(a) A powerful vacuum cleaner has a hose 2.86 cm in diameter. With no nozzle on the hose, what i

step 1 The diameter is given as 2 .86 cm. Now the force or the weight of the brick can be obtained as f

(a) A powerful vacuum cleaner has a hose 2.86 cm in...

(a) A powerful vacuum cleaner has a hose 2.86 $\mathrm{cm}$ in diameter. With no nozzle on the hose, what is the weight of the heaviest brick that the cleaner can lift (Fig. Pl4.10a)? (b) What If? An octopus uses one sucker of diameter 2.86 $\mathrm{cm}$ on each of the two shells of a clam in 0an attempt to pull the shells apart (Fig. Pl4. 10 b). Find the greatest force the octopus can exert in seawater 32.3 $\mathrm{m}$ deep. Caution: Experimental verification can be interesting, but do not drop a brick on your foot. Do not overheat the motor of a vacuum cleaner. Do not get an octopus mad at you.

Key Concepts

Cross-sectional Area Calculation

In problems involving pressure-induced forces, calculating the cross-sectional area of a circular opening is essential. The area is typically determined by the formula A = ?(d/2)², where d is the diameter. This calculation allows one to convert a pressure difference into a force acting over that specific area.

Hydrostatic Pressure

Hydrostatic pressure refers to the pressure exerted by a fluid at equilibrium due to the weight of the fluid above a given point. It increases linearly with depth according to the relation P = ?gh, where ? is the fluid density, g is the gravitational acceleration, and h is the depth. Understanding hydrostatic pressure is crucial in analyzing forces in fluid environments and underwater applications.

Pressure and Force Relationship

This concept involves understanding that force is generated when a pressure difference acts over an area. The relationship is given by the equation F = P × A, where F is force, P is pressure difference, and A is the area. This fundamental principle is widely used in analyzing systems where pressure differences move or lift objects.

Vacuum and Pressure Differential

A vacuum is a region of space with pressure significantly lower than the surrounding atmosphere. Creating a vacuum results in a pressure differential, where the higher external pressure exerts force towards the lower pressure area. This principle is critical in understanding how devices that use suction generate lifting or pulling forces.

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