It is known that the force of dry friction between two bodies is practically independent of the area of contact between these bodies. However, the deeper the cork is inserted into the neck of a bottle, the more difficult it is to remove it. Why?
Decision:
Indeed, the force of friction is directly proportional to the force of normal pressure $N$
$F_{T} = \mu N$,
where ($\mu$ is the coefficient of friction between the contacting surfaces. In the situation under consideration, the force of normal pressure is directly proportional to the area of contact between the surfaces of the cork and the neck of the bottle. Therefore, the deeper the cork is inserted into the neck of the bottle, the greater the friction force between the contacting surfaces and the more firmly the cork is held in the neck of the bottle
Decision:
Indeed, the force of friction is directly proportional to the force of normal pressure $N$
$F_{T} = \mu N$,
where ($\mu$ is the coefficient of friction between the contacting surfaces. In the situation under consideration, the force of normal pressure is directly proportional to the area of contact between the surfaces of the cork and the neck of the bottle. Therefore, the deeper the cork is inserted into the neck of the bottle, the greater the friction force between the contacting surfaces and the more firmly the cork is held in the neck of the bottle