A cake and plate weighing 1.5 lb rest at the center of a circular table. Without touching the cake a boy attempts to remove the 2-ft-radius tablecloth by quickly pulling on it horizontally. If slipping between the cake plate and tablecloth occurs at all times, determine the longest time the tablecloth can remain in contact with the plate without having the cake wind up on the floor. The coefficient of kinetic friction between the cake plate and the tablecloth is μ_k = 0.3 and between the cake plate and the table surface μ′_k = 0.4. Apply the principles of impulse and momentum and work and energy to the cake for x ft, the distance the cake plate remains on the tablecloth, and for (2 - x) ft when it remains on the table.

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2 ft