Solid Matter

1
Solid Matter
Points to take away

• Solid materials are not absolutely rigid.
• We can think of solids as atoms/molecules that
  are connected by springs.
• Nothing is truly rigid, everything can be
  deformed we talk about stresses and strains that
  change solids.
• Changes in the sizes of solids are described by
  elastic moduli.

2
How Solids Behave

• Some solids are easy to deform.
• Others are generally difficult to deform.

3
How Solids Behave

• But, even rocks can get deformed.

4
How Solids Behave

• We explain the elastic behavior of solids by
  thinking of the bonds between atoms/molecules in
  a solid as springs.
• You can move each piece, but the springs restore
  the positions to the original locations.

5
Stress

• In physics, stress is more than what you feel
  before an exam.
• When a force acts on a solid body, it is often
  applied perpendicular to a surface think about
  pushing a box along a horizontal surface.

Stress F/A
6
Stress

• If you dont have a box, the stress will be
  different since A will be different.
• In the spherical cow approximation, bones are
  cylinders.
• Forces applied to the ends of bones then act on
  an area A p r2

7
Strain

• Strain is a dimensionless scalar number that
  tells you how the size of the solid changes under
  stress.
• If there are forces that act in one direction
  only, then the strain will measure how the length
  in that dimension changes.
• one-dimensional strain ?L/L0

8
Linking Stress Strain

• In general, we link stress and strain with
  numbers called elastic moduli.
• e.m. stress/strain
• For our bone squashing example, the elastic
  modulus is called Youngs modulus.
• When we change the volume of a solid by applying
  forces, we will talk about the bulk modulus.

9
Youngs Modulus

• Youngs modulus is represented by ?.
• From our definition of ?,
• ? (F/A) / (?L/L0)
• F/A ? (?L/L0)
• How does ?L change with ??
• ?L (FL0/A) (1/?)
• ? values for common materials are listed on page
  297.

10
Whole Class Discussion

• Shaquille ONeal has let himself go in the
  offseason. His mass has increased to about 180
  kg. When he puts all of his weight on one leg,
  what is the percent change in his femur length?
  Assume ?bone 1.5 x 1010 N/m2, rfemur 2 cm.

11
Bulk Modulus

• If a solid is surrounded by forces acting on it,
  every dimension can be changed.
• The bulk modulus B is just like Youngs modulus,
  except the strain is given by
• strain ?V/V0
• So,
• B (F/A)/(?V/V0)

12
Shear

• In addition to compressing and stretching, solids
  can be deformed by shearing.
• Shear is caused by forces that lie along surfaces
  of a solid, unlike stresses that are caused by
  perpendicular forces.
• Despite this difference, we discuss shear in the
  same way as stress.
• Define a shear modulus that connects force/area
  to strain.

13
Shear

• Think about pushing horizontally on the top of a
  cube like the one to the right.
• Static friction keeps the bottom side from
  moving, but the top side responds to your applied
  force.
• strain x/h
• S (F/A)/(x/h)

14
So What?
15
NEXT

• Section 9.2 Fluids
• Pressure
• depth
• measurements
• incompressible fluids
• air pressure
• Pascals principle