2.11
Define Elasticity
A property of matter that enables an object to return to its original size
and shape when the force that was acting on it is removed.
No external force is applied.
Molecules are at their equilibrium separation.
Intermolecular force is equal zero.
Compressing a solid causes its molecules to be displaced closer to
each other.
Repulsive intermolecular force acts to push the molecules back to
their original positions.
Stretching a solid causes its molecules to be displaced away from
each other.
Attractive intermolecular force acts to pull back the molecules to their
original positions.
Stretching a wire by an external
force:
 Its molecules are slightly displaced away from one another.
 Strong attractive forces act between the molecules to oppose the
stretching
When the external force is removed:
 The attractive intermolecular forces bring the molecules back to
their equilibrium separation.
 The wire returns to its original position
131
State Hooke’s Law
The extension of a spring is directly proportional to the applied force
provided the elastic limit is not exceeded.
F = kx
F= force on the spring
x = extension
k = force constant of the spring
Force extension graph
Based on the graph:
Relationship between F & x :
F is directly proportional to x
The gradient of the graph represent = force constant of the spring, k
Area under the graph equal to the work done to extent the spring:
2
= elastic potential energy = ½ Fx = ½ kx
The elastic limit of a spring
The maximum force that can be applied to a spring such that the
spring will be able to be restored to its original length when the force
is removed.
If a force stretches a spring beyond its elastic limit, the spring cannot
return to its original length even though the force no longer acts on it.
The Hooke’s law is not obeyed anymore.
Force constant of the spring, k
The force required to produce one unit of extension of the spring.
k
F
x
-1
-1
unit N m or N cm or N mm
-1
k is a measurement of the stiffness of the spring
 The spring with a larger force constant is harder to extend and is
said to be more stiff.
 A spring with a smaller force constant is easier to extend and is
said to be less stiff or softer.
Factors that effect elasticity
Factor
Length
Diameter of spring wire
Diameter spring
Type of material
Change in factor
How does it affects the elasticity
Shorter spring
Less elastic
Longer spring
More elastic
Smaller diameter
More elastic
Larger diameter
Less elastic
Smaller diameter
Less elastic
Larger diameter
More elastic
Springs made of different materials
Elasticity changes according to the type of material
132
Describe
applications of
elasticity
(1) Cushion / mattress: The spring in a cushion or mattress undergo many cycles of
compression during use and each time the cushion is able to return to its original
shape. This is due to the elasticity of the springs.
(2) Electric meter : Electric meters such as ammeter, voltmeter and galvanometer have
spiral springs. The springs are used to stop the pointer at a specific point on the
scale or to return the pointer to the zero mark on the scale after a measurement has
been taken
(3) Weighing apparatus: A weighing apparatus such as spring balance , a spring is
either extended or compressed and it obeys the
Hooke ‘ law and it caused the apparatus has a linear scale.
(4)
Vehicles spring support: It enables the
passengers in a vehicle to be seated in a comfortable position when the vehicle
goes on a bumpy road because springs shock absorbers are mounted on the
wheels of vehicles to absorb impacts and damp vibrations resulting from movement
on the bumpy road or uneven road surface.
(5) In sports : The elastic strings of a tennis or a badminton racket enable them to
rebound the ball or shuttle.
The ropes used by rock climbers have elastic properties that can save lives during
climbing accidents. The ropes are made of a continuous-drawn nylon fibre core and
a protective textile covering . This reduces the stopping force acting on a falling
climber.
A bow bends or elastic twine of the bow is stretched to store the elastic potential
energy used to propel the arrow.
Arrangement of the spring
In series
The same load is applied to each spring.
Tension in each spring = W
Extension of each spring = x
Total extension = 2x
If n springs are used:
The total extension = nx
In parallel
The load is shared equally among the springs.
Tension in each spring =
W
2
Extension of each spring =
x
2
If n springs are used:
The total extension =
x
n
133
Example 1
The original length of a spring is 5 cm. With a
load of mass 20 g, the length of the spring is
extended to 7 cm.
