Lesson 2.1(a)Elasticity

8/7/2019 Lesson 2.1(a)Elasticity

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Meaning of Elasticity

Elasticity is the property of a substance whichenables it to return to original shape @ size @ lengthafter an applied external force( compressive force

or stretching force) is removed.

Why is a solid is elastic ?

The property of elasticity is caused by the existenceof two forces between molecules or atoms in thesolid material.The two forces are force of repulsion and force ofattraction between molecules.When a compressive force is applied to the solid,

force of repulsion between the molecules pushes themolecules back to their equilibrium positions.When a stretching force is applied to the solid forceof attraction between the molecules pulls themolecules back to their equilibrium positions.In the absence of an applied external force on thesolid, the force of attraction is balanced by the forceof repulsion or the resultant force is zero.

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Graph of force between molecules , F againstthe distance between molecules, x.

At distance X1 : is the equilibrium position where theresultance force is zero.At distance X < X1 : the solid is compressed whereforce of repulsion > force of attraction.

At distance X1 < X force of repulsion until the forceof attraction reaches a maximum value at X2.At distance X > X2 : the force of attraction willdecrease and the molecular layer will begin to slipand solid will permanently change its shape. Thepoint where the solid loses its elastic characteristicsis call as the elastic limit. After this limit , the solidwill not return to its original shape.

Restoring Force

Figure(a): The spring is unstretched , i.e at naturallength and exerts zero force on the trolley.Figure(b): As the spring is stretched to the right, itexerts a force to the left on the trolley. This is calleda restoring force.

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Hookes LawHookes Law states that the extension of an elastic

substance is directly proportional to the stretchingforce acting on it provided that the elastic limit isnot exceeded.

@ F x F = k x

F = the acting force or the effortX = extensionk = the spring constant

Spring constant , k

F = kx,k = F

xthe unit of k is Nm-1

spring constant , k = Gradient of the graph

A larger value of k or gradient indicates a stifferspring.

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P: stiff spring

Q: soft spring

Graph of Stretching Force, F against Springextension,A : Elastic limitOA : The graph is a straight line passing through theorigin. Thus the stretching force is directlyproportional to the extension of the spring andHookes law is obeyed.

AB: The graph takes the form a curve, that is thestretching force is not vary directly with extension ofthe spring and Hookes law is no applicable.

Why does the oscillation of a spring stops?

If you leave a mass on a spring oscillating iteventually slows down and stops. Air resistanceslows the object down. Energy is lost from thesystem in overcoming this friction. This effect iscalled damping.

In an ammeter or in a cars suspension needs to stopthe oscillations as quickly as possible .So dampingprocess should be happen as quickly as possible.

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Factors affecting the rate of extension orstiffness of a spring

Type of spring material: A spring made from ahard material extending shorter than a springmade from a soft material. For example a steelspring extending shorter than a copper spring.Diameter of spring coil: A spring coil of a largerdiameter is easier to stretch ( the rate of extension

is high) compared to a spring coil of smallerdiameter.Diameter of the wire of the spring : A spring coilmade from a thicker wire is harder ( the rate ofextension is low) compared a spring made from athinner wire.The original length of the spring: Stretch of alonger spring is more easier than stretch of ashorter spring .The spring constant , k: The spring which has alarger value of k is the spring which more stiff(therate of extension is low)Spring arrangement: Stretch of a spring in seriesis more easier than stretch of a spring in parallel.

Use of Elasticity in Everyday Life:(1) Cushion / mattress: The spring in a cushion or

mattress undergo many cycles of compressionduring use and each time the cushion is able to

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return to its original shape. This is due to theelasticity of the springs.

(2) Electric meter : Electric meters such asammeter, voltmeter and galvanometer havespiral springs. The springs are used to stop thepointer at a specific point on the scale or to

return the pointer to the zero mark on the scaleafter a measurement has been taken

(3) Weighing apparatus: A weighing apparatussuch as spring balance , a spring is eitherextended or compressed and it obeys theHooke law and it caused the apparatus has alinear scale.

(4) Vehicles spring support: It enables thepassengers in a vehicle to be seated in acomfortable position when the vehicle goes on abumpy road because springs shock absorbers aremounted on the wheels of vehicles to absorb

impacts and damp vibrations resulting frommovement on the bumpy road or uneven roadsurface.

