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?

🤓 Based on our data, we think this question is relevant for Professor Mon's class at UGA.

FREE Expert Solution

Part A

Exerted force:

Ftop=Pt

P = mv

Ftop=mvf-mv0t

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?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Intro to Pressure concept. You can view video lessons to learn Intro to Pressure. Or if you need more Intro to Pressure practice, you can also practice Intro to Pressure practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Mon's class at UGA.