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Its not a paradox.

I as generally am understanding it.
Moving along horizontal surface in ideal don't need of energy at all.Isn't it ?
Without change height. If it wasn't for the damn friction.
The fact is that adherents of free energy saw in their time a source of OU in this.
The allegedly tilted barrel falls all the time, and we only need to shift the fulcrum so that it does not fall at all. Allegedly, gravity moves the barrel itself. But I doubt it myself.It Related to this product below. But this is not on the topic of the branch, okay, I'm finishing.

Its not a paradox.

In practice...

The same amount of energy is used  TO MOVE A BARREL on wheels
as is used to slide the barrel. 

In the case of sliding the barrel, a greater amount of additional energy is used
TO OVERCOME FRICTION
    than
the is amount of additional energy used to overcome friction when instead, a
barrel is rolled.

The PORTION of the energy that goes into MOVING THE BARREL is the same, in
both cases.

Coincidentally, if you tilt the barrel at a slight angle and roll it around on its’ lower rim
You can move it anywhere you want even uphill
Expending only a fraction of the normal energy required to do so


Concerning the energy spent tilting the barrel:
There is initial input to tilt the barrel from vertical to an angle
If you mark the horizontal line at the top of the barrel,
You see that a fraction of the barrel is moved to a higher point
the lifting of this portion as well as energy spent in shifting the center of balance
However, after having relocated your barrel this energy is still stored as potential energy
by slightly nudging the barrel towards falling straight up again, you could theoretically recover this


The energy required to move the barrel is LESS for several reasons, i will mention some:
Friction is one: the surface area of a point along the lower rim can be negligible


Moment of Inertia: this is assisted by Gravity, along a curved surface
Similar to how a Rocking Chair functions


Angular Momentum: the rolling mass of the barrel carries itself along
A small child can easily move a barrel weighing several hundred pounds
all around the ranch…..

Coincidentally, if you tilt the barrel at a slight angle and roll it around on its’ lower rim
You can move it anywhere you want even uphill
Expending only a fraction of the normal energy required to do so

smoky2

1. Your comments are off topic.

2. Your statement above is utterly unclear.
i.e. What does the phrase "the normal energy required to do so" mean ?
           and
3. what it implies is utterly untrue.