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I understand that a car slips because friction is lessened, but why?

With my understanding, all objects are only touching at a very minimal number of points on the atomic level (in reality, not touching at all, but we'll call "touching" what we see as touching). However, as water is a liquid and forms to the shape of its surrounding why is it that with a greater area of connection between the wheel and the road is the friction not increased.

I ran a small test at my desk. When I put my cup in a thin layer of water and try to move it I feel a stronger force being exerted on my hand than when I pick it straight off the desk.

Thanks.

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Let's go first with the car, and do it first macroscopically:

The car moving on the asphalt experience a friction force due the interaction between the tires and the road. This friction can be formulated in terms of the coefficent of friction between the tire and the asphalt $\mu_1$, dependent on the characteristics of both surfaces, like rugosity, elasticity, area and so on. In fact will be due small imperfections in the meterials:

Friction due small imperfections between two surfaces

The car moving over a puddle which is deep enough to consider it as a different surface, but not enough to introduce new physics (the puddle is not a pool, the car is not moving in the water but over it, so we don't need to be aware of dragging forces and hydrodynamics) will experience also a friction force defined by a friction coefficent $\mu_2$. Experimentally one finds that $\mu_1>\mu_2$ for the same tire. The water will form a small film that will "correct" the imperfections in the materials. The asphalt and the tire are, hence, in "less contact" since they are "floating" over the film of waterFriction reduced by a layer of water

Microscopically the friction coefficent relates with electromagnetic both surfaces. The tire and the asphalt create brief bonds between their atoms. those are not very strong bonds, but strong enough to have an effect on the dynamics. When water is added part of the bonds between the asphalt and the tire are replaced by bonds between the tire and the water. Since water molecules move more freely than those in the asphalt, the molecules (and with them the bonds) are dragged, resulting in effectivelly less fixed bonds to the tire and the total friction force is reduced.

Now with the cup. The previous argument still holds, and you can check that the cup moves easier when sliden on the desk if you put a very thin layer of water or oil (with oil will be even better, since the molecules stack beter than the woter molecules but e interactions between fatty acids is weaker than the hidrogen bonds in the water, the result is that a thin layer of oil is dragged with the moving surface, giving even less friction than with water). However when you try to pick up the cup, the physics is completelly different:

Normaly cups have a small concavity at the bottom (in this way they are more stable and are easier to manufacture). The borders of the concavity are, again, not perfect, but with some irregularities. Trhough this irregularities the air can flow to the bottom of the glass and the internal and external pressure are the same, the only forcing acting against the pick up is gravity (and air resistance which for sake of simplicity we will ignore).

Picking up a dry glass.

However if there is water on the surface, the irregularities of the glass are smoothed. The film now act as a seal of the inner cavity. If you try to lift the glass, the iner cavitty increases slightly in volume, and, therefore, the preasure inside disminishes. The very small difference between the inner pressue in the cavity and the atmosferic preasure outside is manifest in a total net force that opposes to the lift.

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