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Physics – The Foundational Science
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Chapter 5 – The Solid State
Key Equations
𝐹𝑡 = 𝑘𝑥
𝐹𝑟 = −𝑘𝑥
𝐹
𝐴
∆𝑙
𝐹
0
𝐴
=𝑌𝑙
=𝑆
∆𝑥
𝑑
∆𝑉
∆𝑃 = −𝐵 𝑉
0
Questions
1. Define rigidity and resilience.
2. Define plasticity.
3. Describe three industrial processes for working metal.
a.
b.
c.
4. State Hooke’s law (a) for the tensile force and (b) for the restorative force. Identify each
variable.
a.
b.
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5. How is stress defined? How is strain defined?
6. What is the relationship between stress and strain for small deformations of a solid material?
7. What is the proportionality constant for tensile strength called? To what is it equal?
8. Name and define four points on the graph of stress vs. strain found in the text.
a.
b.
c.
d.
9. What kinds of deformation are related to Young’s modulus? To the shear modulus? To the
bulk modulus?
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10. Give three examples of shear (not in the text).
a.
b.
c.
11. Write the equation for shear modulus. Define each variable.
12. Why is there no elastic limit or ultimate strength for volume stress?
Problems
1. A 1.50 kg mass is hung from a vertical spring with k = 30.0 N/m. (a) What is the magnitude
and direction of the tensile force acting on the spring? (b) How far did the spring stretch in
meters and centimeters?
2. Find the magnitude and direction of the spring’s restorative force on an object if it is attached
to a spring with k = 250 N/m and compressed 6.0 cm?
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3. A copper wire is 3.0 m long and with a cross-sectional area of 0.050 cm2 is subjected to a
tension of 84 N. Calculate (a) its elongation and (b) the force due to tension required to reach the
elastic limit.
4. A steel wire 16 m long and with a cross-sectional are of 16 mm2 is subjected to a tension of
65 N. Calculate (a) its elongation and (b) the tension required to reach the elastic limit.
5. A brass wire 2.5 m long has a radius of 1.0 mm and hangs from the ceiling. If an object
weighing 12.2 N is suspended from the lower end, what will be (a) the elongation? Calculate the
tension required to reach (b) the elastic limit and (c) the ultimate tensile strength.
6. An aluminum wire 6.0 m long and with a diameter of 1.00 mm hangs from the ceiling. If a
mass weighing 140 N hangs from the lower end, find (a) the elongation. Calculate the tension
required to reach (b) the elastic limit and (c) the ultimate tensile strength.
7. A platform is supported by four solid steel bars, each 54 cm long and with a cross-sectional
area of 3.6 cm2. By how much is each compressed if an 18,000-N elephant stands on the
platform? (Assume each leg supports one fourth of the weight).
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8. A steel chisel 1.5 cm in diameter and 22 cm long is struck by a hammer with a force of
31,500 N. What is the maximum compression of the chisel? Assume the chisel is of uniform
diameter.
9. How much deformation is produced in an aluminum picture nail 1.85 mm2 in cross-sectional
area when a picture weighing 108 N is hung from it? The picture wire rests at the nail head,
which is 4.00 mm from the wall.
10. A 5.0 cm cube of lead is held on its bottom surface on a table, while a shearing force of 3.0
kN is applied to the top surface. Find how much the top surface is displaced.
11. If a steel anchor whose volume is 450 cm3 is lowered to a depth of 1.5 km in seawater, by
how much does the volume decrease? Assume the density of seawater is 1030 kg/ m3.
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