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448 CHAPTER 14 Statics and Elasticity

Table 14.1 includes values of bulk moduli for solids.This table also includes values of
bulk moduli for some liquids.The force per unit area,F A, is also known as the pressure:
F
pressure [pressure] (14.21)
A
The formula (14.20) is equally valid for solids and for liquids—when we squeeze a
liquid from all sides, it will suffer a compression. Note that Table 14.1 does not include
values of Young’s moduli and of shear moduli for liquids. Elongation and shear stress
are not supported by a liquid—we can elongate or shear a “block” of liquid as much as
we please without having to exert any significant force.

The lifting cable of a tower crane is made of steel, with a diam-
Concepts EXAMPLE 8
in eter of 5.0 cm.The length of this cable, from the ground to the
Context
horizontal arm, across the horizontal arm, and down to the load, is 160 m (Fig.
14.28). By how much does this cable stretch in excess of its initial length when
carrying a load of 60 tons?

Total cable length
is 160 m. 60 t

Cable stretches
due to load.

FIGURE 14.28 Elongation
of a tower crane cable.

SOLUTION: The cross-sectional area of the cable is
2
3
2
A pr p (0.025 m) 2.0 10 m 2
and the force per unit area is
2
F (60 000 kg 9.81 m/s ) 8 2
2.9 10 N/m
3
A 2.0 10 m 2
Since we are dealing with an elongation, the relevant elastic modulus is the Young’s
10
2
modulus. According to Table 14.1, the Young’s modulus of steel is 22 10 N/m .
Hence Eq. (14.18) yields
¢L 1 F 1 8 2
2.9 10 N/m
10
L Y A 22 10 N/m 2
1.3 10 3

The change of length is therefore
3 3
¢L 1.3 10 L 1.3 10 160 m
0.21 m