The pressure inside a bottle of champagne is 4.5 atm higher than the air pressure outside. The neck of the bottle has an inner radius of 1.1 cm. What is the frictional force on the cork due to the neck of the bottle?
2007-07-17 08:15:52 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Physics
This is an easy one.
f = ma = F - C - A = 0; where f is the net force on the cork of mass m and acceleration a = 0 since the cork is stuck in the neck. F is the force on the cork from the bottle, C is the cork friction force, and A is the force on the cork from outside the bottle.
f = P pi r^2 - C - Patm pi r^2 = 0; so that (P - Patm)pi r^2 = C; where C is the cork friction force, P = Patm + 4.5 atm the pressure in the bottle acting on a cork area of a = pi r^2. Pa = F and Patm = 1.0 atm ambient pressure.
From (P - Patm)pi r^2 = C we see that C = 4.5 atm * pi (1.1 X 10^-2 m)^2; so that the cork friction force = C = 4.5 atm * pi * 1.21 X 10^-4 m^2. Find what 1 atm is in Newtons/m^2 and work this equation with the Newton/m^2 instead of atm. That will give you C, the cork friction, in Newtons.
The physics lesson here is that the cork needs to add a force equivalent to the difference of the internal force on the cork and the external force on the cork. That results because there is no net force on the cork when it is static.
2007-07-17 08:40:41 · answer #1 · answered by oldprof 7 · 0⤊ 0⤋
at least enough to withstand 1 atm/ square cm of pressure. The frictional force itself cannot be determined without the coefficient of friction between cork and glass and the size and shape of the neck of the bottle the cork fits into.
2007-07-17 08:39:06 · answer #2 · answered by SteveA8 6 · 0⤊ 1⤋
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2016-10-04 00:49:01 · answer #3 · answered by Anonymous · 0⤊ 0⤋
the frictional force is equal to the product of the pressure difference and the cross section, e.g.,
f = 4.5*3.14*(1.1)**2
2007-07-17 09:40:46 · answer #4 · answered by yan k 1 · 0⤊ 0⤋
p=f/A
first convert atm to pascals
then use pi*r^@ to get area and convert to m^2
then f = AxP
2015-11-11 04:13:36 · answer #5 · answered by senya 1 · 1⤊ 0⤋