211_elasticitydoc

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Define Elasticity A property of matter that enables an object to return to its original sizand 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 toeach other.Repulsive intermolecular force acts to push the molecules back totheir 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 theioriginal positions.

Stretching a wire by an externalforce:

Its molecules are slightly displaced away from one another.

Strong attractive forces act between the molecules to oppose thestretching

When the external force is removed:

The attractive intermolecular forces bring the molecules back totheir equilibrium separation.

The wire returns to its original position

2.11


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State Hookes LawThe extension of a spring is directly proportional to the applied forceprovided the elastic limit is not exceeded.

F = kx

F= force on the springx = extensionk = 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:= elastic potential energy = Fx = kx

2

The elastic limit of a spring The maximum force that can be applied to a spring such that thespring will be able to be restored to its original length when the forceis removed.If a force stretches a spring beyond its elastic limit, the spring cannotreturn to its original length even though the force no longer acts on itThe Hookes law is not obeyed anymore.

Force constant of the spring, k The force required to produce one unit of extension of the spring.

x

Fk unit N m

-1or N cm

-1or 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 issaid to be more stiff.

A spring with a smaller force constant is easier to extend and issaid to be less stiff or softer.

Factors that effect elasticityFactor Change in factor How does it affects the elasticity

Shorter spring Less elasticLengthLonger spring More elastic

Smaller diameter More elasticDiameter of spring wireLarger diameter Less elasticSmaller diameter Less elasticDiameter spring

Larger diameter More elasticType of material Springs made of different materials

Elasticity changes according to the type of material


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Describeapplications ofelasticity

(1) Cushion / mattress: The spring in a cushion or mattress undergo many cycles ofcompression during use and each time the cushion is able to return to its originalshape. This is due to the elasticity of the springs.

(2) Electric meter : Electric meters such as ammeter, voltmeter and galvanometer havespiral springs. The springs are used to stop the pointer at a specific point on thescale 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 iseither 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 vehiclegoes on a bumpy road because springs shock absorbers are mounted on thewheels of vehicles to absorb impacts and damp vibrations resulting from movemenon the bumpy road or uneven road surface.

(5) In sports : The elastic strings of a tennis or a badminton racket enable them torebound the ball or shuttle.

The ropes used by rock climbers have elastic properties that can save lives duringclimbing accidents. The ropes are made of a continuous-drawn nylon fibre core ana protective textile covering . This reduces the stopping force acting on a fallingclimber.

A bow bends or elastic twine of the bow is stretched to store the elastic potentialenergy used to propel the arrow.

Arrangement of the springIn series

The same load is applied to each spring.Tension in each spring = WExtension of each spring = xTotal extension = 2xIf n springs are used:The total extension = nx

In parallel

The load is shared equally among the springs.

Tension in each spring =2

W

Extension of each spring =2

x

If n springs are used:

The total extension =n

x


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Example 1

The original length of a spring is 5 cm. With aload of mass 20 g, the length of the spring isextended to 7 cm.

Determine

(a) the extension of the spring with a load40 g

(b) the length of the spring with a load 60 g.the load required to extend the spring to20 cm.

Example 2

Spring A extends by 2 cm when it hung witha 10 g weight. Spring B extends by 4 cm

when it hung with a 10g weight. Find thetotal stretch in each of the spring systemsshown in the following figure.

Example 3

The original length of a spring is 12 cm. Witha load of 20 g , the length of the spring isextended to 15 cm. What is the elasticpotential energy stored in the spring?

Example 4Figure shows a graph of force, F againstextension, x for a spring. What is thepotential energy stored when the spring isextended by 0.4 m?

Example 5

Figure shows a ball of mass 10 g pushedagainst one end of a spring on a smoothsurface. The original length of the spring is14 cm and its spring constant is 200 N m

-1.

Determine

(a) the elastic potential energy stored inthe spring.

(b) the maximum velocity reached by theball after the compressive force on thespring is removed.


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TUTORIAL 2.11

1 The relationship between stretchingforce, F, with the extension, x, of aspring, is given by the equation:

F = kx

where k is the spring constant. What isthe unit of k? (2005)A. N m

-1

B. N m-2

C. kg m-1

D. kg m-2

2 A spring produces an extension of 4 cmwhen a stretching force of 1.2 N isapplied to it. What is the elasticconstant of the spring?A. 30 N m

-1

B. 40 N m-1

C. 60 N m-1

3 The diagrams show the position of asteel ball bearing when the spring iscompressedand after the spring is released.

The distance xcan be increased byusingA a softer springB a longer springC a spring with a larger diameterD two similar springs arranged in

parallel

Question 1Figure 1 shows a boy extending the elasticrubber of a catapult.

Figure 1

(a) State the type of energy stored in theelastic rubber.

(b) Explain the change of energy when

the stone is released from the elasticrubber of the catapult.

(c) What happens to the maximumdisplacement if a smaller stone ofsimilar mass is used?

(d) If the elastic rubber is extended 20cm by a force of 8 N,

(i) what is the storedpotential energy in theelastic rubber?

(ii) If the mass of the stone is20 g, what is the velocityof the stone.


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Question 2Figure 2 shows the arrangement of anapparatus in an experiment to determine therelationship between the extension e of aspring T with weight W. The relationship of ewith W is shown in the graph in Figure 2.1

Figure 2.1

(a) (i) State the SI unit of weight.

(ii) State the relationship between e andW.

(iii) Name the scientific law involved inthe relationship stated in (a)(ii).

(b) (i) What is the elastic limit of a spring.

(ii) Mark with a cross (x) the elastic limitof 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 isextended. Calculate the energy stored in

the spring when it is extended by 4 cm.

(e) Another spring, identical to spring T, isadded to the arrangement in Figure 2.1.This new arrangement is shown in Figure2.2. The experiment is then repeated.

Figure 2.2

Sketch the graph of x against F for thisexperiment in Figure 2.1.

Question 3Figure (a) shows an archer shoots a targetFigure (b) the archer shoots the same targetbut at different distance.

Observe the conditions of each bow and thedistance of the target from the archer.

Based on the observations:(a) State one suitable inference that can bemade.

(b) State one appropriate hypothesis for aninvestigation.

(c) With the use of apparatus such as trolley,ticker timer and other apparatus ,describe an experimental framework totest 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 themanipulated variable and the method of

measuring the responding variable.(vi) Way you would tabulate the data(vii) Way you would analysis the data

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