Materials

Question 1

Define density and give the relevant equation for it including units

Answer 1

The density of a substance is its mass per unit volume

ρ (kgm⁻3)= m (kg) / v (m³)

Question 2

State Hooke’s Law and give the formula

Answer 2

The force needed to stretch a spring is directly proportional to the extension of the spring from its natural length.

F = kΔL
(Where k is the spring constant)

Question 3

What happens to a spring when the force applied has been removed beyond its elastic limit?

Answer 3

It does not regain its initial length when the force applied is removed

Question 4

Give an expression for Hooke’s law for 2 springs in parallel

Answer 4

W = Fp + Fq = kpΔL + kq∆L = kΔL

Where k = kp + kq

Question 5

Give the equation for tensile stress and give its units

Answer 5

Stress (Pa) = Tension / Cross-sectional area
σ = T / A

(Where 1Pa = 1Nm⁻³)

Question 6

State the equation for tensile strain and give its units

Answer 6

Strain = Extension / Length
ε = L / ΔL
(Strain is a ratio and has no units)

Question 7

How would you measure the diameter of a wire accurately?

Answer 7

By using a micrometer in different places along the wire and taking a mean value

Question 8

Give the formula for the Young modulus

Answer 8

E = σ / ε = TL / AΔL

Question 9

How many gcm⁻³ in 1000kgm⁻³?

Answer 9

1000kgm⁻³ = 1gcm⁻³

Question 10

Describe how you would measure the density of a regular solid

Answer 10

Measuring its dimensions and its mass and using the equation ρ = m / v

Question 11

Describe how you would measure the density of an irregular solid

Answer 11

Measure its mass and then immerse it in a measuring cylinder full of water; its volume is the change in water level
Use the equation ρ = m / v

Question 12

Describe how you would measure the density of a liquid

Answer 12

Measuring the mass of an empty measuring cylinder before adding the liquid to it and measuring again. Volume can be read from the meniscus of the measuring cylinder and density can be calculated by the equation ρ = m / v

Question 13

Define an alloy and give an example

Answer 13

An alloy is a solid mixture of two or more metals

Example: brass is an alloy of copper and zinc

Question 14

Derive the equation to calculate the density of an alloy of volume V, consisting of metals A and B

Answer 14

• Volume of metal A = Vᴬ, the mass of metal A = ρᴬVᴬ
• Volume of metal B = Vᴮ, the mass of metal B = ρᴮVᴮ
• The mass of the alloy m = ρᴬVᴬ + ρᴮVᴮ
• Hence the density of the alloy:
  ρ = m / v = (ρᴬVᴬ + ρᴮVᴮ) / V = (ρᴬVᴬ / V) + (ρᴮVᴮ / V)

Question 15

Define tension in a spring

Answer 15

• The tension in the spring is the pull it exert on the object holding each end of the spring
• Is equal and opposite to the force needed to stretch the spring

Question 16

Define elastic limit

Answer 16

If a spring is stretched beyond its elastic limit, it does not regain its initial length when the force applied to it is removed

Question 17

Define spring constant and give its units

Answer 17

The spring constant is a measure of a spring’s stiffness

Units: Nm⁻¹

Question 18

Describe a Force vs. Extension graph

Answer 18

The graph of F against ΔL is a straight line with gradient k which passes through the origin

Question 19

Describe how you would measure the spring constant of a spring

Answer 19

My hanging different masses off it and calculating the extension from the length the mass hangs at - the original length. Plotting a graph of Force vs. Extension gives a straight line through the origin with gradient k

Question 20

Give an expression for Hooke’s law for 2 springs (spring A and spring B) in series supporting a weight W

Answer 20

The tension is the same in each spring and is equal to the weight W, therefore:
- Extension of spring A, ΔLᴬ = W / kᴬ
- Extension of spring B, ΔLᴮ = W / kᴮ
where kᴬ and kᴮ are the spring constants of A and B
- ΔL = ΔLᴬ + ΔLᴮ = W / kᴬ + W / kᴮ = W / k
where k, the effective spring constant, is given by
1/k = 1/kᴬ + 1/Kᴮ

Question 21

State the equation for the energy stored in a stretched spring

Answer 21

Elastic Potential, Eᴘ = ½FΔL = ½kΔL²

Question 22

State how you would find the elastic potential of a spring from a graph of force vs. extension

