Materials

Question 1

How is density defined?

Answer 1

The mass per unit volume. [kgm^-3]

Question 2

How do you convert ²,³,⁴ etc… units to SI units?

(eg 5cm³ to m³)

Answer 2

Whatever you do to the unit, you do the same to the prefix

(eg 5cm³ = 5x(10^-2)³m³ = 5x10^-6m³)

Question 3

How do you measure the density of an irregular solid?

Answer 3

1. Read off the volume from the beaker or measuring cylinder without and with the object submerged in water
2. The difference in volumes is the volume of the solid
3. Measure the mass using a balance

Calculate density using ρ=M/V

Question 4

How do you calculate the average density of an alloy?

(Eg 200cm³ 5kg rod of 60% copper (8960kgm^-3) and 40% aluminum (2700kgm^-3) by volume?)

Answer 4

1. Work out the mass of each and the volume of each
2. Add together to get the total mass and volume
3. Then do the density calculation

Question 5

Define Hooke’s Law

Answer 5

When a material is stretched, its extension is proportional to the force applied, up until the limit of proportionality

F=kx

Question 6

Define the limit of proportionality

Answer 6

The point at which the material stops obeying Hooke’s law.

The graph is no longer a straight line.

Question 7

Define the elastic limit

Answer 7

The point at which when stretched further the material no longer returns to its original length (there is a permanent extension)

Question 8

What do the gradient and area of a force extension graph tell you for a spring.

Answer 8

Gradient → The spring constant (must be taken before limit of proportionality)

Area under line → The strain energy stored loading the spring or energy released unloading the spring

Question 9

What equation calculates energy stored when a material is stretched?

Answer 9

E=½Fx

Question 10

What is the difference between the elastic limit and the limit of proportionality?

Answer 10

Limit of proportionality is the point at which a stretched spring (or wire) stops obeying Hooke’s law.

The elastic limit is the point at which it doesn’t return to its original length when unloaded.

Question 11

Will this spring return to its original length if it has been stretched to 35mm?

Answer 11

Yes, because it has not passed the elastic limit

Question 12

What is a ductile material?

Answer 12

A material with a large plastic region.

Question 13

What is a brittle material?

Answer 13

A material with a small plastic region.

Question 14

What is the fracture point of a material?

Answer 14

The point at which a material breaks

Question 15

How do you know the rubber hasn’t stretched passed its elastic limit?

Answer 15

It still returns to its original length when unloaded.

Question 16

What is the formula for Young’s Modulus that you need to remember?

Answer 16

Question 17

What does the gradient and area under a stress-strain graph give?

Answer 17

Gradient → Young’s modulus (before the limit of proportionality)

Area → strain energy per unit volume

Question 18

What is elastic behaviour?

Answer 18

When a sample that has been deformed by a force returns to its original shape once the force causing the deformation is removed

Question 19

What is plastic behaviour?

Answer 19

The opposite of elastic behaviour. When the deforming force is removed, the object does not return to its original shape

Question 20

How is rubber different to a typical spring?

Answer 20

If the deforming force is unloaded at any point before the fracture point, it will return to its original shape

Question 21

What is different between a force-extension graph for rubber and for a spring?

Answer 21

The gradient of the graph for rubber is constantly changing and so there is no limit of proportionality or region obeying Hook’s Law

Question 22

The difference between the area under the graph when rubber is being stretched and the area under the graph when the deforming force is removed from the rubber gives…..

Answer 22

The energy retained by the rubber as heat

Question 23

What does the spring constant represent?

Answer 23

A measure of the resistance to stretching (stiffness).

Units are N/m

Question 24

How do you combine spring constant in series?

Answer 24

1/K_tot = 1/K_p + 1/K_q

_{Springs in series sit on top of one another}

Question 25

How do you combine spring constants in parallel?

Answer 25

K_tot = K_p + K_q

Springs in parallel sit alongside each other

Question 26

What is the equation for the energy stored stretching a spring / energy released when unloading a spring

Answer 26

E = ½k x ΔL²

Question 27

How do you find the work done permanently deforming a spring?

Answer 27

Area under the graph where work is being done stretching the spring - Area under the graph where the spring is unloaded

Question 28

What is the formula for stress and what are the units?

Answer 28

Stress = F / A

Units are Nm^-2

Question 29

What is the formula for strain and what are the units?

Answer 29

change in L / L

Strain has no units

Question 30

If you are given the dimensions of a string and have a stress - strain graph available, can you find the strain energy?

Answer 30

Yes
- Find the energy under the graph (strain energy per unit volume)
- Find the volume
- Multiply area under graph by volume for strain energy