Upon grabbing a glass with your fingers, the downward motion of the glass is halted by the frictional force, which is directed upward and related to the amount of force your fingers exert toward the glass (barely gripping a cold glass of water on a hot summer day will not be sufficient to prevent the glass from falling). Since the frictional force directed upward is proportional to the strength with which you grip the glass, why doesn't the glass move upward the harder you grip it?
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$\begingroup$ A wet slick glass just might if you squeeze too hard... $\endgroup$– Jon CusterCommented Aug 15, 2017 at 19:33
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2 Answers
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The frictional force directed upward is not proportional to the strength with which you grip the glass (i.e. the normal force between the glass and your fingers). Remember, this is static friction, so the maximum frictional force which can be exerted by your fingers on the glass will be proportional to the normal force, but the actual frictional force is whatever it has to be to prevent the glass from moving.
$$f_s \leq \mu f_N$$
The inequality is important.
answered Aug 15, 2017 at 19:21
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Since the frictional force directed upward is proportional to the strength with which you grip the glass [...]
It isn't. If the glass is held still so it doesn't fall, then there is static friction between your hand and the glass. You seem to be confusing the two frictions:
- Kinetic friction (when sliding) is proportional to the pressing force, yes, $f_k=\mu_k n$, but
- but static friction (when no sliding) is not. The maximum value static friction can take is proportional to the pressing force, $f_s\leq \mu_s n$, but noone knows if the actual static friction force is at it's maximum value. You can easily be holder on with smaller force.
Think of a table being pushed over the floor. It experiences kinetic friction, which is proportional to the table weight (which acts as the pressing force in this case). If you don't push it over the floow, then there is no friction at all - but there is still a weight (a pressing force). If you now push it slightly, without moving it, then a small static friction has appeared to hold back against your push - but the weight (and pressing force) is unchanged.
Conclusion: A static friction can take any value from zero and up to it's maximum value. You can't assume proportionality here. It just takes whatever value it needs in order to hold back against whatever it has to hold back against.
