elasticity | strain and stress | modulus of elasticity | NEB Physics short question answers | Knowledge of Physics
Q.1.) List the general properties of matter.
Ans: Some properties of matter which are common to all states of matter can be listed as below.
- Matter occupies certain space and possesses mass in all states.
- matter possesses inertia, that is, inability to change its state by itself.
- matter in all states is divisible into smaller portion. The smallest particle of matter is called molecule. molecules are formed by single or multiple atoms.
- Matter possesses adhesive and cohesive forces. The force of attraction between molecules of same matter is called cohesive force while force of attraction between molecules of different matters is called adhesive force.
- Matter in all states possesses elasticity, that is, the property due to which the body regains its original same and size after removal of deforming force applied on the body.
- Matter possesses compressibility. Three states of matter, that is, gas, liquid and solid, has the degree of compressibility in following order: gas > liquid > solid.
- Matter in all states has porosity, that is, the space due to the distance between particles of matter.
- matter in all states expand on heating.
Matter: Everything that is present around us is called matter. We eat matter, we drink matter, we use matter, we stay on matter, we are made of matter, we are alive because of matter. The presence of matter is detected by five senses: seeing, hearing, smelling, tasting and touching.
Q.2.) Explain elastic nature of matter.
Ans: When a small force is applied on a rubber string along its length, the shape and size of the string change. Such change in shape and size of body due to the application of external force is called deformation. The applied force is called deforming force. If the force is removed, the rubber string regains its original shape and size. Similarly, when a copper wire attached to some rigid support gets stretched as a mass object is hung on another free end of the wire. The wire regains its original shape and size right after the mass is removed. Such kind of property of matter by the virtue of which the matter regains its original shape and size after the deforming force is removed is called elastic property of matter. Elastic property is often called elasticity.
Q.3.) What is elasticity?
Ans: The elasticity of a body is defined as the property due to which the body regains its original shape and size after the removal of the force of deformation.
Q.4.) Define stress and strain. Also write their dimensional formulae.
Ans:
Stress:
When the deforming force is applied to the body, it changes shape and size of the body. As the deforming force is removed, the body regains its original shape and size. This is because of the resistive property of the matter of body to keep its shape and size as they were when no external force is applied on it. Such resistive property of body is defined as the restoring force, and it opposes the deforming force. Thus, the stress is defined as the restoring force per unit cross section area of the body. As the restoring force opposes the deforming force, the magnitude of these two forces are same.
`\therefore` Stress = `\frac{F}{A}` ..................(1)
Where, F = External force, A = cross section area of the body on which F is acting.
Strain:
When external force is applied to the body, the dimensions(shape and size) of the body change.
The change in dimension of the body per unit original dimension is known as strain.
`\therefore` Strain = `\frac{\Delta D}{D_0}` ..........(2)
Where, `\Delta D` = change in dimension, `D_0` = original dimension
The dimension of the body refers to the physical quantities such as length or radius(or diameter) or area or volume of the body.
Fig.1. Deformation of body
Dimension formulae of Stress and Strain:
For Stress:
From equation (1), Force (F) is measured in Newton(N) whose dimensional formula is `[MLT^-2]` and Area is measured in meter squared(`m^2`) whose dimensional formula is `[M^0L^2T^0]` or `[L^2]`.
`\therefore` dimensional formula for stress = `\frac{[MLT^-2]}{[L^2]}`
= `[ML^-1T^-2]`
Actually, stress is equivalent to pressure. So, stress and pressure have same units and same dimensional formula.
For Strain:
From equation (2), change in dimension is measured in meter(m) or meter squared(`m^2`) or meter cube(`m^3`) while change in original dimension is also measure in same way. So both quantities have same units. Therefore, strain becomes unit less quantity. Hence, strain has no dimensional formula.
i.e. dimensional formula for strain = [`M^0L^0T^0`].
Note:
From figure 1, deforming force F is applied to a body of original length `L_0` and the length becomes `L_1` after the deformation, then
original length = `L_0`
change in length = `L_1 - L_0`
`\therefore` strain = `\frac{L_1 - L_0}{L_0}`.
Q.5.) Define the following terms: rigid body, plastic body, elastic body.
Ans:
Rigid Body:
A body which does not undergo any change in shape and size when subjected to deforming force is known as rigid body. Example: rigid rotator, molecules in matter etc.
Plastic Body:
A body which does not regain its original shape and size after the deforming force is removed is known as plastic body. Example: glass, stones etc.
Elastic Body:
A body which regains its original shape and size after the deforming force is removed is known as elastic body. Example: rubber string, coper wire etc.
Q.6.) Which is more elastic, rubber or steel? Explain.
Ans: Steel is more elastic than rubber. Modulus of elasticity is the ratio of stress and strain. So, of the same force is applied to wires of steel and rubber having same length and cross section area, the extension produced in rubber is more than the extension produced in steel. Therefore, steel is more elastic than rubber.
Q.7.) Why are bridges are declared unsafe after long use?
Ans: Due to alternate cycles of stress and strain, bridges get fatigue after a long use. Once a bridge is fatigue, the strain produced for a given stress in the bridges will be very large. As a result, the bridge will collapse. It is, therefore, the bridges are declared unsafe after long use.
Q.8.) Why the spring is made of steel not of copper?
Ans: The elasticity of steel is more than that of copper. The strain or change in dimensions of steel object is less than that of copper object for same stress. Due to this reason, the steel spring can bear more stress than copper. So, steel spring comes to original state quicker than the copper spring after the deforming force is removed. This is why springs are made of steel, not of copper.
Q.9.) Why does the body regain the original shape and size after deforming force is removed?
OR
What is the cause of stress?
Ans: When a body is subjected to external force, the molecules of the body get displaced from their mean position. This destroys the equilibrium between the attractive and repulsive forces of molecules. However, the molecules always tend to have minimum potential energy to be in the equilibrium state. For molecules to attain minimum potential energy, the intermolecular forces (this force decreases with increasing intermolecular distance) come in action. This force per unit cross section area is called tensile stress. Similarly, when the molecule is displaced towards the decreasing intermolecular distance, repulsive molecular force which acts in direction of increasing intermolecular distance becomes effective. This effective force per unit area gives rise to compression stress.
This stress is responsible for taking the molecule to its mean position when the deforming force is removed. Due to the stress developed internally in the body, it regains its original shape and size after the deforming force is removed.
Q.10.) Explain why is steel or iron used widely in constructing bridges?
Ans: A bridge is to be constructed that it can withstand its own weight, the load due to traffic and forces due to other external agents. For bridge to be safe, the depression produced in it due to traffic should not exceed the elastic limit.
The depression produced in a bridge of length (l), breadth(b) and depth(d) due to load (W) is given by
`\delta = \frac{Wl^3}{4YBD^3}` ...........(1)
Where, Y = Young's modulus of elasticity for the material of bridge.
For bridge of given l , b, d and W, the depression (`\delta`) is inversely proportional to Y. It is therefore, the material of the bridge should so chosen that their Young's modulus Y as high as possible in order to have less depression. The steel or iron has high high value of Y, so it is used in constructing bridges.
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