**DOUBLE FORCES OF ATTRACTIVE GRAVITATION PARADOX VII**https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1905467#msg1905467 (part III)

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1910009#msg1910009 (part V)

Two boats on a lake, boat X and boat Y, are being pulled toward each other using a single rope by the two men on each boat.

Of course forces X and Y will ALWAYS be different.

The NET FORCES on each end of the rope might be the same, but the APPLIED FORCES will ALWAYS be different.

Modern Newtonian mechanics has this story to tell:

*The net force on boat x is -A.*

The net force on boat y is -B.

The net force on the string is A+B.

As the string isn't moving, the net force on the string is 0, so A+B=0 so B=-A.

The net force on boat x is -A.

The net force on boat y is A.

The net force on the string is A-A=0.By the very hypothesis, A DOES NOT EQUAL B.

A cannot equal B.

Yet, by using the twisted RE logic, using only a single force acting on boat X (respectively on boat Y), the analysis reaches a point where the absolute value of A equals the absolute value of B. A most direct contradiction of the hypothesis.

The RE analysis leads to a total disaster, where the basic requirement is this |A|=|B|.

Which can NEVER be the case.

Force A can never equal force B.

**Let us suppose now, that only one of the rafts/boats does the pulling (that is, side X will have the rope attached to it, no person X would be pulling).**

Person Y pulls on the rope from the right.

What are the forces on the left side of the rope (in boat X)?

-B (reaction force on force B).Now let us bring person X back.

Both persons are pulling now, force A does not equal force B.

What are the forces on the left side of the rope now?

Yes, person X is pulling with force -A (to the left) BUT ALSO person Y is pulling.

Reaction force is the SAME as in the previous situation: -B.

Then, the net force on the left side of the rope is now: -A + -B, or -A -B.

Very simple to understand.

The fact that force B (and force A) are being applied THROUGHOUT the entire rope is something modern mechanics has yet to acknowledge.

**There will be action-reaction pairs diagrams at each end of the rope, involving BOTH PULLING FORCES A and B.**On solid ground (or someone who is in a truck), there will always be FRICTION to deal with (F

_{A}, the frictional force on player A exerted by the ground, and F

_{B}, the frictional force on player B exerted by the ground).

When the forces are unbalanced, the system accelerates in the direction of the net force.

The acceleration is caused by the imbalance of frictional forces at different parts of the system.

The tug-of-war is won by the person who applies a larger force on the ground (which is equal to the frictional force by Newton's third law), and not by the person who pulls the rope harder.

There is also the matter of the static friction force between the rope and the person's hands.

The standard analysis for the two boats connected by a rope on a lake fails miserably.

By contrast, the FE analysis is very well defined.

Two boats pulled toward each other on a lake.

Man from boat X is pulling with force A, directed to the left.

Man from boat Y is pulling with force B, directed to the right.

Forces A and B are, of course, of different magnitude.

What are the forces acting on boat X?

To the left we will have a negative direction.

Boat X will be acted upon by TWO FORCES: A (the reaction force on the action force -A) and B.

What are the forces acting on the left end side of the rope?

-A and -B.

What are the forces acting boat Y?

To the right we will have the positive direction.

Boat Y will be acted upon by two forces: -B (the reaction force on the action force B) and

-A.

What are the forces acting on the right end side of the rope?

A and B.

Net force on boat X: A + B

Net force on boat Y: -A - B

Net force on the string: [-A - B] + [A + B]

The string/rope will not move: [-A - B] + [A + B] = 0

All forces balance out perfectly.

But they include TWICE THE FORCES NEEDED in the Newtonian system.

The man in boat X is pulling on the rope, while at the same time boat Y is pulling on that same rope with force B. The correct analysis must take these facts into account.

A perfect demonstration that there are indeed two forces acting on boat X, respectively on boat Y: the equations work out in total balance.