3.4 Materials

Question 1

How the force constant, k, be found from a force extension graph?

Answer 1

It is equal to the gradient. For rubber bands it varies and is indicated by the gradient of a tangent to the stretching curve.

Question 2

State Hooke’s law.

Answer 2

The extension of a spring is directly proportional to the force exerted on it, as long as the limit of proportionality is not exceeded

Question 3

What is the formula for Hooke’s law?

Answer 3

F = kx

Question 4

State the formula to find the combined force constant, k꜀, for springs combined in parallel.

Answer 4

k꜀ = k₁ + k₂ + …

Question 5

State the formula to find the combined force constant, k꜀, for springs combined in series.

Answer 5

1 / k꜀ = 1/ k₁ + 1/ k₂ + …

Question 6

When two springs are placed in parallel, how does the force constant change?

Answer 6

It doubles.

Question 7

When two springs are placed in series, how does the force constant change?

Answer 7

It halves.

Question 8

On a force-extension graph, what does the area beneath the loading line represent?

Answer 8

The energy stored in the material as it is deformed

Question 9

On a force-extension graph, what does the area beneath the unloading line represent?

Answer 9

The energy transferred back out of the material into external stores as the load is removed.

Question 10

If a material obeys Hooke’s law, how would this be represented on a force-extension graph?

Answer 10

There will be a straight line through the origin.

Question 11

What is the unit of stress?

Answer 11

The pascal (Pa)

Question 12

What is the unit of strain?

Answer 12

It does not have a unit - it is a ratio.

Question 13

What is the unit of Young’s modulus?

Answer 13

The pascal (Pa)

Question 14

What is a material that behaves elastically?

Answer 14

A material that deforms when a force is applied, but returns to its original shape when the force is removed.

Question 15

What is a material that has plastic behaviour?

Answer 15

A material that deforms when a force is applied, and stays in its deformed shape when the force is removed.

Question 16

What is a brittle material?

Answer 16

A material which breaks through cracks / fracture with little plastic deformation.

Question 17

What are tensile forces?

Answer 17

Forces which stretch / pull an object

Question 18

What are compressive forces?

Answer 18

Forces that compress an object

Question 19

What is a ductile material?

Answer 19

A material which undergoes large plastic deformation under tensile forces.

Question 20

What is a malleable material?

Answer 20

A material which undergoes plastic deformation under compressive forces.

Question 21

What is a tough material?

Answer 21

A material that can withstand large dynamic loads without breaking.

Question 22

What is a hard material?

Answer 22

A material which is resistant to scratching. The harder a material is, the more difficult it is to dislodge atoms from its surface

Question 23

What is a stiff material?

Answer 23

A material which requires a lot of force for only little deformation.

Question 24

What is a strong material?

Answer 24

A material which can widthstand large static loads without breaking.

Question 25

What is a polymeric material?

Answer 25

A material made from long chain molecules.

Question 26

What is the difference between static and dynamic loads?

Answer 26

Static loads are applied gradually and don’t change in magnitude, while dynamic loads can change rapidly and exert more force.

Question 27

Define the elastic limit of an object or material.

Answer 27

The point beyond which it becomes permanently deformed and will not return to its original length or shape once any forces are removed.

Question 28

How can the Young’s modulus of a material be found from its stress-strain graph?

Answer 28

From the gradient of the initial straight-line section of its stress-strain graph.

Question 29

What does the area under the straight line section of a material’s stress-strain graph represent?

Answer 29

The energy stored in the material per unit volume.

Question 30

Define the Ultimate Tensile Stress (UTS) of a material. What does a higher UTS indicate?

Answer 30

The maximum stress the material experiences. This means it is a measure of the material’s strength; a higher UTS indicates a stronger material.

Question 31

What type of material has a high Young modulus?

Answer 31

A stiff material.

Question 32

What type of material has a high UTS and breaking point?

Answer 32

A strong material.

Question 33

Describe a stress-strain graph for a typical ductile material.

Answer 33

After the limit of proportionality, There is a curve in the line before the elastic limit (from which the material starts to behave plastically).

Question 34

Describe a stress-strain graph for a typical brittle material.

Answer 34

• The graph is linear with a steep slope, indicating that the material obeys Hooke’s Law up to its breaking point.
• There is little to no plastic deformation, and the material fractures suddenly after a small amount of strain.

Question 35

Describe a stress-strain graph for rubber, a typical polymeric material.

Answer 35

The loading and unloading curves for rubber are different - the energy released when the rubber is unloaded is less than the work done to stretch the rubber. This is because some of the elastic potential energy in the rubber is converted to heat.

Question 36

If a material obeys Hooke’s law, how would this be represented on a stress-strain graph?

Answer 36

It will have a straight line through the origin.