Flight Safety, I did get the two examples mixed up. I now see what you were comparing with the 2x4 analogy.
The steel ball travelling in a circle at a constant speed is continually accelerating. You must accept that to see why centrifugal forces are considered apparent forces.
Because the ball is accelerating, the net force on it must be non-zero, in fact it must be pointing towards the center of the circle with a magnitude of m v^2 / r (usual variable defs). That force is the required centripetal force. It is real. It is created mechanically through tensile forces in the string.
The stationary observer sees no effect of a force exerted on the ball oriented outwards. The only way that such a force can be observed is by putting yourself on the ball and ignoring the motion of the ball. In this case you feel a force that is magically pushing you away from the rope. In fact there is no force directed outwards at all, that is merely an explanation for what you observe in that rotating reference frame. It is not a force, it is just your body wanting to go in a straight line. When you counter that force by holding on to the ball, you are accelerating yourself towards the center of the circle.
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When you lean on a wall, you do transmit energy to the wall. To make it simple, consider instead the ideal gas law, PV=nRT. Increase pressure and temperature (average kinetic energy) increases. The same is true with liquids and solids.