Impulsive force:

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

Speed before the collision is equal to speed before the collision but direction changes.

v_{f} = -v_{0}

ΔP = mv_{f} - mv_{0} = m(-v_{0}) - mv_{0} = -2mv_{0} = - 2 × 0.48 × 5.00 = -4.8 kg•m/s

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.

What is the force that the fist exerts on the top of the bottle?

Express your answer in newtons.

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