Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

9.7 Conservation of Mass 241

Example 9.2 Determine the linear momentum of a person whose mass is 80 kg and who is running at a rate

of 3 m/s. Compare it to the momentum of a car that has a mass of 2000 kg and is moving at a

rate of 30 m/s in the same direction as the person.

We will use Equation (9.14) to answer the questions.

Kinetic energy is another quantity that is mass dependent and is used in engineering analysis

and design. An object having a mass m and moving with a speed Vhas a kinetic energy, which

is equal to

1

⁄ 2 mV

2

. In Chapter 13, we will explain the concept of kinetic energy in more detail
after we define mechanical work.

9.7 Conservation of Mass

Recall that in Chapter 6 we mentioned that engineers are good bookkeepers. In the analysis of

engineering work we need to keep track of physical quantities such as mass, energy, momentum,

and so on. Let us now look at how engineers may go about keeping track of mass and the asso-

ciated bookkeeping procedure (see Figure 9.4). Simply stated, the conservation of mass says that

we cannot create or destroy mass. Consider the following example. You are taking a shower in

your bathtub. You turn on the water and begin to wash yourself. Let us focus our attention on

the tub. With the drain open and clear of any hair and dead skin tissue, the rate at which water

comes to the tub from the showerhead is equal to the rate at which water leaves the tub. This is

a statement of conservation of mass applied to the water inside the tub. Now what happens if

the drain becomes plugged up by hair or dead skin tissue? Many of us have experienced this at

one time or another. Liquid Dra-no

®

time! The rate at which water comes to the tub now is not

exactly equal to the rate at which water leaves the tub, which is why the water level in the tub

begins to rise. How would you use the conservation of mass principle to describe this situation?

Car: L

!

mV

!

 1 2000 kg 21 30 m/s 2 60,000 kg#m/s

Person: L

!

mV

!

 1 80 kg 21 3 m/s 2 240 kg#m/s

Control volume

■Figure 9.4

The rate at which water enters

the container minus the rate at

which water leaves the container

should be equal to the rate of

accumulation or depletion of

the mass of water within the

container.

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