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

Example 10.15 When we were defining the bulk modulus of compressibility we said that as the pressure is

increased, the volume of fluid is decreased, and consequently the density of the fluid is increased.

Why does the density of a fluid increase when its volume is decreased?

Recall that density is defined as the ratio of mass to volume, as given by

From examining this equation, for a given mass, you can see that as the volume is reduced; the

density is increased.

Example 10.16 For water, starting with 1 m

3

of water in a container, what is the pressure required to decrease

the volume of water by 1%?

From Table 10.7, the compressibility modulus for water is 2.24  10

9

N/m

2

. It would
require a pressure of 2.24  10
7
N/m
2
to decrease the original 1 m
3
volume of water to a final
volume of 0.99 m
3
, or, said another way, by 1%. It would require an equivalent pressure of
221 atm (2.24  10
7
N/m
2
) to reduce the pressure of a unit volume of water by 1%.

10.7 Linear Impulse–Force Acting Over Time

Up to this point, we have defined the effects of a force acting at a distance in terms of creating

moment, and through a distance as doing work. Now we will consider force acting over a period

of time. Understanding linear impulse and impulsive forces is important in the design of prod-

ucts such as air bags and sport helmets to prevent injuries. Understanding impulsive forces also

helps with designing cushion materials to prevent damage to products when dropped or when sub-

jected to impact. On TV or in the movies, you have seen a stuntman jumping off a roof of a mul-

tistory building onto an air mat on the ground and not getting hurt. Had he jumped onto concrete

pavement, the same stuntman would most likely be killed. Why is that? Well, by using an inflated

air mat, the stuntman is increasing his time of contact with the ground through staying in touch

with the air mat for a long time before he is completely stopped. This statement will make more

sense after we show the relationship between the linear impulse and linear momentum.

Linear impulserepresents the net effect of a force acting over a period of time. There is a

relationship between the linear impulse and the linear momentum. We explained what we mean

by linear momentum in Section 9.6. A force acting on an object over a period of time creates a

linear impulse that brings about a change in the linear momentum of the object, according to

(10.31)

where

Faverageaverage magnitude of the force acting on the object (N)

ttime period over which the force acts on the object (s)

mmass of the object (kg)

F

!

average¢tmV

!

fmV

!

i

density

mass

volume

290 Chapter 10 Force and Force-Related Parameters

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