UNDERSTANDING
ELASTICITY
Elasticity
• A force can change the size and
shape of an object in various ways:
stretching, compressing, bending,
and twisting.
• Elasticity is property of matter that
enable an object to return to its
original size and shape when the
force that was acting on it is
removed.
Elasticity
• The elasticity of solids is due to
the strong inter-molecular forces
between the molecules of the
solid.
• No external force is applied.
Molecules are at their equilibrium
separation. Intermolecular force
is equal to zero
Elasticity
Attractive force
• Stretching a solid causes its
molecules to be displaced away
from each other.
• A strong attractive intermolecular
force acts between the molecules to
oppose the stretching.
Elasticity
Repulsive
force
Repulsive
force
• Compressing a solid causes its
molecules to be displaced closer to
each other.
• A strong repulsive intermolecular
force acts between the molecules to
appose the compression.
Relationship Between
Force and Extension of a
spring.
• Hooke’s law states that the extension of a
spring is directly proportional to the
applied force provided the elastic limit is
not exceed.
Fx
F = kx
• Elastic limit- max force that can be applied
to a spring such that the spring will be able
to restore to its original length when the
force is removed.
Hooke’s law
• If the elastic limit is exceeded,
the length of the spring is
longer than the original length
even though the force no longer
acts on it. The spring is said to
have permanent extension.
• If the elastic limit is not
exceeded, the spring obeys
Hooke’s law.
Question 1
• A spring has a force constant of
25 N cm-1. What is the force that
will cause a 3 cm extension of
the spring?
F = kx
= 25 x 3
= 75 N
Question 2
• The length of a spring is increased from
23.0 cm to 28.0 cm when a mass of 4 kg
was hung from the end of a spring.
a) What is the load on the spring in
newton?
b) What is the extension of the spring?
c) Calculate the force constant of the
spring. [Assume g= 10 ms-2]
Ans a) 40 N b) 5.0 cm
c) 8 N cm-1
Questions
1. A 4N force on a spring
produces an extension of 3cm.
What is the extension when
the force is increase to 10N?
2. A force of 8N on a spring
compresses the spring from 18
cm to 15cm. What is the force
constant of the spring?
Bungee jumping
Bungee jumping
• In bungee jumping, the
transformation of energy during
the downward motion is from
gravitational potential energy to
kinetic energy to elastic
potential energy.
Elastic Potential Energy
• When a force extends a spring, work
is done because the force moves
through the distance.
• The work done on the spring is the
energy transferred to the spring and
stored as elastic potential energy.
• Elastic potential energy stored in a
stretched spring;
Ep = ½
2
kx
Questions
1.
If a 12N force extends a spring from 10
cm to 12 cm,
a) what is the force constant of the
spring?
b) calculate the elastic potential energy
stored in the spring
2.
The length of a spring is extended from
12 cm to 15 cm by a 4N force. What is
the elastic potential energy stored in the
spring?
Factor that affect
elasticity
• Length of spring
• Diameter of spring wire
• Diameter of spring
• Type of material
Factor that affect
elasticity
• Length of a spring
Shorter spring is less elastic than longer spring
Factor that affect
elasticity
• Diameter of spring wire
Smaller diameter – more elastic
Factor that affect
elasticity
• Diameter of spring
Smaller diameter – less elastic
Factor that affect
elasticity
• Type of material
Steel
Copper
Elasticity changes according to the
type of material
Factor that effect
elasticity
Factor
Change in factor
Effect on
elasticity
length
Shorter spring
Longer spring
Less elastic
More elastic
Diameter of
spring
Smaller diameter Less elastic
Larger diameter More elastic
Diameter of
spring wire
Smaller diameter More elastic
Larger diameter Less elastic
Type of material
The elasticity change with the type
of material.
System of spring
• Spring in series
•Load in each spring = M
x
•Extension = x
•Total extension = 2x
x
M
System of spring
• Spring in parallel
Load in each spring = M/2
X
Extension = x/2
2
M
Total extension = x/2
System of spring
(i)
(ii)
spring (i)
Spring (ii)
Force = M/2
Force = M/2
Extension = x/2
Extension = x/2
Spring (iii)
Force = M
M
Extension = x
(iii)
Total extension = x/2 + x
Question 1
• Figure shows three similar
springs used to support a 20 kg
mass. Each spring will stretch 6
cm when it supports a load of
mass 10kg. What is the total
extension of the system.
• Ans: 18 cm
20 kg
Questions 2
2cm
500 g
• Figure shows a spring
extended by 2 cm when
a mass of 500 g is hung
on it. What is the mass
necessary to produce a
5 cm extension of the
spring?