RNT1 Lecture Notes - Lecture 5: Amorphous Solid, Vacuum Cleaner, Celsius

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26 Sep 2019
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Chapter 12 Solids
Recall the rigid body model that we used when discussing rotation.
A rigid body is composed of a particles constrained to maintain the same distances from and
orientations relative to the particles around them.
Rigid bodies reasonably well describe solids.
The role of the particles is played by atoms.
An amorphous solid is one where the atoms have no regular structure.
In a crystalline solid, atoms are placed in an orderly structure.
Most of the glass you see on a daily basis is amorphous.
Crystalline glass usually makes goblets and punch bowls.
The sodium (Na) and chlorine (Cl) atoms in
salt form a cubic structure.
Sugar is amorphous.
Elasticity
Consider a rod — immobilize one end of the
rod — apply a force F to the other end. The
force will cause the rod to change in length by )L.
As long as the force is not too large, the
force and the change in length are
proportional.
How the force and change in length are
related depends on the geometry of the rod.
Suppose we apply the same force F to two
rods of the same material and same length,
one fat and one skinny.
The skinny rod will stretch farther than the fat one.
The amount that a rod stretches depends on the cross-sectional area of the rod A.
If we change the quantity causing the deformation from force to force per unit area, we get a
relation that does not depend on area.
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We define the stress produced by the force F on the rod as the force divided by the cross-sectional
area of the rod:
If we apply the same stress to any rod made of the same material and the same length, we find
the same change in length.
Suppose I have two rods identical except that one rod is longer than the other.
Applying the same stress to both rods produces a larger change in length for the longer rod.
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Model a rod as a string of atoms separated by springs.
Each atom is at rest, which means that the net force on each atom is the zero. This means that
each spring has the same force F applied to it — each spring stretches the same amount.
The more springs in the rod, the more stretch for the rod.
The fractional stretch — change in length divided by the length — will be the same for both the
short rod and the long rod.
We define strain to be the change in length divided by the length:
Stress is the force-like quantity that causes deformation.
Strain is related to the deformation.
Stress causes strain.
As long as the stress is not too large, the stress and strain are proportional.
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The constant of proportionality is called the elastic modulus or Young’s modulus. It depends on
the material in question.
Scaling
Giant Ants
Small ant of size about 2 mm
Large ant of size 20 m
Large ant is 10,000 times as large as the small ant.
A small ant can lift 10 times its own weight
Assume that the large ant is made of the same material as the small ant.
Note that the lifting capability of an ant is proportional to the size of the ant.
This means that the large ant can lift 10,000 times as much as the small ant.
The strength of an ant leg is proportional to the leg’s cross-sectional area, which is proportional
to the square of the length of the ant.
This means that the strength of the large ant leg is 10,0002 = 100,000,000 times stronger than
the small ant leg.
The weight of an ant is proportional to its volume, which is proportional to the cube of the size of
the ant.
This means that the weight of the large ant is 10,0003 = 1,000,000,000,000 times the weight of
the small ant.
Since the weight increases by a trillion times and the lifting ability by only 10,000 times, the
large ant can lift one-100 millionth of its weight.
It legs are 10,000 times weaker compared to its weight for the large ant vs. the small ant.
The large ant can’t stand up and if it tries, it will break its legs.
Chapter 13 Liquids
Liquids take the shape of their container.
Consider a glass of water — it’s hard to think of the force of the water
on the glass or the force of the glass on the water.
We can think of the force applied to a small area on the side of the
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