# Problem: 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 Dtop = 2.00 cm and the bottom of the bottle has a diameter of Dbot = 6.50 cm. The glass breaks when it is exposed to pmax = 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 vi = 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.

###### FREE Expert Solution

Impulsive force:

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

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

vf = -v0

ΔP = mvf - mv0 = m(-v0) - mv0 = -2mv0 = - 2 × 0.48 × 5.00 = -4.8 kg•m/s

###### Problem Details

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 Dtop = 2.00 cm and the bottom of the bottle has a diameter of Dbot = 6.50 cm. The glass breaks when it is exposed to pmax = 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 vi = 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?