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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 / m 3 or g / cm 3 English: lbm / ft 3
Example 1: An object has a mass of 550 g and a volume of 500 cm 3. What is the objects density?
Given: m = 550 g, V = 500 cm 3 Unknown: D = ? Equation: D = m / V Substitution: D = 550 g / 500 cm 3 Solution: D = 1.1 g / cm 3
Ex 2: What is the volume of my 2.16 g titanium wedding band if the density is 4.50 g/ cm 3 ?
G: m = 2.16 g, D = 4.50 g/cm 3 U: V = ? E: D = m / V V = m/D S: V = 2.16 / 4.50 g/cm 3 S: V = 0.48 cm 3
Weight Density Is 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 Limit The distance beyond which stretching or compressing results in permanent distortion.
Hookes Law As long as the the elastic limit is not exceeded, the amount of stretch or compression is directly proportional to the applied force
F elastic = -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 masss 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 = 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/s 2 U: k = ? Spring is in equilibrium. F elastic = F g
G: x = -23 cm = m m = 400 g = 0.4 kg g = 10 m/s 2 U: k = ? Spring is in equilibrium. F elastic = F g = mg
E: F elastic = -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.
Scaling The 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 (= 2 2 ) times the cross section. 4 times the strength.
It has 4 (= 2 2 ) times the surface area. 4 times the heat loss/gain
It has 8 (= 2 3 ) times the volume. 8 times the weight Needs 8 times the nutrients
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