Hooke's Law and Deformation

1. Materials
6.1-6.3 – Hooke’s Law and Deforming materials

2. Springs – remember this?!
• A pair of equal and opposite forces can be used
to alter the shape of an object.
• Forces that produce extension are know as
tensile forces.
• Forces that shorten the object are know as
compressive forces.
• We call this process deformation.

3. Identify where these forces act on the Forth
Road Bridge

4. Hooke’s Law
Springs stretch when under the effect of a force, and
consequently exert a matching counteractive force (Newton’s
3rd law).
The more a spring is stretched, the greater the force needed
to stretch it further.
A spring obeys Hooke’s Law:
For a material obeying Hooke’s law the extension is directly
proportional to the force applied to it

5. Hooke’s law
• Where F is the force in Newtons applied to the spring.
• Δx is the change in length in metres of the spring
• k is known as the spring constant (a.k.a. stiffness constant) and defines the
force needed to extend the spring by 1m.
• Units for k are Nm-1

6. It’s not just springs:

7. Combining spring effects
Predict and explain what you think the effect of joining two
springs together in series and parallel will be.

8. Springs in parallel
Spring constant for parallel
springs is the sum of individual
spring constants

9. Springs in series
The reciprocal of the spring constant
for springs in series is equal to the
sum of individual reciprocals

10. Spring behaviour
F
ΔL
Starts at origin (no force = no extension)
Proportional region where
Hooke’s law is obeyed
Limit of Proportionality
Elastic Limit

11. Elastic and plastic deformation
When the elastic limit of an object is
exceeded it won’t return to its original
shape once the load is removed.
We can refer to the object being as
plastically deformed.
As opposed to being elastically deformed
(returns to its original shape when the
load is removed).
Note that they can still behave like a
spring (i.e. follow Hooke’s law), but with
a different value for k.
Elastic Limit

12. Elastic Strain
Energy/Elastic
Potential
Energy
F
ΔL
For an object obeying
Hooke’s Law F=kΔL, so:
Since work done is Force x
distance, the area beneath
line is stored elastic potential
energy (equivalent to work
done to stretch spring)

13. Questions
4.1N 0.17J 9.2m/s

14. Recap - Springs
Draw a load vs extension sketch graph for a particular spring with k = 400 Nm-1.
Add some appropriate labels and numbers to the axes.
On the same graph add a line for a spring with k = 800Nm-1
Calculate the elastic potential energy stored in each of the two springs represented for the
same extension x = 5.0cm.
If the two springs above were connected together in series and a 12N load hung from the
end, calculate the extension of the combination and the total energy stored in the
combination.
Answers: 0.55J, 1.1J, x = 4.5cm, 0.27J

15. Material properties
Different materials behave differently
under tensile forces:
• Springs follow Hooke’s law (up to
limit of proportionality).
• The gradient of a line represents its
stiffness.
• Elastic bands have less give to start,
then become stretchy, but again
stiffen at higher force values.
• Polythene is quite stretchy at first
but then stiffens suddenly towards
higher values.
F
ΔL

16. Brittle vs ductile
• A brittle material fails under load by
cracking and displays little or no plastic
deformation.
• A ductile material can be drawn into
wires and has a large plastic region.

17. Rubber - Hysteresis loop
For some materials such as
rubber the area under the
loading line is larger than the
area under the unloading
line.
What does this suggest might
be happening in terms of
energy?