**Part A**

Exerted force:

$\overline{){{\mathbf{F}}}_{\mathbf{t}\mathbf{o}\mathbf{p}}{\mathbf{=}}\frac{\mathbf{\u2206}\mathbf{P}}{\mathbf{\u2206}\mathbf{t}}}$

P = mv

${\mathit{F}}_{\mathbf{t}\mathbf{o}\mathbf{p}}\mathbf{=}\frac{\mathbf{m}{\mathbf{v}}_{\mathbf{f}}\mathbf{-}\mathbf{m}{\mathbf{v}}_{\mathbf{0}}}{\mathbf{\u2206}\mathbf{t}}$

v_{f} = v_{0}, therefore:

**Breaking a Glass Soda Botle**

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. (Figure 1) 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 force that her fist exerts on the top of the bottle? Express your answer in newtons to three significant figures.

**(b) **What is the magnitude of the force exerted on the bottom of the bottle?

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