Calculating Friction Force from Pressure in a Bottle of Champagne

In summary, 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 1.0 cm (.01 m). The frictional force on the cork due to the neck of the bottle that keeps the cork in the bottle is 143.24 N.
  • #1
trickymax301
5
0
Here's my homework question...

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 1.0 cm (.01 m). What is the frictional force on the cork due to the neck of the bottle that keeps the cork in the bottle?

1 atm = 101,325 pascles
 
Physics news on Phys.org
  • #2
What have you done on this? do you have a free body diagram for this? do you have a realtionship between force and pressure? Do you have any ideas on why they gave you a radius?
 
  • #3
Force = Pressure x Area.
 
  • #4
Let me see if my conversions are correct first. I assumed the air outside is equal to 1 atm. soo

Pressure inside the bottle (Pbottle) = (4.5)(101,325) = 455962.5 Pa
Pressure outside the bottle (Pair) = (1)(101,325) = 101.325 Pa

If my conversion is wrong, please correct me

And, since I'm dealing with fluids, I assumed the radius was given to me so that I could plug numbers into Bernouli's equation [(P1-P2)V] or plug numbers into the Continuity equation (A1V1 = A2V2). I first looked at Bernouli's equation since my problem deals with pressure, but I'm not given a velocity. Any hint which equation I should use?

As for the relationship between force and pressure, I know Pressure = Force/Area. If my conversion above for the Pbottle is correct, I can figure out that Force = Pressure*Area. So the force that the inside of the champagne has on the cork is F = 455962.5*(pi)(.01^2) = 143.24 N. This is how I tried the problem the first time, thinking the friction of the cork had to be equal to or greater than the force being pushed up by my champagne. But that answer seemed to easy to get. More suggestions would be helpful. Thanks!
 
  • #5
Venturing into dealing with velocities shouldn't be necessary. There are basically two forces in your system; the force F1 exterted downwards on the cork due to the outside pressure, and the force F2 exerted upwards due to the internal pressure.

In order for the cork to stay in place, the frictional force must overcome the net of these two forces, e.g.

Ff >= F2 - F1.
 
  • #6
But watch the numbers you are using for the pressure, as you state:
trickymax301 said:
4.5 atm higher than the air pressure outside
.
wouldn't that be 5.5 atm then?
 
  • #7
Yeah I saw the same thing...isnt that 5.5atm?
And yes it's only a force problem.
 
  • #8
it's simple u just hav to draw it u'll find the force of atm outside the bottle and also the friction force directing downwards and let's call the force inside the bottle dueto the pressure "F3" so F1+F2=F3
where F1 is the atm force
and F2 is the friction force
and since F1 and F3 are forces due to pressure then get them from F=P*A
P:pressure
A:area

and about the pressure inside the bottle it's a gauge pressure and outside pressure is given in absolute pressure so as we all know we can't put in the same law different units so u'll have to convert one of them to the other; by the way the atm in gauge is zero pa and in absolute it's 101,325 pa
and the conversions is as follows
absolute pressure = gauge pressure + 101,325pa
 

1. How do I calculate the friction force from pressure in a bottle of champagne?

To calculate the friction force, you will need to use the equation F = P x A, where F is the friction force, P is the pressure, and A is the area. You will also need to know the coefficient of friction, which can be found by dividing the friction force by the normal force.

2. What is the relationship between pressure and friction force in a bottle of champagne?

The relationship between pressure and friction force in a bottle of champagne is direct. This means that as the pressure increases, the friction force also increases. This is because the higher pressure creates more contact between the bottle and the cork, resulting in a stronger friction force.

3. How does the shape of the bottle affect the calculation of friction force from pressure in a bottle of champagne?

The shape of the bottle can affect the calculation of friction force from pressure in a bottle of champagne. A bottle with a wider opening will have a larger area in contact with the cork, resulting in a higher friction force. On the other hand, a bottle with a narrower opening will have a smaller area in contact with the cork, resulting in a lower friction force.

4. Can the temperature of the champagne affect the calculation of friction force from pressure?

Yes, the temperature of the champagne can affect the calculation of friction force from pressure. This is because as the temperature increases, the pressure inside the bottle also increases. This means that there will be a higher friction force between the bottle and the cork, resulting in a different calculation.

5. How can I use the calculation of friction force from pressure to open a bottle of champagne?

To open a bottle of champagne, you can use the calculation of friction force from pressure to determine the amount of force needed to remove the cork. You can use the equation F = P x A to calculate the force, and then apply this force to the cork in a twisting motion to loosen it from the bottle.

Similar threads

  • Introductory Physics Homework Help
Replies
6
Views
247
  • Introductory Physics Homework Help
Replies
8
Views
664
Replies
15
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
186
  • Introductory Physics Homework Help
Replies
1
Views
912
  • Introductory Physics Homework Help
Replies
3
Views
3K
  • Thermodynamics
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
18
Views
20K
Replies
27
Views
15K
  • Introductory Physics Homework Help
Replies
4
Views
1K
Back
Top