Hookes Law
.
Robert Hooke 1635-1703
• Researched and wrote papers on Geometry,
Snowflakes, Heat, Astronomy, Fossils, Air Pumps,
Light, Watches, Telescopes and
Silkworms…..among other things
• Continually squabbled with Newton with whom
he was miffed because Newton seemed to get all
the attention and credit..Hookes Law was one of
the few things he was popularly credited with
• A rather crabby individual but credited with the
invention of universal joints, the balance wheel
and the iris diaphragm
What did Hooke discover ?
• the more force that was put on materials the
more they extended
• With some materials they also extended in a
regular way eg if the force was doubled so
did the extension
• this was true as long as their elastic limit
was not exceeded
What does this mean?
What the graph shows
E xtension (m )
E xtension proportional to
Force. Straight line graph.
O bject w ill return to
original shape. (E lastic)
B reakage
E lastic
Lim it
E xt’ not proportional to
Force. O bject w ill not
return to original shape.
(N ot E lastic).
Force (N ew tons)
What is the elastic limit?
• The material no longer shows elastic
behaviour (ie does not return to original size
when stretching force is removed)
• The material is permanently deformed ie is
larger or longer than originally
• The material is weaker as the above effects
are caused by fracture of some atomic
bonds
Since Force is proportional
to extension Hookes Law
could be put as
Fx
Where F is the applied force in Newtons
x is the extension in metres
Or if k is the proportionality constant
F=kx
What does k mean in F=kx?
• k is called the spring constant and is a measure of
the stiffness of the spring or material
• It has units of Nm-1 (newtons per metre)
• The higher the k the stiffer the spring
• Materials with a high k need a large force to for a
given extension
• adding springs in series or parallel changes k
Series and parallel springs
Series
k decreases by 2
Combined springs slacken
compared with single spring
extension doubles
Parallel
k increases by 2
Combined springs stiffen
compared with single spring
extension halves
So what?
• Understanding Hookes law is critical to the
construction of any structure eg bridges
buildings
• Deformation of materials is also critical in
vehicle design though in practice the terms
stress ( the force per square metre) and
strain (the extension per unit length) are
more commonly used instead of simply
force and extension
Summary:
A material is said to obey
Hookes Law if its extension is
directly proportional to the
applied force
More info on Hooke at
http://www.roberthooke.org.uk/