Unit 1.5) Solids under stress

Question 1

Define the spring constant

Answer 1

The force per unit extension required to stretch a spring.
Denoted by K.
Inherent property of the spring.

Question 2

State Hooke’s law

Answer 2

Extension(denoted by x) is directly proportional to Force applied(F),given that the environmental conditions are kept constant.

F=Kx (where k is the spring constant in Nm^-1)

Question 3

What is meant by tensile stress?

Answer 3

The force applied per unit cross sectional area.
Stress, = F/A
Stress units: Nm^-2
Force units: N
Cross sectional area units:m^2

Question 4

What is tensile strain?

Answer 4

A measure of how a material stretches. It is equal to the extension divided by the original length(L), Strain is a ratio so it has no units.
Strain, = x/L

Question 5

What is the difference between elastic and plastic deformation

Answer 5

Elastic deformation: when the force is removed the object will return to its original shape.
Plastic deformation: after the load is removed the object will not return to its original shape. It has been stretched beyond its elastic limit.

Question 6

What is breaking stress?

Answer 6

The minimum stress needed to break a material.

Question 7

What is meant when a material is described as brittle?

Answer 7

It does not extend much when a force is applied(tensile strain stays low). The material tends to break rather then stretch under a large force.

Question 8

What is the elastic limit(sometimes called limit of proportionality)?

Answer 8

The point after which plastic deformation occurs. It is also sometimes referred to as the ‘limit of proportionality’.

Question 9

What does the area underneath a force extension graph represent?

Answer 9

The energy stored in the material.

Question 10

Give the equation that calculates elastic strain energy in terms of the spring constant and extension.

Answer 10

E = 1/2kx^2
(extension could also be ΔL)

Question 11

What is young’s modules?

Answer 11

Young’s modules = tensile stress/ tensile strain

Question 12

How do you find the young’s modules from a stress-strain graph?

Answer 12

Using the gradient of the line.

Question 13

How can a force extension graph show Hooke’s law is being obeyed?

Answer 13

When it is a straight line through the origin-force and extension are directly proportional.

Question 14

What is the limit of proportionality and what does it look like on a force extension graph?

Answer 14

The point after which Hooke’s law is no longer being obeyed. It is shown by the line beginning to curve on a force-extension graph.

Question 15

What is meant by elastic strain?

Answer 15

Strain that disappears when a stress is removed-the material returns to its original shape.

Question 16

What is meant by plastic(or inelastic) strain?

Answer 16

Strain that decreases only slightly when stress is removed. The material does not return to its original shape.

Question 17

How is the work done to stretch or compress a material stored?

Answer 17

It is stored as elastic strain energy.

Question 18

Why are the loading and unloading lines parallel on a force-extension graph for a plastically deformed material?

Answer 18

The stiffness constant(k) has not changed- the forces between the atoms are the same when loading and unloading

Question 19

Why isn’t all work done stored as elastic strain energy when an object undergoes plastic deformation?

Answer 19

Work is done to move atoms apart, so energy is not stored as elastic strain energy.

Question 20

How is the dissipation of energy in plastic deformation used to design safer vehicles?

Answer 20

Crumple zones deform plastically in a crash using the car’s kinetic energy, so less energy is transferred to the passengers.
Seat belts stretch to convert the passenger’s kinetic energy into elastic strain energy.

Question 21

outline the energy changes that occur when a spring fixed at the top is pulled down and released.

Answer 21

The work done is pulling the spring down (stretching it) is stored as elastic strain energy. When the spring is released, this is converted to kinetic energy, which is then converted to gravitational potential energy as the spring rises.

Question 22

Do stress-strain graphs show the behaviour of a material or a specific object?

Answer 22

Material

Question 23

Where would you find the ultimate tensile stress on a stress-strain graph?

Answer 23

The highest point on the graph. It is the maximum stress a material can withstand.

Question 24

What is a ductile material?

Answer 24

A material that can be drawn out into a wire-plastic deformation occurs when there is enough stress.

Question 25

What is meant by ductile fracture(necking)?

Answer 25

The process of fracture in a ductile material: there is local thinning, which increases the stress(as the area decreases and stress = force/area), before the material breaks.

Question 26

What is a brittle material

Answer 26

A material that does not plastically deform.
Under tension, the material fractures.

Question 27

What is meant by brittle fracture?

Answer 27

The fracture of brittle materials when they are put under tension.
This occurs by cracks spreading through the material.

Question 28

What is elastic hysteresis?

Answer 28

When a material(e.g. rubber) is put under stress and then the stress is removed , the stress-strain graphs for loading and unloading do not overlap but form a loop.

Question 29

What is a crystal?

Answer 29

A solid in which the atoms are arranged in a regular array.
There is a long-range order, meaning that there is a pattern that repeats itself periodically over the entire crystal.

Question 30

What is a crystalline solid?

Answer 30

A solid mode of one or many crystals(usually arranged randomly).
In cases where it is made of many crystals, it is called a polycrystalline solid (e.g. metals).

Question 31

What is an amorphous solid?

Answer 31

A solid in which the atoms are arranged randomly.
These are rare, so in practice, solids like glass or brick(that have no long-range order) are referred to as amorphous.

Question 32

What is a polymeric solid?

Answer 32

A solid that is made up of chain-like molecules.

Question 33

What is meant by dislocations in crystals?

Answer 33

Faults in crystal structures which reduce the stress required for planes of atoms to slide( if there are not too many faults).
What is meant by grain boundaries?
The boundaries between crystals(grains) in a polycrystalline material.

Question 34

How do you calculate the work required to stretch a spring?

Answer 34

W = 1/2KΔx^2
Where:
Δx^2 is equal to (X1^2 - X0^2)
X1 is final extension X2 is initial extension)

Work done is also equal to ΔPE. Inital PE - Final PE.