Intro to Pressure Video Lessons

Concept

# Problem: Breaking a Glass Soda BotleA 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 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.(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?

###### FREE Expert Solution

Part A

Exerted force:

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

P = mv

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

vf = v0, therefore:

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###### Problem Details

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 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.

(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?