ch. 18 solids. characteristics are due to its structure, or arrangement of its atoms

Ch. 18 Solids

Characteristics are due to its structure, or arrangement of its atoms.

Most solids have a crystal structure.

•Why do some object float while others sink or are suspended somewhere in between?

Density•Is the mass of a substance divided by the volume of that substance.

Density Equation Mass

Density = Volume

Density Units•Metric: kg / m3

or g / cm3

•English: lbm / ft3

Example 1: An object has a mass of 550 g and a volume of 500 cm3. What is the objects density?

Given: m = 550 g, V = 500 cm3

Unknown: D = ? Equation: D = m / VSubstitution: D = 550 g /

500 cm3 Solution: D = 1.1 g / cm3

•Ex 2: What is the volume of my 2.16 g titanium wedding band if the density is 4.50 g/ cm3?

G: m = 2.16 g,

D = 4.50 g/cm3

U: V = ?

E: D = m / V V = m/D

S: V = 2.16 / 4.50 g/cm3

S: V = 0.48 cm3

Weight DensityIs the ratio of the weight to the volume.

Commonly used for Liquids.

Elasticity• Is the property of a body/material that when it is deformed by a force, it will return to its original shape when the force is gone.

So things are either elastic or inelastic.

Elastic LimitThe distance beyond which stretching or compressing results in permanent distortion.

Hooke’s LawAs long as the the elastic limit

is not exceeded, the amount of stretch or compression is directly proportional to the

applied force

Felastic = -kx•F = Spring Force

•x = distance stretched or compressed

•k = proportionality constant of elongation

The (-) sign signifies that the direction of the force is always in the direction opposite the mass’s displacement.

Ex 3: A spring has been stretched 0.3 m, how much force is necessary to stretch it, if its spring constant is 12 N/m?

G: x = 0.3 m, k = 12 N/m

U: F = ?

E: F = -kx

S: F = -(12 N/m)(0.3 m)

S: F = - 3.6 N

Ex 4: A spring has been stretched 23 cm by a hanging mass of 400 g, what is the spring constant of the spring?

G: x = 23 cm

m = 400 g

G: x = 23 cm = 0.23 m m = 400 g = 0.4 kg

g = 10 m/s2

U: k = ?Spring is in equilibrium.

Felastic = Fg

G: x = -23 cm = -0.23 m m = 400 g = 0.4 kg

g = 10 m/s2

U: k = ?Spring is in equilibrium.

Felastic = Fg = mg

E: Felastic = -kx

mg = -kx

k = mg/-x

S: k = (0.4)(10)/-(-0.23)

S: k = 17.4 N/m

Compression & Tension

• Compression is squeezing.

• Tension is stretching.

• Beams can be both under tension and compression at the same time. –Top under tension, bottom under compression, or vice versa.

• I-beams.

ScalingThe study of how the size affects the relationship between weight, strength, and surface area.

Strength is proportional to cross-section

area.

Heat transfer is proportional

to surface area.

Weight is proportional to

volume.

Food requirement is proportional to

volume.

Double each side of a cube.

•It has 4 (= 22) times the cross section.

•4 times the strength.

•It has 4 (= 22) times the surface area.

•4 times the heat loss/gain

•It has 8 (= 23) times the volume.

•8 times the weightNeeds 8 times the nutrients

Surface Area

Surface Area

Volume

Volume

Volume