solids
DESCRIPTION
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?. compression. tension. Structure of Solids. Atoms and molecules connected by chemical bonds - PowerPoint PPT PresentationTRANSCRIPT
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 SolidsAtoms are always “attracting each other when they are a little distance apart, but repelling upon being squeezed into one another”
distance
force
0
equil
apart
toward
apartequil
Structure of SolidsAtoms are always “attracting each other when they are a little distance apart, but repelling upon being squeezed into one another”
distance
force
0
equil
apart
toward
Force and Distance
distance
force0
equil
apart
toward
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
Hooke’s Law GraphF
orce
exe
rted
by
the
sprin
g
Displacement from equilibrium position
0
0
slope < 0
forw
ard
back
war
d
forwardbackward
Hooke’s Law Formula
F = force exerted by the spring
k = spring constant; units: N/m; k > 0
x = displacement from equilibrium position
negative sign: force opposes distortion
F = –kx
Poll Question
forward
backward
Displacement
Spring’s Force
What direction of force is needed to hold the object (against the spring) at its plotted displacement?
A. Forward (right).
B. Backward (left).
C. No force (zero).
D. Can’t tell.
forwardbackward
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.
0 N10 N
10 N0 N
Work to Deform a Spring
• To pull a distance x from equilibrium
x
kxforce
displacement
kx212
=
slope = k
area = W
• Work = F·x ;12 F = kx
• Work = kx·x12
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