Chapter 14: Q. 14 (page 384)

What is the minimum hose diameter of an ideal vacuum cleaner that could lift a $10 k g$ ( $22 l b$ ) dog off the floor?

Short Answer

Expert verified

The minimum hose diameter of an perfect vacuum cleaner is $d = 3.51 c m$

Step by step solution

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

Find A to derive diameter.

calculating the force $F$ ,

localid="1650283275175" $F = m g$

localid="1650283280316" $F = (10 kg) (9.8 \frac{m}{s^{2}})$

localid="1650283284371" $F = 98 N$

In the case of an perfect vacuum, the air pressure localid="1650283354042" $P$ is localid="1650283288842" $1.013 \times 10^{5} \frac{N}{m^{2}}$

localid="1650283292792" $P = \frac{F}{A}$

localid="1650283296736" $A = \frac{98 N}{1.013 \times 10^{5} \frac{N}{m^{2}}}$

localid="1650283300351" $A = 9.674 \times 10^{- 4} m^{2}$

Find the diameter of the hose.

Solving for the diameter of the opening of the hose,

$A = π r^{2}$

$9.674 \times 10^{- 4} m^{2} = π {(\frac{d}{2})}^{2}$

$9.674 \times 10^{- 4} m^{2} = π \times {\frac{d}{4}}^{2}$

$d = \frac{4 (9.674 \times 10^{- 4} m^{2})}{π}$

$d = \sqrt{\frac{4 (9.674 \times 10^{- 4} m^{2})}{π}}$

$d = 0.351 m$

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What is the minimum hose diameter of an ideal vacuum cleaner that could lift a $10 k g$ ( $22 l b$ ) dog off the floor?

Short Answer

Step by step solution

Force.

Find A to derive diameter.

Find the diameter of the hose.

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

Short Answer

Step by step solution

Force.

Find A to derive diameter.

Find the diameter of the hose.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Astrophysics

Fundamentals of Physics

Famous Physicists

Magnetism and Electromagnetic Induction

Physics of Motion

Fluids

Study anywhere. Anytime. Across all devices.

What is the minimum hose diameter of an ideal vacuum cleaner that could lift a $10 k g$ ( $22 l b$ ) dog off the floor?