1. Hooke’s Law ?

3. Hooke’s Law
In 1660, a scientist called Robert Hooke discovered a law for elastic materials.
He was trying to improve the type of clocks that were used on ships (pendulum clocks) and theorized that a spring would work better on a pitching ship.

4. We are familiar with spring scales
Not used in industry, b/c
can’t be calibrated accurately
and can become overstretched

5. Hooke's Law, elasticity
If a material returns to its original size and shape when you remove the forces stretching or deforming it (reversible deformation), we say that the material is demonstrating elastic behaviour.
If you apply too big a force a material will lose its elasticity.
Hooke discovered that the amount a spring stretches is proportional to the amount of force applied to it. This means if you double the force its extension will double, if you triple the force the extension will triple and so on.

6. If you measure how a spring stretches (extends its length) as you apply increasing force and plot extension (x) against force (F);
the graph will be a straight line.

10. The elastic limit can be seen on the graph.
This is where it stops obeying Hookes law.
Elastic limit can be seen on the graph. Anything before the limit and the spring will behave elastically. This is where the graph stops being a straight line. If you stretch the spring beyond this point it will not return to its original size or shape.

12. You can write Hooke's law as an equation:
F = k ∆ x
Where:
F is the applied force (in newtons, N),
x is the extension (in metres, m) and
k is the spring constant (in N/m).
∆x = stretched length – original length.

13. x = 0 x = 0 H___________ Law: The compression or elongation x of an
ideal spring from its e________________ position (x = 0)
is d____________________________to the applied force Fs.
Hooke's
equilibrium
directly proportional
Fs = kx
compression:
stretching or elongation:
x = 0
x = 0 x x Fs Fs
More F  more s____________ or c__________________.
stretch
compression

14. Fs = Hooke's Law is often written: - kx
This is because it also describes the force that the
s _____________ exerts on an o___________ that is attached
to it. The negative sign indicates that the direction of
the spring force is always o _____________ to the
displacement of the object
spring itself
object
opposite

15. 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?

16. 8.7 N 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

17. Fs = kx Fs direct Ex: A force of 5.0 N causes t0.015 m.
How far will it stretch
if the force is 10 N?
he spring to
stretch 10 5
2 (0.015 m)
= m
.015 ? x
What quantity does the slope represent?
slope = =
Dy/Dx k
Fs/x
the spring constant, k.
The slope represents _______________________________

18. 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

19. ____________ 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

20. Hold on a minute, K? Spring Constant?!
The spring constant measures how stiff the spring is.
The larger the spring constant the stiffer the spring.
You may be able to see this by looking at the graphs below:
The spring constant k is measured in Nm-1 because it is the force per unit extension.
The value of k does not change unless you change the shape of the spring or the material that the spring is made of.
k is measured in units of newtons per metre (Nm -1).

21. A spring is 0. 38m long. When it is pulled by a force of 2
A spring is 0.38m long. When it is pulled by a force of 2.0 N, it stretches to 0.42 m. What is the spring constant? Assume the spring behaves elastically.
Extension, ∆x = Stretched length – Original length = m – 0.38m = 0.04 m
F = k ∆ x
2.0N = k x 0.04m
So, k = 2.0 N
0.04 m
= 50 N m-1

22. Elastic behaviour – Car Safety
Elastic behaviour is very important in car safety, as car seatbelts are made from elastic materials. However, after a crash they must be replaced as they will go past their elastic limit.
Why have seat belts that are elastic?
Why not just have very rigid seatbelts that would keep you firmly in place?
The reason for this, is that it would be very dangerous and cause large injuries. This is because it would slow your body down too quickly. The quicker a collision, the bigger the force that is produced.

23. Key Definitions
Hooke’s Law = The amount a spring stretches is proportional to the amount of force applied to it.
The spring constant measures how stiff the spring is. The larger the spring constant the stiffer the spring.
A Diagram to show Hooke’s Law
F = k ∆ x