madrid (tmm2353) – HW 42 – Antoniewicz – (56445)
1
This printout should have 12 questions.
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the next column or page – fnd all choices
beFore answering.
001
8.0 points
IF a chain oF 30 identical short springs linked
end to end has a sti±ness oF 220 N
/
m, what is
the sti±ness oF one short spring?
Correct answer: 6600 N
/
m.
Explanation:
Springs in series have the e±ective sti±ness
K
, where
K
is given in terms oF the sti±nesses
oF the individual springs as Follows:
1
/K
= 1
/k
1
+ 1
/k
2
+
· · ·
+ 1
/k
N
.
²or identical springs, we have
k
=
NK
, where
k
is the sti±ness oF a single spring. ThereFore
k
= (30)(220 N
/
m)
=
6600 N
/
m
.
002
8.0 points
You place 35 identical springs side by side (in
parallel) and connect them to a large, massive
block. The sti±ness oF the 35spring combi
nation is 20025 N
/
m. What is the sti±ness oF
one oF the individual springs?
Correct answer: 572
.
143 N
/
m.
Explanation:
Springs in parallel have an e±ective sti±ness
K
, where
K
is given in terms oF the sti±nesses
oF the individual springs as Follows:
K
=
k
1
+
k
2
+
· · ·
+
k
N
.
²or identical springs, we have
K
=
Nk
, or
k
=
K/N
, where
k
is the sti±ness oF a single
spring.
ThereFore,
k
=
20025 N
/
m
35
=
572
.
143 N
/
m
.
003 (part 1 of 4) 3.0 points
One mole oF tungsten (6
.
02
×
10
23
atoms)
has a mass oF 184 g, and its density is
19
.
3 g
/
cm
3
, so the centertocenter distance
between atoms is 2
.
51
×
10

10
m. You have a
long, thin bar oF tungsten, 2
.
2 m long, with a
square cross section, 0
.
13 cm on a side. You
hang the rod vertically and attach a 420 kg
mass to the bottom, and you observe that
the bar becomes 1
.
32 cm longer. ²rom these
measurements, it is possible to determine the
sti±ness oF one interatomic bond in tungsten.
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 Fall '08
 Turner
 Atom, Mole, Correct Answer, rod

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