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If I were to hold a block against a vertical wall that has a static and kinetic friction coefficient of 0, would the block fall down?

I think that it would fall down because the only force holding it up is the friction force acting against gravity. However, since the coefficients of friction are zero, there will be no friction force, no matter how hard I push the block against the wall.

However, this doesn't make intuitive sense because I'm sure that a block would still stay in place if you pushed it against the wall with a lot of force, no matter how frictionless the wall is.

We are assuming that the wall is rigid and won't deform under the block's pressure.

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Yes it would slide down, if the objects that applies the vertical force also has a zero coefficient. This could be achieved by a pusher with a (frictionless) roller on the end, or the object that applies the force has the same attributes.

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  • $\begingroup$ Oh, I forgot that there would also be a friction force between my finger and the block since I did not specify that they were frictionless, thanks. $\endgroup$
    – Some Guy
    Jan 11 at 0:34
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If you apply your force sideways (trying to push the block into the wall), and everything is frictionless and there are no deformations, then yes, the block would indeed slide down, as there are no forces to pull it up.

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