Chapter 12: Solids

Density DEFINITION

measure of the compactness of matter

Density SIMPLE

how packed together something is

Density FORMULA

Density = mass ÷ volume

Density EQUATION FORM

see picture

p=

density

Density SI UNIT

kg/m^3

Volume =

how much space it takes up

What happens to the volume of a loaf of bread that is squeezed? The mass? The density?

A. Increases, decreases, stays the same.

B. Stays the same, increases, decreases.

C. Increases, stays the same, decreases.

D. Decreases, stays the same, increases

Decreases, stays the same, increases

Density and volume are _____

inverse

Which of the following has a greater density?

A. 3 kg aluminum.

B. 10 kg aluminum.

C. The same.

D. It depends on the volume.

C. The same

t’s the SAME material →

density doesn’t change

Is iron heavier than wood?

 It depends on how much you have!

A tiny piece of iron could be lighter than a huge piece of wood

BUT iron is more dense, so same size → iron is heavier

Elasticity DEFINITION

the property of a material by which it changes shape when a deforming force acts on it and returns to its original shape when the force is removed.

Elasticity SIMPLE

Ability to change shape and go back

Materials that return to their original shape are ____

elastic

Materials that do not return to their original shape are ____

inelastic

Under the same force, the ____a material changes shape, the more elastic it is.

less

Steel spring → barely stretches →

very elastic

Rubber band → stretches a lot →

less elastic (even though it’s flexible!)

Is rubber more elastic than steel?

NO, steel is actually more elastic!

Elastic = returns to original shape perfectly

Steel does this better than rubber

Hooke's law:

The stretch of a spring is directly proportional to the force applied to it

F

stretch

x=

length of spring

Elastic limit:

If stretched beyond certain amount, it will not return to its original shape.

Stretch is _____proportional to weight (or force) as long as the spring is elastic.

directly

Doubling the mass doubles the force →

doubles the stretch.

If a 1-kg object stretches a spring by 2 cm, then how much will the spring be stretched when it supports a 2-kg object? (Assume the spring does not reach its elastic limit.)

A. 1 cm

B. 3 cm

C. 4 cm

D. 6 cm

C. 4 cm

A 10-cm-long spring extends to 12 cm when a 1-kg load is suspended from it. What would be its length if a 3-kg load were suspended from it?

A. 14 cm

B. 16 cm

C. 20 cm

D. 24 cm

B. 16 cm

Suppose you drill a hole horizontally through a tree branch as shown. Where will the hole weaken the branch the LEAST?

A. Near the top

B. Near the bottom

C. Near the middle

D. It does not matter

C. Near the middle

Tension = pulling/stretching →

gets longer and thinner

Compression = pushing/squishing →

gets shorter and wider

a

Tension (pulling/stretching)

b

Compression (pushing/squishing)

c

neutral layer

Scaling DEFINITION

the study of how size of any object affects the relationships among its strength, weight, and surface area

Scaling SIMPLE

Study of how size affects:

• Strength

• Weight

• Surface area

Strength ~

cross sectional area.

Weight ~

volume

Strength ~ area

(square) ²

Weight ~ volume

(cube) ³

When something gets bigger:

Weight increases ________ than strength

FASTER

Suppose you could somehow be scaled up to twice your size-that is, every linear dimension increased by a factor of 2. Would you be twice as strong and be able to lift yourself twice as easily?

No

Who is stronger, an ant or an elephant?

Ants win here!

Some ants can lift 20–50 times their own body weight.

How strong would an ant be if it were scaled up to the size of an elephant?

The ant would be weaker relative to its own weight.

Could the super giant ant carry the weight of several elephants?

NO, When an ant is scaled up to elephant size, its weight increases faster than its muscle strength, so it cannot lift nearly as much relative to its body

surface area grows as»»»

(square) ²

volume grows as»»»

(cube) ³

When a shape gets bigger, the _____ grows faster than the surface, so the surface area compared to volume gets _____.

volume;smaller

If a 1-cm3 cube is scaled up to a cube that is 10 cm long on each side, how does the surface area to volume ratio change?

A. 1/100 of original

B. 1/10 of original

C. 10 times original

D. 100 times original

1/10 of original

Surface area =

total “skin” or “covering” of an object

Volume = how much space is inside the cube.

Volume = 1 × 1 × 1 = 1 cm³ ✅

scale up an object

make it bigger in all directions