The required minimum grip must be greater than the sliding friction.
Sliding friction is the friction required for the bottle to slip from the hand.
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Static friction does not increase, always equal to the weight of the bottle. However, the holding force and the reaction force of the bottle will increase. 1, that is, static friction. The relative motion between objects produces dynamic friction, and there will be friction between all moving objects in the world! At this time, people will ask, if you pull an object with a force, if you just let it move without moving, will it be subjected to friction? That's right! It will be rubbed. At this time, it is not dynamic friction, but static friction. Dynamic friction can be calculated by formula, but static friction is a range. The biggest static friction between two objects is their dynamic friction, so the greater the force that makes them move relatively, the greater the static friction ... 2. It's not that your bottle is getting heavier and heavier, but that the bottle is slowly slipping away from your friction resistance. You must increase the friction to prevent it from moving. When holding a bottle, static friction equals gravity. At this time, no matter how hard you hold it.
The coefficient in the static friction formula f = μ n is the static friction coefficient. It is used to find the maximum static friction. For example, μ = 0.2, n = 10N, and f = 2 N, that is, when you hold it with 10N, you can hold it to the maximum extent, that is, you can just hold a bottle with G = 2 N ... If you want to hold a heavier bottle, you should increase your hand grip, that is, increase the maximum static friction.
About your question: In the above example, when the hand has been held with a force of 10N, the bottle is only 1N, so of course it can be held. If the weight of the bottle increases to 1...0, hold the bottle by hand. Why do you have to hold the bottle harder when it is heavier?
I'm sorry, the harder you hold it, why does the static friction increase? Can you prove it by formula?