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It doesn't work that way - friction is not something that is "produced". The way it works is that you have a coefficient of friction for two surfaces that are in contact. Then you use that coefficient of friction, and multiply it by the normal force, to calculate the actual FORCE of friction.For the coefficient of friction, you need to specify a PAIR of substances; for example, carpet against glass would probably have less friction than carpet against rubber.

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Q: How much friction thick carpet produces?
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