(5) In sports : The elastic strings of a tennis or abadminton racket enable them to rebound theball or shuttle.The ropes used by rock climbers have elasticproperties that can save lives during climbingaccidents. The ropes are made of a continuous-drawn nylon fibre core and a protective textilecovering . This reduces the stopping force actingon a falling climber.

A bow bends or elastic twine of the bow isstretched to store the elastic potential energyused to propel the arrow.

Spring SystemsThere are two ways to arrange a spring, that is,

(a) Series arrangement(b) Parallel arrangement

Series Parallel

In series arrangement same load is applied to eachspring i.e W

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In parallel arrangement the load is shared equallyamong the springs . i.e W2

Example 1The original length of a spring is 5 cm. With a load of

mass 20 g, the length of the spring is extended to7 cm.Determine(a) the extension of the spring with a load 40 g(b) the length of the spring with a load 60 g.(c) the load required to extend the spring to 20 cm.

Solution

Example 2

Spring A extends by 2 cm when it hung with a 10 gweight. Spring B extends by 4 cm when it hung witha 10g weight. Find the total stretch in each of thespring systems shown in the following figure.

Solution

Elastic Potential Energy ( Ee)

Elastic potential energy is the energy stored in aelastic matter when it is extended or compressed.Thus,

Ee = F x = kx2 = Area under the

graph F vs. x

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F = Forcex = extension k = spring constant

Example 3The original length of a spring is 12 cm. With a load

of 20 g , the length of the spring is extended to 15cm.What is the elastic potential energy stored in thespring?

Solution

Example 4

Figure shows a graph of force, F against extension, xfor a spring.

What is the potential energy stored when the springis extended by 0.4 m?

Solution

Example 5

Figure shows a ball of mass 10 g pushed against oneend of a spring on a smooth surface. The originallength of the spring is 14 cm and its spring constantis 200 N m-1.

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Determine(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.

Solution

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1 property of elasticity is caused by the existenceof

A theforce of repulsion between moleculesB the force of attraction between moleculesC theforce of repulsion and attraction between

molecules

2 The relationship between stretching force, F, withthe extension ,x , of a spring is given by theequation;

F = kxwhere k is the spring constant.What is the unit of K?

A N m-1 B N m-2

C kg m-1 D kg m-2

3 The spring constant ,k increases when

A the spring length increasesB the diameter of the sprig increasesC the diameter of the spring wire increases

4 The figure shows two springs with a differentoriginal length . A piece of wood slowly movedtowards the wall with a force F so that thesprings are compressed together with a distance,

xWhich one of the following graph is true?

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5 The figure shows a force- extension graph for aspring.

Which section of the graph Hookes law isobeyed?

A AOB AB

C At point BD After point B

6 A spring extends by 4 cm when it hung with aload of 8N. Find the weight of a load when hungfrom the same spring, produces an extension of5 cm.

A 9 N B 10 NC 12 N D 14 NE 16 N

7 The figure shows a spring of length 18 cmcompressed to a length of 10 cm by a load ofP and compressed to a length of 8 cm by aload of 10 kg.

What is the value of P ?

A 4 kg B 6 kgC 8 kg D 9 kgE 12 kg

8 Figure shows (a) the pointer reading of a springwithout load. Figure (b) and (c) show the pointer

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reading of the spring when it is loaded with adifferent load.

What is the value of M?

A 100g B 180gC 200 g D 240g E 300g

9 Figure (a) and (b) show the two positions of a pinwhen a spring is loaded with two differentweights.

What is the reading on the pin when 20 g of theload in Figure (b) is removed.

A 5.00 cm B 10.00 cm

C 15.00 cm D 18.75 cm E 20.00 cm

10 The figure shows a load M supported by thearrangements of springs, P, Q and R. All thesprings are identical.

P Q R

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Which comparison is correct about the extensionof P,Q and R?

A P < Q < R B Q< R< PC R< Q < P D Q< P< R

11 The figure shows two springs K and L having and

original length 5 cm each are connected in seriesto a 400 g weight .[ Spring K extends 2 cm when it is hung with a

200 g .Spring L extends 3 cm when it is hung with a100 g ]

What is the length of AB?

A 16 cm B 21 cmC 23 cm D 24 cmE 26 cm

12 Figure(a) shows a spring of length 10 cmcompressed to a length of 8 cm by a load of

20 N. Figure (b) shows five identical springs arecompressed by a load of 60 N to a length of L.

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What is the value of L?


