springs and elasticity classact srs enabled. in this presentation you will: explore the concept of...

Springs and Elasticity

ClassAct SRS enabled.

In this presentation you will: Explore the concept of elasticity as exhibited by springs.


The elasticity of a material, rather than the elasticity of an object, is measured using a different property. It looks at the relationship between the stress applied to an object and the strain produced. This takes account of the dimensions of the material being examined. This property is known as the Young’s Modulus.

Many objects deform when a force is applied and return to their original shape as soon as the force is removed. The relationship between force and extension for an elastic object was first formulated, in the seventeenth century, by Robert Hooke.

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Elasticity of a Spring

Although the wire that a spring is made of may not be very elastic itself, the particular shape of a spring provides it with an elastic behavior which helps in order to study elasticity.

Elasticity is the property of a material that allows it to return to its original shape after having been deformed, and to exert a force while deformed.

When a weight is applied to a fixed spring, it produces a force that stretches the spring.

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Extension of a Spring

The extension of a spring, when different forces are applied, can be measured and a graph of force against extension can be drawn.

When the weight is removed, the spring returns to its original length. The spring behaves in an elastic manner.

The difference between the spring's extended length and its unstretched length is called the extension.

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1

Elasticity is the ability of that material to resist the distorting force and to return to its original size and shape when the force is removed. Is this statement true or false?

Answer True or False.

Question


2

Springs behave in a elastic manner because...?

Question

A) the materials that springs are made of are very elastic.

B) the particular form of the spring provides it with elastic behavior.

C) the strain of the materials that springs are made of is very high.

D) springs do not behave in an elastic manner but in a plastic manner.


F = kx

F x

Spring Constant

This can be represented with the following equation:

which can be rewritten as:

Experimentation shows that the extension is directly proportional to the amount of force exerted on the spring. If force is plotted against extension, it will produce a straight-line graph passing through the origin.

where F is force in newtons, k is the constant of proportionality called the spring constant in newton meters and x is the extension in meters.

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3

What is the spring constant?

Question

A) The maximum extension of a spring.

B) The force that a spring can hold just before it breaks.

C) The force that a spring can hold before it starts extending.

D) The ratio between the force applied to a spring and its extension.


Hooke’s Law

Different springs have different elastic limits. Hooke's Law is only true for a spring that has not been extended beyond its elastic limit.

If a spring has been stretched beyond its elastic limit, it reaches plastic deformation and the spring will not return to its original shape when the force is removed.

The relationship between the applied force and the extension of a spring is known as Hooke’s Law.

Hooke’s Law states that the extension is proportional to the force provided the elastic limit has not been exceeded.

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4

If a spring obeys Hooke's Law and you double the force pulling on the spring, the extension will halve. Is this statement true or false?


Question


5

What is the elastic limit of a spring?

Question

A) The maximum extension of a spring before it breaks.

B) The maximum extension of the spring at which it will not return to its original shape when the force is removed.

C) The maximum weight that a spring can hold before it breaks.

D) The minimum weight a spring needs to start extending.


6

The extension of a material is directly proportional to the tension applied, and this means that...

Question

A) if the tension is doubled, the extension doubles.

B) if the tension is doubled, the extension halves.

C) if the tension is halved, the extension doubles.

D) if the tension is doubled, the extension is not affected.


Solids Deformation

The applied forces such as tension, compression, shear and torsion, act in different directions.

When a force is applied to a solid material, it distorts in some way.

An elastic material, on the other hand, resists the distorting force and returns to its original size and shape when the force is removed.

Some materials are called flexible or plastic since they keep the deformed state once the force is removed.

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Stress and Strain

Different materials have different elastic properties which can be measured as stress and strain.

The response of an object to a particular force depends on its size, its shape and the material it is made from.

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Stress

Stress, σ,is the applied force per unit area and can be calculated from the equation:

Where σ is the stress in pascals, F is the force in newtons applied to the object and A is the cross-sectional area of the object in m2.

ForceStress

Area

1 Pa = 1 Nm-2

Stress can be measured in Nm-2 or pascals (Pa). One pascal equals one newton per square metre.

F =

A

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7

Which unit is used to measure the stress of a material?

Question

A) Square metres

B) Newtons

C) Newtons per unit of length

D) Pascals (Pa) or Nm-²


Strain

The strain on a body is a comparison between the original size and the size after being stressed.

When stress is applied to a body, the shape of it changes as a result of the applied stress.

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Strain

When the forces of tension are applied to opposite ends of the object, they produce an extension x and the strain, , is given by:

Since strain is a ratio, it has no units and can be expressed as a percentage change in length by multiplying the ratio by 100.

change in length (extension)strain =

original length =

x

L

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8

The strain of a material is the ratio of the change in length of that material under tension, compared with the stress of that material. Is this statement true or false?


Question


Young’s Modulus

This ratio is called the Young’s Modulus, E, of the material:

Many solid materials as well as springs obey Hooke’s law, so that the ratio of stress to strain of a solid material is a constant.

where E has the same unit as stress, Nm-2 or pascals (Pa).

tensile stressYoung's modulus, E =

tensile strain

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Young’s Modulus

Since stress = F / A (force / area) and strain = x / L (extension / original length)

we obtain the function:

Engineers can then predict the effect of applying tensile forces in structures, whatever the size or shape of the object, made from a particular material.

FFLA

E = = x AxL

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Plastic Deformation

The material then retains some of its extension if the stress is removed.

The increased elastic deformation of materials reaches a point called the elastic limit where plastic deformation starts.

The maximum stress that a material can bear before it fractures is called the ultimate tensile stress and it is a useful measure of the strength of a material.

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9

Why would it be useful for a structural engineering team to know the ultimate tensile stress of the wires that they are going to use to build a suspension bridge?

Question

A) So they can calculate the strain of the rest of the materials used in the bridge.

B) So they can calculate how much time it will take to build the bridge.

C) So they can calculate the cost of the bridge.

D) So they know the maximum force that can be applied to each wire.


After completing this presentation you should be able to:

Identify the effects of tension applied to solid objects.

Show knowledge and understanding of the concepts of stress and strain.

Show understanding of the concepts of elasticity and plasticity.

Show knowledge and understanding of the Young’s Modulus of materials.

Summary

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springs and elasticity classact srs enabled. in this presentation you will: explore the concept of...

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