Example 4
Figure shows a graph of force, F against
extension, x for a spring. What is the
potential energy stored when the spring is
extended by 0.4 m?
Determine
(a) the extension of the spring with a load
40 g
(b) the length of the spring with a load 60 g.
the load required to extend the spring to
20 cm.
Example 2
Spring A extends by 2 cm when it hung with
a 10 g weight. Spring B extends by 4 cm
when it hung with a 10g weight. Find the
total stretch in each of the spring systems
shown in the following figure.
Example 5
Figure shows a ball of mass 10 g pushed
against one end of a spring on a smooth
surface. The original length of the spring is
-1
14 cm and its spring constant is 200 N m .
Determine
Example 3
The original length of a spring is 12 cm. With
a load of 20 g , the length of the spring is
extended to 15 cm. What is the elastic
potential energy stored in the spring?
(a)
the elastic potential energy stored in
the spring.
(b) the maximum velocity reached by the
ball after the compressive force on the
spring is removed.
134
TUTORIAL 2.11
1
2
3
The relationship between stretching
force, F, with the extension, x, of a
spring, is given by the equation:
F = kx
where k is the spring constant. What is
the unit of k? (2005)
-1
A. N m
-2
B. N m
-1
C. kg m
-2
D. kg m
A spring produces an extension of 4 cm
when a stretching force of 1.2 N is
applied to it. What is the elastic
constant of the spring?
-1
A. 30 N m
-1
B. 40 N m
-1
C. 60 N m
The diagrams show the position of a
steel ball bearing when the spring is
compressed
and after the spring is released.
Question 1
Figure 1 shows a boy extending the elastic
rubber of a catapult.
Figure 1
(a) State the type of energy stored in the
elastic rubber.
(b) Explain the change of energy when
the stone is released from the elastic
rubber of the catapult.
(c) What happens to the maximum
displacement if a smaller stone of
similar mass is used?
(d) If the elastic rubber is extended 20
cm by a force of 8 N,
(i)
what is the stored
potential energy in the
elastic rubber?
The distance x can be increased by
using
A a softer spring
B a longer spring
C a spring with a larger diameter
D two similar springs arranged in
parallel
(ii)
If the mass of the stone is
20 g, what is the velocity
of the stone.
135
Question 2
Figure 2 shows the arrangement of an
apparatus in an experiment to determine the
relationship between the extension e of a
spring T with weight W. The relationship of e
with W is shown in the graph in Figure 2.1
Figure 2.2
Sketch the graph of x against F for this
experiment in Figure 2.1.
Question 3
Figure (a) shows an archer shoots a target
Figure (b) the archer shoots the same target
but at different distance.
Figure 2.1
(a)
(i) State the SI unit of weight.
(ii) State the relationship between e and
W.
(iii) Name the scientific law involved in
the relationship stated in (a)(ii).
(b) (i) What is the elastic limit of a spring.
(ii) Mark with a cross (x) the elastic limit
of the spring on the graph.
(c) Based on the graph in figure 14.1,
determine the force constant of a spring,
k,.
(d) The spring stores energy when it is
extended. Calculate the energy stored in
the spring when it is extended by 4 cm.
(e) Another spring, identical to spring T, is
added to the arrangement in Figure 2.1.
This new arrangement is shown in Figure
2.2. The experiment is then repeated.
Observe the conditions of each bow and the
distance of the target from the archer.
Based on the observations:
(a) State one suitable inference that can be
made.
(b) State one appropriate hypothesis for an
investigation.
(c) With the use of apparatus such as trolley,
ticker timer and other apparatus ,
describe an experimental framework to
test your hypothesis. In your description
, state clearly the following:
(i) Aim of the experiment
(ii) Variables in the experiment
(iii) List of apparatus and materials
(iv) Arrangement of the apparatus
(v) The procedure of the experiment which
include the method of controlling the
manipulated variable and the method of
measuring the responding variable.
(vi) Way you would tabulate the data
(vii) Way you would analysis the data
136