Solids
A simple model of elasticity
Objectives
• Describe the deformation of a solid in
response to a tension or compression.
What’s the point?
• How do solids react when deformed?
Structure of Solids
• Atoms and molecules connected by
chemical bonds
• Considerable force needed to deform
compression
tension
Structure of Solids
Atoms are always “attracting each other when they
are a little distance apart, but repelling upon being
squeezed into one another”
apart
force
0
toward
equil
equil
apart
distance
Structure of Solids
Atoms are always “attracting each other when they
are a little distance apart, but repelling upon being
squeezed into one another”
apart
force
0
toward
equil
distance
Force and Distance
apart
force
0
toward
equil
distance
Elasticity of Solids
Small deformations are proportional to force
small stretch
larger stretch
Hooke’s Law: ut tensio, sic vis (as the pull,
so the stretch)
Robert Hooke, 1635–1703
forward
slope < 0
0
backward
Force exerted by the spring
Hooke’s Law Graph
backward
0
forward
Displacement from equilibrium position
Hooke’s Law Formula
F = –kx
F = force exerted by the spring
k = spring constant; units: N/m; k > 0
x = displacement from equilibrium position
negative sign: force opposes distortion
Poll Question
backward
forward
What direction of
forward
force is needed to Spring’s
hold the object
Force
backward
(against the
spring) at its
Displacement
plotted
displacement?
A. Forward (right).
C. No force (zero).
B. Backward (left).
D. Can’t tell.
Group Work
A spring stretches 4 cm when
a load of 10 N is suspended
from it. How much will the
combined springs stretch if
another identical spring also
supports the load as in a and
b?
Hint: what is the load on each
spring?
Another hint: draw force
diagrams for each load.
0N
10 N
0N
10 N
Work to Deform a Spring
• To pull a distance x from equilibrium
slope = k
kx
area = W
force
displacement
• Work =
1
2
• Work =
1
2 kx·x
F·x ; F = kx
1
=
2
kx2
x
Potential Energy of a Spring
The potential energy of a stretched or
compressed spring is equal to the work
needed to stretch or compress it from its
rest length.
PE = 1/2 kx2
The PE is positive for both positive and
negative x.
Group Poll Question
Two springs are gradually stretched to the
same final tension. One spring is twice as
stiff as the other: k2 = 2k1.
Which spring has the most work done on it?
A. The stiffer spring (k = 2k1).
B. The softer spring (k = k1).
C. Equal for both.
Reading for Next Time
• Vibrations
• Big ideas:
– Interplay between Hooke’s force law and
Newton’s laws of motion
– New vocabulary that will also apply to waves
A Word