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Friction - Coin in a Glass

The frictional force between the card and the coin depends upon the normal force directed from card to coin and the coefficient of friction for the two surfaces in contact (Frictional force = mass of coin x acceleration due to gravity x coefficient of friction). For the card to accelerate a force is applied to it (force = mass of card x acceleration of card). For the coin move with the card it must have the same acceleration as the card. It must therefore experience a force. This force is supplied by friction as long as the acceleration required of the coin is low enough so that F=ma of the coin is less than the frictional force. If the force required for the coin to have the same acceleration as the card is greater than can be supplied by friction then the coin will not accelerated but the card will.

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