MECHANICAL PROPERTIES OF MATERIALS: HOOKE’S LAW

Keywords

• Flexibility
• Malleability
• Strength
• Brittle
• Ductility
• Elasticity

By the end of this chapter, you will be able to

 (a) Understand the properties of different materials, how they are affected by heat and how they can be used to make different architectural structures.

(b)  Calculate the tensile strength of a given material.

 (c) Understand that the tensile strength of materials is determined by properties of the substances of which they are composed.

Introduction

Mechanical properties involve those properties that different materials like glass, wood or metal are made of. Before using them, we have to determine their behavior when subjected to a force or stress of any magnitude. Some materials, such as glass, may break easily, others have an elastic property and yet others cannot easily bend when forced to. So for this reason, they can be used to build several sorts of structures including bridges and the roofs of buildings, to mention but a few.

In this chapter, you will investigate and understand how the mechanical properties of the different materials are related to their application.

 Activity 4.1 determining the strength of materials

 Key Question: How can you determine the strength of spaghetti sticks?

What you need

• Spaghetti sticks, wet clay, wooden sticks, bicycles spokes.

What to do

(a) Using spaghetti sticks and wet clay design the structure shown in Figure 4.1 and call it structure A.

(b) Repeat the same design using wooden sticks and name it structure B, and the third one using bicycle spokes and name it structure C.

Figure 4.1: A model of a strong bridge made of wood

1. Arrange the structures in order starting from the strongest to the weakest
2. Explain why you have chosen that arrangement
3. Comparing what you have designed to the structures in your community, identity four other materials that you can use for the same purpose

4.1 Stress and Strain in Beams

The strength of materials is focused on analyzing stresses and deflections in materials of a structure.

When a force is applied to a member of a structure, both stress and strain as a result of force applied will develop on that part of a structure.

Stress, therefore, is defined as the force per unit area applied on a member of a structure. That is:

 Activity 4.2 investigating the relationship between force and extension for a spring

What you need

• A retort stand, clamp, spring, mass holder, 4 masses of 100g. A metre rule, pointer.

(a) Arrange the apparatus as shown above.

(b) Measure and record the initial position of the pointer before masses as L_o

(c) Hang 100g masses one at a time, as you measure and record the new length, L. At every stretch of the spring, measure and record extension,

 e = L – L_o

(d) Tabulate the results of m (kg) , l(m), e(m) and mg(N).

(e) Plot a graph of extension, e(m) against force mg(N).

1. Comment on the following :
2. Nature of the graph.
3. The impact of the variation of masses on the extension of the elastic spring.
4. The impact on different sizes (dimensions) of the stretching material (spring).
5. In groups, using the internet and other sources, state Hooke’s law and its relevance to the above activity.

 3. (a) Explain stress lines of beams under tension and compressive stress.

(b) Explain how reinforcing concrete changes the properties of the material of the structure present your findings to the rest of the class before your teacher.

4.2 Examples of Mechanical Properties of Materials

There are several mechanical properties that we can discuss in physical science and some of these include:

Elasticity

The ability to deform with respect to the applied load and regain its original shape when the load is removed.

• Elasticity is the tensile property of the material.

Hardness

The ability to resist scratches, marks and wear and tear when the body is subjected to contact with another body. Hardness is the ability of a material to resist scratching, abrasion, cutting or penetration.

Malleability

The ability to be stretched / deformed / moulded into a sheet.

• Aluminum , copper, silver, tin, steel etc. are malleable metals.

Ductility

 The ability to deform under tensile stress. This is often characterized by the material’s ability to be stretched into a wire.

• The materials that possess this property are used in industries for manufacturing wires. Examples are gold, copper, iron, mild steel etc.

Strength

This is the ability or capacity of a material to withstand or support a load without fracturing

• The stronger the material, the greater the load it can handle. Therefore, this determines the ability of a material to withstand stress without failure
• The strength of materials varies according to the types of load.
• The maximum stress (force per unit area) that a material can withstand before destruction is called the ultimate strength.

Flexibility

It is defined as the ability of the material to bend easily.

• This mechanical property of a material allows it to form into any shape.

Brittleness

This is the ability to break without significant deformation / develop cracks with respect to the applied load.

• There are so many materials which break without showing much permanent distortion. Such materials are said to be brittle, for example glass and cast iron.
• Brittleness is the opposite of ductility?

Activity 4.3 Determining mechanical properties of balloons

 Key Question: How can you determine the elasticity of a balloon?

What you need

• Balloon, thread.

What to do

 Note the initial size of a balloon by simply observing it.

1. Inflate that balloon to any size, as shown above.
2. Tie the neck of the balloon using a string to keep the pressure inside and observe its size
3. Remove the string and then note what happens to the balloon
4. Imagine the pressure is continuously increased. What do you think would happen to the balloon?
5. Which mechanical property do you think the balloon exhibited?
6. Why do you think the balloon behaves like that?
7. Mention any other two materials you have observed at home which have the same mechanical property

 Mention two examples of materials that present each of the mechanical properties described in (v) above.

Assessment 4.1

Imagine you were given the following constructional materials: wood / timber, iron bars, glass, nails, bricks, grass, iron sheets and plastic materials.

Explain the mechanical properties of these materials that make them good for the construction of a strong house.

Project Work 4.1

What you need

• Water, cement, gravel (pounded stones), spade, sand

Timeframe: In a period of 2-3 days within the vicinity of your school or home.

What to do

1. While in groups, try and get all the materials mentioned above
2. From your deductions, advise one on how to make a strong concrete given the kind of structure to be constructed.
3. By varying the proportions of cement, sand and gravel, make three samples of concrete.
4. After like 2-3 days, observe your samples and comment on its strength.
5. Thus, using this knowledge and experience, explain the choice of constructional materials like glass, wood, ceramics and steel in construction.
6. Together with fellow members of the group, make a comprehensive report and present it to your teacher and finally to the whole class,

EFFECT OF TEMPERATURE ON THESE PROPERTIES

Activity 4.4 explaining the effect of temperature on properties

 In groups, explain in terms of particle theory why heating materials like plastic bottles changes their structure and properties.

 It must also be noted that different materials are affected differently by changes in temperature. Since they have different melting points and heat capacities, they will expand at different rates when the same amount of heat energy is supplied, and so their nature will differ, yet nature affects properties such as hardness, ductility and malleability.

Assignment 4.2

With reference to Activity 4.2.

1. State and explain other factors that affect the properties of a material.

 2. In groups, investigate what we can do to a concrete to make it stronger, and also compare the strength of two steel rods of different diameters by applying the same stress. Write down the observations and thereafter discuss in class.

Chapter Summary

• In this chapter, you have learnt that:
• Different materials can have a variety of mechanical properties that enable engineers to use them to design lots of mechanical structures
• Hooke’s law is a statement that defines the relation between the tress and train in beams.
• Elastic limit is the lowest stress point at which permanent deformation occurs.
• Temperature has an effect on the mechanical properties of different materials.