Minimum force necessary to push out a cork

In summary, the two arms of a u-tube are not identical in diameter, with one being twice the size of the other. The narrow arm has a cork that requires a force of 16n to remove it. When filled with water, the wide arm has a piston and the minimum force needed to push out the cork is 64n, not 32n as initially calculated. This is due to an error in the calculation, as the correct value should be pi*4r^2, not pi*2r^2. Using a dimensional argument may have resulted in a more accurate calculation.
  • #1
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Homework Statement


2 arms of a u-tube are not identical, one having twice the diameter of the other. a cork in the narrow arm requires a force of 16n to remove it. the tube is filled with water and the wide arm is fitted with a piston. the min force that must be applied to the piston to push out cork is?


Homework Equations


p=f/a


The Attempt at a Solution


p1=f1/(pi*r^2), p2=f/pi*2r^2, p1=p2, f1/(pi*r^2)=f2/(pi*2r^2)...f2=(pi*r^2)*f1/(pi*r^2) which gives me 32. The answer is actually 64. What am i missing?
 
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  • #2
hi drunknfox! :smile:

(have a pi: π and try using the X2 icon just above the Reply box :wink:)
drunknfox said:
p1=f1/(pi*r^2), p2=f/pi*2r^2, p1=p2, f1/(pi*r^2)=f2/(pi*2r^2)...f2=(pi*r^2)*f1/(pi*r^2) which gives me 32. The answer is actually 64. What am i missing?

it isn't π*2r2 :redface:

(and using a dimensional argument would be much quicker, and less likely to lead to a mistake)
 

1. What is the minimum force necessary to push out a cork?

The minimum force necessary to push out a cork varies depending on various factors such as the size and shape of the cork, the type of bottle it is in, and the lubrication present. However, on average, it takes around 8-12 pounds of force to push out a cork from a standard wine bottle.

2. How does the size of the cork affect the minimum force required to push it out?

The size of the cork plays a significant role in determining the minimum force necessary to push it out. A larger cork will require more force to push out compared to a smaller cork due to the increased surface area and tighter fit in the bottle.

3. Can the type of bottle affect the minimum force needed to push out a cork?

Yes, the type of bottle can affect the minimum force necessary to push out a cork. For example, a bottle with a narrower neck will require more force to push out the cork compared to a bottle with a wider neck, as the cork will have a tighter fit in the narrow neck bottle.

4. How does lubrication impact the minimum force needed to push out a cork?

Lubrication can significantly reduce the minimum force necessary to push out a cork. A lubricated cork will have less friction against the bottle, making it easier to push out. This is why it is common to see people twist and wiggle a cork before pushing it out, as it helps to lubricate the cork and reduce the force needed.

5. Is there a specific technique to apply the minimum force necessary to push out a cork?

While there is no specific technique, there are some tips that can help reduce the minimum force needed to push out a cork. These include twisting and wiggling the cork, using your dominant hand to push down while your other hand holds the bottle, and applying gradual and consistent pressure rather than a sudden forceful push.

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