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Chapter 14: Q. 14 (page 384)

What is the minimum hose diameter of an ideal vacuum cleaner that could lift a 10kg(22lb) dog off the floor?

Short Answer

Expert verified

The minimum hose diameter of an perfect vacuum cleaner isd=3.51cm

Step by step solution

01

Force.

A force may be a push or pull on an object caused by the interaction of the thing with another object.

Anytime two things interact, a force is exerted on each of them.

The 2items do not feel the force after the interaction ends.

02

Find A to derive diameter.

calculating the force F,

localid="1650283275175" F=mg

localid="1650283280316" F=(10kg)9.8ms2

localid="1650283284371" F=98N

In the case of an perfect vacuum, the air pressure localid="1650283354042" Pis localid="1650283288842" 1.013脳105Nm2

localid="1650283292792" P=FA

localid="1650283296736" A=98N1.013脳105Nm2

localid="1650283300351" A=9.674脳10-4m2

03

Find the diameter of the hose.

Solving for the diameter of the opening of the hose,

A=蟺r2

9.674脳10-4m2=蟺d22

9.674脳10-4m2=蟺脳d42

d=4(9.674脳10-4m2)蟺

d=49.674脳10-4m2蟺

d=0.351m

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