Density, Hookes Law

1
Density, Hookes Law Scaling

• Chapter 18
• Sections 2, 3, 4, 5

2
Density

• Densitya measure of how much matter is squeezed
  into a given space
• The amount of mass per unit volume
• Density is NOT the same as mass
• Two objects can have the same mass, but not the
  same density
• 1 kg of iron and 1 kg of feathers have the same
  mass, but very different densities
• Two objects can have the same density, but not
  the same mass
• A cup of water and a gallon of water have the
  same density, but the gallon of water has more
  mass than the cup

3
Density

• Density depends on
• Atom mass
• Spacing between atoms
• Osmium is the densest substance on Earth (22.6
  g/cm3)
• Density varies with temperature and pressure
  (table on p 261 densities are given at 0C and
  atmospheric pressure)
• Water is the densest at 4 C

4
Density

• The planet Saturn has a mass of 5.69 x 1026 kg
  and a volume of 8.01 x 1023 m3. What is the
  density of Saturn? Would Saturn sink or float if
  you could place it in a gigantic bathtub filled
  with water (water has a density of 1000. kg/m3)?
• Diamond has a density of 3520 kg/m3. During a
  physics lab a diamond drops out of Virginias
  necklace and falls into her graduated cylinder
  filled with 5.00 x 10-5 m3 of water. This causes
  the water level to rise to the 5.05 x 10-5 m3
  mark. What is the mass of Virginias diamond?

5
Density

• Weight densitythe amount of weight a body has
  per unit volume
• Weight density is used in liquid pressure
• Specific gravity is a standard measure of density
• the ratio of the mass (or weight) of a substance
  to the mass (or weight) of an equal volume of
  water
• the ratio of the density of the material to the
  density of water
• Has no units
• If a substances weighs 3 times as much as an
  equal volume of water, its specific gravity is 3

6
Density

• What happens to the density of each piece of an
  object when it is cut into pieces?
• Each piece has the same density as the original
  object had
• Which has a greater density, a kilogram of lead
  or a kilogram of feathers?
• Any amount of lead is more dense than any amount
  of feathers.

7
Elasticity Hookes Law

• Elasticitythe property of a body by which it
  experiences a change in shape when a deforming
  force acts on it, and by which it returns to its
  original shape when the deforming force is
  removed
• Materials that do not return to their original
  shape are call inelastic
• Elastic limitthe distance at which permanent
  distortion occurs in an elastic material
• Hanging a weight on a spring causes it to stretch
• The amount the spring stretches is dependent upon
  the amount of mass on the spring

8
Hookes Law

• Hookes Law the amount of stretch/compression of
  a spring is directly proportional to the applied
  force
• Felastic kx
• k spring constant (units N/m)
• x displacement (units m)
• Hookes law holds as long as the spring is not
  compressed beyond its elastic limit

9
Hookes Law

• A 76 N crate is hung from a spring (k 450 N/m).
  How much displacement is caused by the weight
  of this crate?
• A spring of k 1962 N/m loses its elasticity if
  stretched more than 50.0 cm. What is the mass of
  the heaviest object that the spring can support
  without being damaged?

10
Scaling

• True or False When a structure is scaled up or
  down in size, its properties go up or down in
  direct proportion.
• Falsesome properties such as weight, strength,
  surface area, and volume do not increase in
  direct proportion to an increase in linear
  dimensions.
• Scalingthe study of how size affects the
  relationship between weight strength, and surface
  area
• As the size of something increases it grows
  heavier much faster than it grows stronger

11
Scaling

• Weight depends on volume
• Strength depends on cross sectional area
• Volume and weight increases much faster than
  corresponding increase in cross sectional area
• Volume (and weight) grows as the cube of linear
  enlargement
• Surface area grows as the square of linear
  enlargement
• Compareelephant and a deer, tarantula and daddy
  long legs
• These larger animals have disproportionately
  thick legs compared to their smaller counterparts
  as a result of scaling
• Smaller objects also have more surface area per
  kilogram
• Greater surface area?greater cooling ability
• Crushed ice cools a drink faster than a cube of
  ice
• An elephant has large ears to cool itself