Chapter 4.1-4.5

• Interatomic Forces• Micro - Macro

The Atomic “hypothesis” (p. 139)

• All matter consists of atoms, whose typical radius is about 1×10-10m• Atoms attract each other when they are close to each other but not too close.• Atoms repel each other when they get too close to each other.• Atoms in solids, liquids, and gases keep moving even at very low temperatures.

Seeing atoms

A 180×190 Å2 Image of the Pt(001)-hex reconstructed surface taken with a custom Scanning Tunneling Microscope at Aarhus University’s Scanning Probe Microscopy lab. The dark spot

near the center is a single, missing atom.

Hex Reconstruction of Pt(001) Surface

• Platinum Crystal– Unit Cell– Bulk

Condensed Matter / Surface Science

Atomic separationatom

atom

Volm

densityVolM

total

total 3d

matom31

densitymd atom

Example: separation of Si atomsOne mole of silicon (6×1023 atoms) has a mass of 28 grams. The density of silicon is 2.33 grams/cm3. What is the typical separation of a silicon atoms (i.e., ~ their diameters) assuming their arranged cubically?

Wires as Masses on Parallel and Series Springs

Question

A series of identical springs attached end to end is _____________ compared to only one of those springs.

a) Stifferb) Less Stiffc) Just as stiff

21

21

21

111kk

k

kF

kF

kF

sskF

skF

ser

ser

ser

ser

|F|= k2 s2

Springs in Series

Spring 1un

stre

tche

d

stre

tche

d

|F|= k1 s1

s1

unst

retc

hed

stre

tche

d

s2

Spring 2

stre

tche

d

s2

Springs 1 & 2

s1

serkkk

1

21

11|F|= kser s

Demonstration

You hang a 1 kg mass from a spring, which stretches 0.4 m.You link the spring end to end with another identical spring, and hang a 1 kg mass from the linked springs.

How much does this longer spring stretch? a. 0.16 mb. 0.2 mc. 0.4 md. 0.8 m

Q4.5.a: Springs in “series”serkkk

1

21

11

Special case: Identical Springs in Series

Identical Springs 1&2

unst

retc

hed

stre

tche

d

s1s1

1

11

11

kk

kser

s1

11

111

kk

kser

211

1k

kser

21kkser

If 3,4,…Nser identical springs in series:

serser N

kk 1

The more springs in series, the less stiff

Q4.5.b: Springs in “series”A short spring has a stiffness of 20 N/m. You link 4 of these springs end to end to make a longer spring.What is the stiffness of the longer spring?

a. 0.2 N/mb. 5 N/mc. 20 N/md. 80 N/m

serser N

kk 1

Question

A set of identical springs attached side by side is _____________ compared to only one of those springs.

a) Stifferb) Less Stiffc) Just as stiff

21

21

21

21

kkk

skksk

sksksk

FFsk

Fsk

par

par

par

par

par

|F2|= k2 s

Springs in ParallelSprings 1 & 2

|F|= kpar s

s|F1|= k1 s

111 2kkkk par

|F2|= k2 s

Springs 1 & 2

|F|= kpar s

s|F1|= k1 s

Special case: Identical Springs in Parallel

If 3,4,…Npar identical springs in parallel:

1kNk parpar

The more springs in parallel, the stiffer

Q4.5.c: Springs in “parallel”You hang a 1 kg mass from a spring, which stretches 0.4 m.You place a second identical spring beside the first, so the 1 kg mass is now supported by two springs.

How much does each spring stretch?a. 0.2 mb. 0.4 mc. 0.5 md. 0.8 m

21 kkk par

Q4.5.d: Springs in “parallel”A short spring has a stiffness of 20 N/m. You use 4 of these springs side by side to support a mass.What is the stiffness of the 4 side-by-side springs, considered as one effective spring?

a. 0.2 N/mb. 5 N/mc. 20 N/md. 80 N/m

Wires as Masses on Identical Parallel and Series Springs

The Micro-Macro Connection: Stiffness for springs in

series and in Parallel

LkF tot

LkNN

Fser

par

1

Area=Npar*d2bond

Length=Nser*dbond

2dAN par

dLN ser

LkLdA

1

1kLd

Aktotal

Q4.6.d: WiresYou hang a 10 kg mass from a copper wire, and the wire stretches by 8 mm.Now you hang the same mass from a second copper wire, whose cross-sectional area is half as large (but whose length is the same).

What happens?a) The second wire stretches 4 mmb) The second wire stretches 8 mmc) The second wire stretches 16 mm

LkLdAF

1

Q4.6.e: WiresYou hang a 10 kg mass from a copper wire, and the wire stretches by 8 mm.Now you hang the same mass from a second copper wire, which is twice as long, but has the same diameter.

What happens?a) The second wire stretches 4 mmb) The second wire stretches 8 mmc) The second wire stretches 16 mm

LkLdAF

1