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Ch. 18 Solids

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

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Most solids have a crystal structure.

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

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

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Density Equation Mass Density = Volume

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Density Units Metric: kg / m 3 or g / cm 3 English: lbm / ft 3

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Example 1: An object has a mass of 550 g and a volume of 500 cm 3. What is the objects density?

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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

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Ex 2: What is the volume of my 2.16 g titanium wedding band if the density is 4.50 g/ cm 3 ?

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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

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Weight Density Is the ratio of the weight to the volume. Commonly used for Liquids.

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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.

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So things are either elastic or inelastic.

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

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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

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F elastic = -kx F = Spring Force x = distance stretched or compressed k = proportionality constant of elongation

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

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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?

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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

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

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G: x = 23 cm m = 400 g

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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

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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 = mg

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E: F elastic = -kx mg = -kx k = mg/-x S: k = (0.4)(10)/-(-0.23) S: k = 17.4 N/m

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Compression & Tension

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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.

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

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Strength is proportional to cross-section area.

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Heat transfer is proportional to surface area.

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Weight is proportional to volume.

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Food requirement is proportional to volume.

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Double each side of a cube. It has 4 (= 2 2 ) times the cross section. 4 times the strength.

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It has 4 (= 2 2 ) times the surface area. 4 times the heat loss/gain

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It has 8 (= 2 3 ) times the volume. 8 times the weight Needs 8 times the nutrients

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Surface Area

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Volume

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FYI: All three types of stress are measured in newtons / meter2 but all have different effects on solids. Materials Solids are often placed under stress.

FYI: All three types of stress are measured in newtons / meter2 but all have different effects on solids. Materials Solids are often placed under stress.

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