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Q. A glass soda bottle is emptied of soda and filled to the very top with water. A cork is carefully fitted into the top of the bottle, leaving no air between the cork and the water. The top of the bottle has a diameter of D_top = 2.00 cm and the bottom of the bottle has a diameter of D_bot = 6.50 cm. The glass breaks while it is exposed to p_max = 70.0 MPa of pressure.
A student hits the cork sharply with her fist and the bottom of the bottle breaks. The student's fist has a mass of m = 0.48 kg and moves downward at the speed of v_i = 5.00 m/s. It collides elastically with the cork and rebounds with the equal speed. The collision lasts for t = 1.2×10-4 s. In this problem, positive direction is upward.
What is the magnitude of the force exerted on the bottom of the bottle?
State your reply in Newton to four significant figures.
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