Physics quiz question: champagne cork in bottleneck

Physics 5A Quiz 5, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 9.78

[3.0 points.] The pressure inside a bottle of champagne is 5.0 atm higher than the air pressure outside. The neck of the bottle has an inner radius of 1.2 cm. What is the frictional force on the cork due to the neck of the bottle?
(A) 46 N.
(B) 2.3 x 10^2 N.
(C) 2.7 x 10^2 N.
(D) 1.1 x 10^9 N.

Correct answer: (B)

A shortcut for the differential pressure force is to calculate:

F_diff = delta(P)*A = (5.0 atm)*(101.3 x 10^3 Pa/atm)*pi*(0.012 m)^2,

and setting this equal to the frictional force of the bottleneck required to keep the cord in place. A more thorough approach is calculate the forces due to the pressure both outside of and inside of the bottle:

F_outside = P_outside*A = (1.0 atm)*(101.3 x 10^3 Pa/atm)*pi*(0.012 m)^2,

F_inside = P_inside*A = (6.0 atm)*(101.3 x 10^3 Pa/atm)*pi*(0.012 m)^2,

And thus from Newton's first law:

F_outside + F_friction = F_inside.

Choice (A) is F_outside only. Choice (C) is F_inside only. Choice (D) is delta(P) divided by area.

Student responses
Sections 0906, 0907
(A) : 5 students
(B) : 17 students
(C) : 15 students
(D) : 2 students