Efficiency

LESSON 2.11 Understanding elasticity.

Meaning of Elasticity Elasticity is the property of a substance which enables it to return to original shape @ size @ length after an applied external force( compressive force or stretching force) is removed. Why is a solid is elastic ?

Graph of force between molecules , F against the distance beween molecules, x. At distance X1 : is the equilibrium position where the resultance force is zero. At distance X < X1 : the solid is compressesd where force of repulsion > force of attraction. At distance X1 < X<X2 : the solid is stretched where force of attraction tarikan > force of repulsion until the force of attraction reaches a maximum value at X2. At distance X > X2 : the force of attraction will decrase and the molecular layer will begin to slip and solid will permanently change its shape. The point where the solid loses its elastic characteristics is call as the elastic limit. After this limit , the solid will not return to its original shape.

The property of elasticity is caused by the existence of two forces between molecules or atoms in the solid material. The two forces are force of repulsion and force of attraction between molecules. When a compressive force is applied to the solid,force of repulsion between the molecules pushes the molecules back to their equilibrium positions. When a stretching force is applied to the solid force of attraction between the molecules pulls the molecules back to their equilibrium positions. In the absence of an applied external force on the solid, the force of attraction is balanced by the force of repulsion or the resultant force is zero.

Restoring Force

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spring constant , k = Gradient of the graph A larger value of k or gradient indicates a stiffer spring. Figure(a): The spring is untstretched ,i.e at natural length and exerts zero force on the trolley. Figure(b): As the spring is stretched to the right, it exerts a force to the left on the trolley. This is called a restoring force.

P: stiff spring Q: soft spring

Hooke’s Law Hooke’s Law states that the extension of an elastic substance is directly proportional to the stretching force acting on it provided that the elastic limit is not exceeded.

Graph of Stretching Force, F against Spring extension, A : Elastic limit OA : The graph is a straight line passing through the origin. Thus the stretching force is directly proportional to the extension of the spring and Hooke’s law is obeyed. AB: The graph takes the form a curve, that is the stretching force is not vary directly with extension of the spring and Hooke’s law is no applicable.

@ F x F=kx F = the acting force or the effort X = extension k = the spring constant Spring constant , k

Why does the oscillation of a spring stops?

F = kx, k=F x

If you leave a mass on a spring oscillating it eventually slows down and stops. Air resistance slows the

the unit of k is Nm-1

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object down. Energy is lost from the system in overcoming this friction. This effect is called damping.

(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 ebnables 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.

In an ammeter or in a car’s suspension needs to stop the oscillations as quickly as possible .So damping proses should be happen as quickly as possible. Factors affecting the rate of extension or stiffness of a spring. Type of spring material: A spring made from a hard material extending shorter than a spring made from a soft material. For example a steel spring extending shorter than a copper spring. Diameter of spring coil: A spring coil of a larger diameter is easier to stretch ( the rate of extension is high) compared to a spring coil of smaller diameter. Diameter of the wire of the spring : A spring coil made from a thicker wire is harder ( the rate of extension is low) compared a spring made from a thinner wire. Spring arrangement: Stretch of a spring in series is more easier than stretch of a spring in parallel. The original length of the spring: Stretch of a longer spring is more easier than stretch of a shorter spring . The spring constant , k : The spring which has a larger value of k is the spring which more stiff(the rate of extension is low) Use of Elasticity in Everyday Life: (1) Cushion/tmattress: 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.

Spring Systems There are two ways to arrange a spring, that is, (a) Series arrangement (b) Parallel arrangement

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Series Parallel In series arrangement same load is applied to each spring i.e W In parallel arrangement the load is shared equally among the springs . i.e W 2

Solution

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. 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.

Elastic Potential Energy ( Ee) Elastic potential energy is the energy stored in a elastic matter when it is extended or compressed. Thus, Ee = ½ F x = ½ kx2 Area under the

= gr

aph F vs. x

Solution

F = Force x = extension spring constant

k=

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? Example 2

Solution

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 4 Figure shows a graph of force,F against extension,x for a spring.

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

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 14 cm and its spring constant is 200 N m-1.

TUTORIAL 2.11 1

property of elasticity is caused by the existence of A B C

2

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

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? A C

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the force of repulsion between molecules the force of attraction between molecules the force of repulsion and attraction between molecules

N m-1 kg m-1

B D

N m-2 kg m-2

3

The spring constant ,k increases when

A the spring length incraeases B the diameter of the sprig incraeases C the diameter of the spring wire increases 4

Which section of the graph Hooke’s law is obeyed?

The figure shows two springs with a different original length . A piece of wood slowly moved towards the wall with a force F so that the springs are compressed together with a distance,x

A B C D 6

A spring extends by 4 cm when it hung with a load of 8N. Find the weight of a load when hung from the same spring, produces an extension of 5 cm. A C E

Which one of the following graph is true?

