swamp. But the Left Hand Side of the equation is obviously zero.

So we arrive at a contradiction, right?

Well you are mostly correct on what you saying. To express this more formally, you need to consider the centre of mass (c.o.m) of the body of Baron. We know that for the c.o.m this equation holds
$$\sum F_{external}=m\frac{d^2x_{com}}{dt^2}$$(we arrive at this equation if we combine Newton's 2nd and 3rd law and the mathematical definition of the c.o.m)

I haven't seen too much about c.o.m, only that the forces come out of it. Can you edplaie this a bit more, please?

 

[Delta2]

So we arrive at a contradiction, right?

Yes it is a contradiction , though it is a bit more complicated than I thought. There is an external force on the Baron and it is his weight (the attractive force from earth). That equation tell us essentially that Baron needs another external force to counter his weight, Baron cannot counter his weight by pulling himself from the hair which is an internal force.

I haven't seen too much about c.o.m, only that the forces come out of it. Can you edplaie this a bit more, please?

Well if you haven't been taught about this equation and its proof it would be hard to explain here. Basically using Newtons 2nd and 3rd Laws and the definition of c.o.m we can prove that equation. But i am sure you use this equation quite often in problems.

 

[Davidllerenav]

Yes it is a contradiction , though it is a bit more complicated than I thought. There is an external force on the Baron and it is his weight (the attractive force from earth). That equation tell us essentially that Baron needs another external force to counter his weight, Baron cannot counter his weight by pulling himself from the hair which is an internal force.

But wouldn't the other external force needed be the normal force?

Well if you haven't been taught about this equation and its proof it would be hard to explain here. Basically using Newtons 2nd and 3rd Laws and the definition of c.o.m we can prove that equation. But i am sure you use this equation quite often in problems.

Yes, I use that equation, so I guess there isn't any problem.

 

[CWatters]

Three laws according to Wikipedia...

First law:In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.[2][3]

Second law:In an inertial frame of reference, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma. (It is assumed here that the mass m is constant – see below.)

Third law:When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

First law: There is no external force so he should remain at rest.
Second law: Zero net force means zero acceleration - so should remain at rest.
Third law: If you consider his hand and hair as two separate bodies he must be breaking this law because to escape the force his hand exerts on his hair must be greater than the force his hair exerts on his hand.

 

[Davidllerenav]

Three laws according to Wikipedia...First law: There is no external force so he should remain at rest.
Second law: Zero net force means zero acceleration - so should remain at rest.
Third law: If you consider his hand and hair as two separate bodies he must be breaking this law because to escape the force his hand exerts on his hair must be greater than the force his hair exerts on his hand.

I understand that now how do I express that analytically?

 

[Delta2]

But wouldn't the other external force needed be the normal force?

Ok the normal force (if baron touches the swamps bottom with his legs) or the buoyancy force cancels out the force of his weight. All these forces are external forces. So at one side of the equation we will have $\sum F_{external}=B-N=0$. (Note that in this sum we don't count the internal force from his hand to his hair/head, because it is an internal force). But on the other side of the equation the term $m\frac{d^2x_{com}}{dt^2}=ma_{com}$ shouldn't be zero for the time interval for which baron moves from swamp to outside of the swamp. So we have a contradiction , that $0=\sum F_{external}=ma_{com}\neq 0$.

 

[Davidllerenav]

Ok the normal force (if baron touches the swamps bottom with his legs) or the buoyancy force cancels out the force of his weight. All these forces are external forces. So at one side of the equation we will have $\sum F_{external}=B-N=0$. (Note that in this sum we don't count the internal force from his hand to his hair/head, because it is an internal force). But on the other side of the equation the term $m\frac{d^2x_{com}}{dt^2}=ma_{com}$ shouldn't be zero for the time interval for which baron moves from swamp to outside of the swamp. So we have a contradiction , that $0=\sum F_{external}=ma_{com}\neq 0$.

I see, thanks. So that would be the way to explain analytically, right?

 

[Delta2]

I see, thanks. So that would be the way to explain analytically, right?

yes according to that equation, baron needs a net external force in order to give acceleration to his c.o.m but there is no net external force provided. The force from his hand to his hair is an internal force.

 

[Davidllerenav]

yes according to that equation, baron needs a net external force in order to give acceleration to his c.o.m but there is no net external force provided. The force from his hand to his hair is an internal force.

Thanks for your help!