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

• 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

Attractive 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.

Elasticity

Repulsive force

Repulsive force

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 xF = 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 kx2

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 elasticityFactor Change in factor Effect on elasticity

length Shorter springLonger spring

Less elasticMore elastic

Diameter of spring Smaller diameterLarger diameter

Less elasticMore elastic

Diameter of spring wire

Smaller diameterLarger diameter

More elasticLess elastic

Type of material The elasticity change with the type of material.

System of spring

• Spring in series

M

•Load in each spring = M

•Extension = x

•Total extension = 2x

x

x

System of spring

• Spring in parallel

M

X

2

Load in each spring = M/2

Extension = x/2

Total extension = x/2

System of spring

M

spring (i)

Force = M/2

Extension = x/2

Spring (iii)

Force = M

Extension = x

Total extension = x/2 + x

(i) (ii)

(iii)

Spring (ii)

Force = M/2

Extension = x/2

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

• 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?

500 g

2cm