You are going to entertain your Aunt Emma by pulling a tablecloth out from under the dishes at her birthday party. The birthday cake is resting on a tablecloth at the center of a round table of radius r. The tablecloth is the same size as the table top. You grab the edge of the tablecloth and pull sharply. The tablecloth and cake are in contact for time t after you start pulling. Then the sliding cake is stopped (you hope) by the friction between the cake and table top. The coefficient of kinetic friction between the cake and tablecloth is µk1, and that between the cake and table top is Hk2. Part A Apply the impulse-momentum relation and the work-energy theorem to calculate the maximum value of t if the cake is not to end up on the floor. Assume that the cake moves a distance d while still on the tablecloth and therefore a distance r - d while sliding on the table top. Assume that the friction forces are independent of the relative speed of the sliding surfaces. You can easily try this trick yourself by pulling a sheet of paper out from under a glass of water, but have a mop handy just in case! Take the free fall acceleration to be g.

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