Solving Pressure Problems: Vacuum Cleaner & Octopus

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The discussion focuses on calculating the lifting capacity of a vacuum cleaner and the force exerted by an octopus in salt water. For the vacuum cleaner, the weight of the heaviest brick it can lift is determined by the pressure generated inside the hose and the area of the hose's opening. The pressure is derived from atmospheric conditions, with the maximum force calculated by multiplying standard atmospheric pressure by the hose's cross-sectional area. In the case of the octopus, the force it can exert is similarly calculated using pressure principles, factoring in the depth of the salt water. Understanding the relationship between pressure, area, and force is essential for solving both problems.
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(a) A very powerful vacuum cleaner has a hose 2.86cm in diameter. With no nozzle on the hose, what is the weight of the heaviest brick it can lift? (b) A very powerful octopus uses one sucker, of diameter 2.86cm, on each side of a shell of a clam in an attempt to pull the shells apart. Find the greatest force the octopus can exert in salt water 32.3m deep.

(a) - I'm not sure how I know the power of the vacuum, but I think I'm suppose to use P = P_0 + pgh although I'm not sure how.

(b) I have no clue how to do this :-\

Could anyone lend a hand?
 
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For the first part you need to know what pressure the vacuum cleaner is generating.

Once you have this you need to think about over what area this pressure is acting.

Remember

Pressure * Area = Force

And the force relates to the weight.

The second part is not so different... :smile:
 
Well, the problem doesn't give me the pressure of the vacuum. Is that something I can assume?
 
Of course, a vacuum cleaner doesn't actually pull anything- it reduces the density of air in it and then the pressure of the outside air pushes things in.
The minimum possible density is, of course, 0 which would result in the air pressure (one atomosphere) pushing against the brick. Multiply standard one atmospher air pressure by the area of the hose to find the maximum possible force.
 

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