1. 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…
elastic
force
deformed
force
bounce back
metal
musical instruments
Many elastic objects obey…

2. ___________ Law: The compression or elongation x of an
ideal spring from its ________________ position (x = 0)
is ____________________________to the applied force Fs.
Hooke's
equilibrium
directly proportional
Fs =
Fs = kx
compression:
stretching or elongation:
x = 0
x = 0 x x Fs Fs
stretch
compression
More F  more ____________ or __________________.

4. Hooke's Law is often written:
Fs =
-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
object
opposite -x
compressed
spring:
Fs ___ 0
> Fs
x = 0
______________
position, Fs = __
equilibrium
undisturbed
spring +x
stretched
spring:
Fs ___ 0
< Fs

5. 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/o weight
w/ weight
Given:
8.7 N
Fs =
190 N/m x
k =
Unknown:
8.7 N
x = ?
Equation:
Fs = kx
8.7 N = (190 N/m) x
x = 4.6 x 10-2 m

6. Fs = kx Fs direct Ex: A force of 5.0 N causes the spring to
stretch m.
How far will it stretch
if the force is 10 N? 10 5
2 (0.015 m)
= m
.015 ? x
What quantity does the slope represent?
slope = =
Dy/Dx
Compare to Fs = kx
Solve for Fs/x = k
Fs/x
the spring constant, k.
The slope represents _______________________________

7. What are the units of the spring constant, k?
Solve… Fs = kx
…for k: k =
units of k: [k] = [ ]/[ ]
= (derived)
This can be also seen from the graph:
Fs/x Fs x
N/m
Fs (N)
k = the slope = Dy/Dx
So k has the same
units as Dy/Dx:
N/m
x (m)

8. stiffer spring  _________ slope  _________ k
Ex. Comparing
two springs that
stretch different
amounts. Fs
spring B
spring A
Applying the same
force F to both springs x xB xA
Which spring stretches more?
Which is stiffer? A B
greater
stiffer spring  _________ slope  _________ k
larger

9. ____________ PE - the energy stored in a spring when work
is done on it to stretch or compress it
Elastic
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?

11. ____________ PE - the energy stored in a spring when work
is done on it to stretch or compress it
Elastic
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
= (N/m)(m2)
= Nm
= J
How much work was done to stretch the spring by
this amount?
W = DPE = 0.76 J

12. PEs = (½)kx2 PES prop. to square What happens to PEs
when you double x?
The PEs quadruples.
When you triple x?
9x more PEs. x
Ex: The elastic PE stored in a spring is 0.70 J when
it is stretched cm. If the same spring is stretched
0.030 cm, how much PE will then be stored in it?
x changes from to  it triples
 9x more PEs  9x (0.70 J) = 6.3 J

13. Ex: Plot F vs. x for
an ideal spring F
F = kx x
What does the grey area represent?
area = (½)bh = =
It represents the ____________ on the spring, and
the ______________________ in it.
(½)xF
(½)x(kx)
(½)kx2
PEs
work done
energy stored
W = DPEs

14. Ex: By looking at the area, you can see why the PE is
proportional to the ___________ of the displacement x:
square F
F = kx x
1 x
2 x
3 x 4 3 A 1 2
1 x
3 x
2 x
____ triangle
area = ____
so PE = ____ 1
____ triangles
area = ____
so PE = ____ 4
____ triangles
area = ____
so PE = ____ 9 A 4A 9A A 4A 9A

15. NO NO YES YES and NO One last warning:
 If a spring is stretched too much, it ____________
permanently, and Hooke's Law (Fs = kx ) _________
______________
Ex: Which of the graphs below shows a spring that
obeys Hooke's Law?
deforms
is no
longer valid. F x F x NO NO A/ C/
YES
and NO F x F x NO
YES B/ D/
YES