Normal force and force of friction inside a tube

[arhg]

Dear all,

Me and some colleagues (non-physicists) are discussing how force works when passing a cylinder (which we are holding) into a narrow tube. As we insert more of the cylinder into the tube, the force we are exerting is increasing. My theory is that the normal force is increasing and his theory is that it is only due to lubricant Stribeck curve.

We understand that surface area is not taken into account for normal force, which normally is the weight. However, in this case, as we insert more of the cylinder into the tube, doesn't the normal force increases? I thought that this case is different because it is not the weight (as we are holding the cylinder straight, in the air) but the pressure that is creating a force, and the pressure the narrow tube is exerting on the cylinder is the same, but as surface area increases, the normal force would increase. What do you think?
Edit: The outside tube in this case is elastic.

 

[kuruman]

I think you are correct. The pressure (force per unit area) exerted by the outer elastic tube is the same, but the contact area increases as the inner cylinder is pushed farther in. If the contact area increases so does the radial total force. This raises the upper threshold of static friction so that more force is needed to push the cylinder farther in.

Assuming that all four of your fingers are equally strong (ignore the thumb), why is it easier to wrap around and hold a heavy rod vertical using all four fingers instead of just one?

 

[arhg]

Thank you so much for the explanation.