Breaking a Glass Soda Bottle
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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 when 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 = 0.480 kg and moves downward at a speed of v_i = 5.00 m/s. It collides elastically with the cork and rebounds with the same speed. The collision lasts for t = 1.20×10−4 s. In this problem, the positive direction is upward.
a). What is the magnitude of the force exerted on the bottom of the bottle?
Express your answer in newtons to four significant figures.
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Solution Summary
This solution calculates the magnitude of force exerted on the bottom of the bottle by finding the final and initial velocity in the elastic collision. All formulas used are included with a brief explanation.
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a)
F = m * (delta V)/(delta t)
Since it is an elastic ...
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