13 Figure (a) shows two springs A and B having an

original length of 10 cm each are loaded with themass of 100 g and 200 g respectively.Figure (b) shows the springs A and B arearranged in series and it is loaded with the massof 300g.

What is the length of P?

A 55 cm B 100 cmC 70 cm D 105 cm E 125 cm

14 Figure(a) shows a spring P extends by 5 cm whenit hung with a 0.5 kg weight. Figure (b) showsfour springs P are arranged in a system and ithung with a 1.0 kg load.

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What is the total extension of the spring system?

A 5.0 cm B 10.0 cmC 15.0 cm D 20.0 cmE 25.0 cm

15 Figure(a) shows a spring J extends to a certainvalue when it hung with a 40 g weight. TheFigure (b) shows three springs K,L and M arearranged in parallel extends to same value asspring J when it hung with a weight P.

What is the value of P if the spring J,K,L and Mare identical springs.

A 60g B 80gC 120g D 160gE 200 g

16 Figure (a) and Figure (b) shows six identicalsprings E, F, G, H, I, and J whose original length is12 cm each.

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What is the value of L?

A 26 cm B 28 cm C 30 cmD 32 cm E 34 cm

17 A spring is compressed with a force of 300 N . If

the compression of the spring is 0.05 m, what isthe potential energy stored in the spring?

A 7.5 J B 15.0 JC 3 000 J D 6000 JE 12 000 J

18 The figure shows a spring having an originallength of 20 cm. When the spring iscompressedby a steel ball of mass 0.1 kg, the length of thespring becomes 14 cm. The steel ball moves up

at a height h when it is released.

What is the value of h ?


19 Figure (a) shows a metal sphere of weight ofF N is placed atop a spring and it is found theextension of the spring is x cm.Figure (b) shows the graph F against x for thespring.When the extension of the spring is 20 cm , themetal sphere is released.

What is the velocity of the metal sphere ?

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A 1 ms 1 B 2 ms-1 C 3ms-1D 4 ms-1 E 6ms-1

20 Figure (a) shows the arrangement of apparatusto investigate the relationship between the

extension, x, of a spring and weight of load W.The relationship between xand W is shown inthe graph in Figure (b).

Figure(a) Figure(b)(a) State the S.I. unit for weight.

..............................................................(b) Name the law that relates x and W.

.............................................................(c) State the relationship between x and W.

............................................................(d) State the physical quantity which can be

represented by the area below the graphline.

............................................................

20 The figure shows a graph extension , x againstForce ,F for two springs A and B. The spring Aand B having an original length of 10 cm each.

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(a) Based on the graph , state the relationshipbetween the extension, x and the force, F.

(b) State the law involved.

(c) What is the physical quantity is represented

by the gradient of the graph?

(d) Which of the spring is the most suitable to

measure the big force. Explain why?

(e) State two factors why the extension of thespring A is different from the extension ofthe spring B?

(f) Create an arrangement of the spring A and B

to get the extension of the spring system is10 cm when a load of 10 N is hung.

21 Figure(a) shows the arrangement of apparatus inan experiment to determine the relationshipbetween the extension e of a spring T withweight W. The relationship ofe with Wis shownin the graph in Figure(b).

Figure(a) Figure(b)

(a) A law states that;

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The extension of a spring is directlyproportional to the force applied if theelastic limit of the spring is not exceeded.(i) Name this law

.

(ii) Mark with a cross (x) the elasticlimit of the spring on the graph inFigure (b).

(b) The spring stores energy when it is extended.Calculate the energy stored in the springwhen it is extend by 4 cm.

(c) Another spring, identical to spring T , isadded to the arrangement in Figure(a). Thisnew arrangement is shown in Figure(c). Theexperiment is the repeated.

Figure(c)

Sketch the graph ofWagainst e for thisexperiment on the graph in Figure (b).

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22 Figure (a) shows an archer shoots a targetFigure (b) the archer shoots the same target

but at different distance.

Observe the conditions of eachbow and the distance of the target from thearcher.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 totest your hypothesis.In your description , state clearly thefollowing:(i) Aim of the experiment(ii) Variables in the experiment(iii) List of apparatus and materials

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(iv) Arrangement of the apparatus(v) The procedure of the

experiment which include themethod of controlling themanipulated variable and themethod of measuring the

responding variable.(vi) Way you would tabulate the

data(vii) Way you would analysis the

data

Lesson 2.1(a)Elasticity

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