7

5

The figure shows a forceextension graph for a spring.

AO AB At point B After point B

9N 12 N 16 N

B D

10 N 14 N

The figure shows a spring of length 18 cm compressed to a length of 10 cm by a load of P and compressed to a length of 8 cm by a load of 10 kg.

What is the value of P ? A C E 8

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4 kg 8 kg 12 kg

B D

6 kg 9 kg

Figure shows (a) the pointer reading of a spring without load. Figure (b) and (c) show the pointer

reading of the spring when it is loaded with a different load.

springs, P, Q and R. All the springs are identical. P Q R

What is the value of M? A C E 9

100g 200 g 300g

D

B 180g 240g

Which comparison is correct about the extension nof P,Q and R? A P C R

Figure (a) and (b) show the two positions of a pin when a spring is loaded with two different weights.

P
B

Q< R<

R< Q < P

D

Q< P<

11 The figure shows two springs K and L having and original length 5 cm each are connected in series to 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 a 00 g ]

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

5.00 cm

B

C

15.00 cm E 20.00 cm

D

10.00

What is the length of AB?

cm cm

18.75

A C E

10 The figure shows a load M supported by the arrangements of

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16 cm 23 cm 26 cm

B D

21 cm 24 cm

12 Figure(a) shows a spring of length 10 cm compressed to a length of 8 cm by a load of 20 N. Figure (b) shows five identical springs are compressed by a load of 60 N to a length of L.

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

What is the value of L? A C E

5 cm 9 cm 15 cm

B D

What is the total extension of the spring system?

7 cm 13 cm

13 Figure (a) shows two springs A and B having an original length of 10 cm each are loaded with the mass of 100 g and 200 g respectively. Figure (b) shows the springs A and B are arranged in series and it is loaded with the mass of 300g.

A C

5.0 cm 15.0 cm

E

25.0 cm

B

10.0 cm D 20.0

cm 15 Figure(a) shows a spring J extends to a certain value when it hung with a 40 g weight. The Figure (b) shows three springs K,L and M are arranged in parallel extends to same value as spring J when it hung with a weight P.

What is the length of P?

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

A C E

A C E

55 cm 70 cm 125 cm

B D

100 cm 105 cm

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60g 120g 200 g

B

80g D 160g

16 Figure (a) and Figure (b) shows six identical springs E, F, G, H, I, and J whose original length is 12 cm each.

A C E

26 cm 30 cm 34 cm

B D

18

7.5 J 3 000 J 12 000 J

D

4 cm 2 cm

28 cm 32 cm

17 A spring is compressed with a force of 300 N . If the compression of the spring is 0.05 m, what is the potential energy stored in the spring? A C E

B D

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

What is the value of L? A C E

6 cm 3 cm 1 cm

What is the velocity of the metal sphere ?

B 15.0 J 6000 J

A C E

The figure shows a spring having an original length of 20 cm. When the spring is compressed by a steel ball of mass 0.1 kg, the length of the spring becomes 14 cm. The steel ball moves up at a height h when it is is released.

20

1 ms –1 3ms-1 6ms-1

B D

2 ms-1 4 ms-1

Figure (a) shows the arrangement of apparatus to investigate the relationship between the extension, x, of a spring and weight of load W. The relationship between x and W is shown in the graph in Figure (b).

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

What is the value of h ?

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(b)

............................................. ................. Name the law that relates x and W.

……………………………………… ………… (d) Which of the spring is the most suitable to measure the big force. Explain why?

............................................. ................ (c) State the relationship between x and W. ............................................. ............... (d) State the physical quantity which can be represented by the area below the graph line.

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

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

……………………………………… ………

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

……………………………………… ……… (f) Create an arrangement of the spring A and B to get the extension of the spring system is 10 cm when a load of 10 N is hung. 21 Figure(a) shows the arrangement of 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(b).

(a) Based on the graph , state the relationship between 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?

Figure(a) Figure(b)

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(a) A law states that; The extension of a spring is directly proportional to the force applied if the elastic limit of the spring is not exceeded. (i) Name this law ……………………… ……………. (ii) Mark with a cross (x) the elastic limit of the spring on the graph in Figure (b). 22 Figure (a) shows an archer shoots a target Figure (b) the archer shoots the same target but at different distance.

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

(c) Another spring, identical to spring T , is added to the arrangement in Figure(a). This new arrangement is shown in Figure(c). The experiment is the repeated.

Observe the conditions of each bow and the distance of the target from the archer. Based on the observations: State one suitable inference that can be made. (b) State one apporopriate hypothesis for an investigation. (c) With the use of apparatus such as trolley, ticker timer and other apparatus , describe an experimental (a)

Figure(c) Sketch the graph of W against e for this experiment on the graph in Figure (b).

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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 wouldttabulate the data (vii) Way you would analysis the data

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