b/ they become ____________ (bent out of shape), and

concretecakeUrban and Civil

Nov 29, 2013 (3 years and 11 months ago)

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Why study springs?

Springs are_____________. This means that if you:

a/ apply a ___________to them, and

b/ they become ____________ (bent out of shape), and

c/ then you remove the ___________, then they

d/ __________________ .


Many things have some elasticity, and so they

behave like springs:


wood



_____________

plastic




concrete


humans


water


air



the sun


atoms


quartz


speakers


water


______________________________


strings, air, drums…

Many elastic objects obey…

elastic

deformed

force

forced

bounce back

metal

musical instruments

___________ Law:

The compression or elongation
x

of an

ideal spring from its ________________ position (x = 0)

is ____________________________to the applied force
F
s
.

F
s

=

stretching or elongation:

compression:

More F


more ____________ or __________________.

x = 0

x = 0

F
s

=

F
s

x

F
s

x

directly proportional

kx

stretch

compression

Hooke's

equilibrium

Hooke's Law is often written:

F
s

=

-
kx


This is because it also describes the force that the

_______________ exerts on an ___________ that is attached

to it. The negative sign indicates that the direction of

the spring force is always _____________ to the

displacement of the object

spring itself

stretched

spring:

compressed

spring:

object

opposite

undisturbed

spring

______________

position, F
s

= __

equilibrium

-
x

+x

F
s

F
s

x = 0

0

F
s

___ 0

F
s

___ 0

>

<

Ex. A weight of 8.7 N is attached to a spring that

has a spring constant of 190 N/m. How much

will the spring stretch?

Equation
:

Given:

Unknown:


x

w/o weight

8.7

N

w/ weight

190 N/m

8.7 N

x = ?

k =

F
s

=

F
s

= kx

8.7 N = (190 N/m) x

x = 4.6 x 10
-
2

m

F
s

= kx

F
s

x

What quantity does the slope represent?

slope =


=

Compare to F
s

= kx


Solve for F
s
/x =

The slope represents _______________________________

direct

Ex: A force of 5.0 N

causes the spring to

stretch 0.015 m.

How far will it stretch

if the force is 10 N?

2 (0.015 m)

= 0.030 m

D
y/
D
x

F
s
/x

the spring constant,
k
.

k

5

10

.015

?

What are the units of the spring constant, k?


Solve…


F
s

= kx

…for k: k =

units of k: [k] = [ ]/[ ]


= (derived)


This can be also seen from the graph:

F
s

(N)

x (m)

k = the slope =
D
y/
D
x



So k
has the same


units as
D
y/
D
x:

F
s
/x

F
s

x

N/m

N/m

F
s

x

stiffer spring


_________ slope


_________ k

spring

A

spring

B

Ex. Comparing

two springs that

stretch different

amounts.

x
B

Applying the same

force F to both springs

Which spring stretches more?

Which is stiffer?

x
A

A

B

greater

larger

____________ PE

-

the energy stored in a spring when work




is done on it to stretch or compress it

PE
s

=

Ex. A spring with a spring constant of 370 N/m is

stretched a distance 6.4 x 10
-
2

m. How much elastic

PE will be stored in the spring?




How much work was done to stretch the spring by

this amount?





(½)kx
2

Elastic

____________ PE

-

the energy stored in a spring when work




is done on it to stretch or compress it

PE
s

=

Ex. A spring with a spring constant of 370 N/m is

stretched a distance 6.4 x 10
-
2

m. How much elastic

PE will be stored in the spring?



PE
s

= (½)kx
2


= (0.5)( 370 N/m)(6.4 x 10
-
2

m)
2



= 0.76 (N/m)(m
2
)


= 0.76 Nm



= 0.76 J


How much work was done to stretch the spring by

this amount?




W =
D
PE = 0.76 J

(½)kx
2

Elastic

PE
s

=

What happens to PE
s

when you double x?

The PE
s

quadruples.

When you triple x?

9x more PE
s
.

Ex: The elastic PE stored in a spring is 0.70 J when

it is stretched 0.010 cm. If the same spring is stretched

0.030 cm, how much PE will then be stored in it?

PE
S

x

prop. to

square

x changes from 0.010 to 0.030


it triples



9x more PE
s



9x (0.70 J) = 6.3 J

(½)
k
x
2

Ex: Plot F vs. x for


an ideal spring


F

x

What does the grey area represent?

area = (½)bh =





=


=







=


It represents the ____________ on the spring, and


the ______________________ in it.




(½)x
F


(½)x(
kx
)

(½)kx
2

PE
s

work done

W =
D
PE
s

energy stored

Ex: By looking at the area, you can see why the PE is

proportional to the ___________ of the displacement x:


F

1 x

x

2 x

3 x

1 x

2 x

3 x

____ triangle


area = ____

so PE = ____

____ triangles


area = ____

so PE = ____

____ triangles


area = ____

so PE = ____

A

1

A

A

square

4

4A

4A

9

9A

9A

1

2

3

4

One last warning:



If a spring is stretched too much, it ____________


permanently, and Hooke's Law (F
s

= kx ) _________


______________

Ex: Which of the graphs below shows a spring that


obeys Hooke's Law?

F

x

F

x

F

x

F

x

YES

and

NO

deforms

is no

longer valid.

A/

B/

C/

D/

Open your

Review Book packet

to pages: 82
-
3



Do problems #

39
-
56