Why study springs?
Springs are_____________.
This means that if you:
elastic
a/ apply a ___________to
them, and
force
b/ they become ____________
deformed (bent out of shape), and
forced
c/ then you remove the ___________,
then they
bounce back
d/ __________________
.
Many things have some elasticity, and so they
behave like springs:
metal
•wood
_____________
plastic
•concrete
humans
water
•air
the sun
atoms
•quartz
speakers
water
musical instruments
•______________________________
strings, air, drums…
Many elastic objects obey…
Hooke's Law: The compression or elongation x of an
___________
equilibrium
ideal spring from its ________________
position (x = 0)
directly proportional
is ____________________________to
the applied force Fs.
Fs =
kx
compression:
stretching or elongation:
x=0
x=0
x
x
Fs
Fs
stretch or __________________.
compression
More F  more ____________
Hooke's Law is often written:
Fs =
-kx
This is because it also describes the force that the
spring itself exerts on an ___________
object
_______________
that is attached
to it. The negative sign indicates that the direction of
opposite
the spring force is always _____________
to the
displacement of the object
-x
compressed
spring:
undisturbed
spring
stretched
spring:
> 0
Fs ___
Fs
x=0
equilibrium
______________
0
position, Fs = __
+x
Fs
< 0
Fs ___
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?
w/ weight
w/o weight
Given:
Fs = 8.7 N
k = 190 N/m
Unknown:
x =?
Equation:
Fs = kx
8.7 N = (190 N/m) x
x = 4.6 x 10-2 m
x
8.7
N
Fs = kx
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
Fs
direct
10
5
.015
?
x
What quantity does the slope represent?
slope = Dy/Dx
=
Fs/x
Compare to Fs = kx
Solve for Fs/x = k
the spring constant, k.
The slope represents _______________________________
What are the units of the spring constant, k?
Solve…
Fs = kx
…for k:
k =
units of k:
Fs/x
[k] = [ Fs ]/[ x ]
=
N/m
(derived)
This can be also seen from the graph:
Fs (N)
k = the slope = Dy/Dx
So k has the same
units as Dy/Dx:
N/m
x (m)
Ex. Comparing
two springs that
stretch different
amounts.
spring
B
Fs
spring
A
Applying the same
force F to both springs
xB
xA
x
Which spring stretches more? A
Which is stiffer? B
greater
larger k
stiffer spring  _________
slope  _________
Elastic
____________
PE - the energy stored in a spring when work
is done on it to stretch or compress it
PEs = (½)kx2
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?
Elastic
____________
PE - the energy stored in a spring when work
is done on it to stretch or compress it
PEs = (½)kx2
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?
PEs = (½)kx2
= (0.5)( 370 N/m)(6.4 x 10-2 m)2
= 0.76 (N/m)(m2)
=
0.76 Nm
= 0.76 J
How much work was done to stretch the spring by
this amount?
W = DPE = 0.76 J
PEs = (½)kx2
What happens to PEs
when you double x?
PES
prop. to
square
The PEs quadruples.
When you triple x?
x
9x more PEs.
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?
x changes from 0.010 to 0.030  it triples
 9x more PEs  9x (0.70 J) = 6.3 J
Ex: Plot F vs. x for
an ideal spring
F
x
What does the grey area represent?
area = (½)bh = (½)xF
=
(½)x(kx)
=
(½)kx2
=
PEs
It represents the ____________
work done on the spring, and
energy stored
the ______________________
in it.
W = DPEs
Ex: By looking at the area, you can see why the PE is
square
proportional to the ___________
of the displacement x:
F
1x
2x
3x
x
4
A
1x
1 triangle
____
A
area = ____
A
so PE = ____
1
2
3
2x
3x
4 triangles
____
4A
area = ____
4A
so PE = ____
9 triangles
____
9A
area = ____
9A
so PE = ____
One last warning:
deforms
 If a spring is stretched too much, it ____________
is no
permanently, and Hooke's Law (Fs = kx ) _________
longer valid.
______________
Ex: Which of the graphs below shows a spring that
obeys Hooke's Law?
F
F
C/
A/
x
x
F
F
D/
B/
x
x
YES
and
NO
Open your
Review Book packet
to pages: 82-3
Do problems #
39-56