Answer 22

Eᴘ = ½FΔL

The area under the line = ½FΔL

Question 23

Define tensile

Answer 23

Deformation that stretches the object

Question 24

Define compressive

Answer 24

Deformation that compresses an object

Question 25

Define elasticity

Answer 25

The elasticity of a solid material is its ability to regain its shape after it has been deformed or distorted, and the forces that deformed it have been released

Question 26

Describe the shape of the graph of extension vs weight for:

i) a steel spring
ii) a rubber band
iii) a polyethene strip

Answer 26

i) A steel spring gives a straight line in accordance with Hooke’s law
ii) A rubber band at first extends easily when it is stretched. However, it becomes fully stretched and very difficult to stretch further when it has been lengthened considerably
iii) A polyethene strip ‘gives’ and stretches easily after its initial stiffness is overcome. However, after ‘giving’ easily, it extends little and becomes difficult to stretch

Question 27

State the apparatus used to measure the extension of a wire under tension

Answer 27

Searle’s Apparatus (or similar apparatus with a vernier scale)

Question 28

Describe how you would measure the extension of a wire under tension

Answer 28

• A micrometer attached to the control wire is adjusted so the spirit level between the control and test wire is horizontal.
• When the test wire is loaded, it extends slightly, causing the spirit level to drop to one side.
• The micrometer is then readjusted to make the spirit level horizontal again
• The change of the micrometer readings is therefore equal to the extension

Question 29

Define tensile stress and give the units

Answer 29

Tensile stress is the tension per unit cross-sectional area:
σ = T / A
where A is the cross-sectional area under tension T

Units: Pascal (Pa) equal to 1Nm⁻²

Question 30

Define tensile stain and give the units

Answer 30

Tensile strain is the extension per unit length:
ε = ΔL / L
where ΔL is the extension from the original length wire L

Units: Strain is a ration and therefore has no units

Question 31

For a wire of uniform diameter d, give its cross-sectional area

Answer 31

A = πd² / 4

Question 32

Describe the stages on a graph of stress vs. strain

Answer 32

• from 0 to the limit of proportionality (P), the stress is proportional to the strain
• Beyond P, the line curves and continues beyond the elastic limit (E) to the yield point (Y₁) - which is where the wire weakens temprarily
• The elastic limit (E) is the point beyond which the wire is permanently stretched and suffers plastic deformation
• Beyond Y₂, a small increase in stress causes a large increase in strain as the material undergoes plastic flow.
  Beyond maximum stress, the ultimate tensile stress (UTS), the wire loses its strength, extends and becomes narrower at its weakest point.
• Increase of stress occurs due to the reduced cross-sectional area and the wire breaks at point B.

Question 33

Define Young’s modulus

Answer 33

A measure of elasticity, equal to the ratio of the stress acting on a substance to the strain produced
E = stress (σ) / strain (ε) = T/A ÷ LΔ/L = TL / AΔL

Question 34

Describe how you would compare the stiffness of materials

Answer 34

The stiffness of different materials can be compared using the gradient of the stress-strain line, which is equal to Young modulus of the material

Question 35

Define strength (of a material)

Answer 35

The strength of a material is its ultimate tensile strength (UTS) which is its maximum stress

Question 36

Describe a brittle material

Answer 36

A brittle material snaps without any noticeable yield

Question 37

Describe a ductile material

Answer 37

A ductile material can be drawn into a wire

Question 38

Describe the loading and unloading curve for a metal when:

i) Its elastic limit is not exceeded
ii) Its elastic limit is exceeded

Answer 38

i) Both the loading and unloading curves are the same straight line. When the load is removed it returns to its original length
ii) If the elastic limit is exceeded, the unloading line is parallel to the loading line. When the load is removed it is slightly longer so has a permanent extension

Question 39

Describe the loading and unloading curve for a rubber band

Answer 39

• The change of length during unloading for a given change in tension is greater than during loading. The rubber band returns to the same unstretched length.
• The unloading curve is lower than the loading curve except at 0 and maximum extension.
• The rubber band remains elastic as it regains its initial length, but has a low limit of proportionality

Question 40

Define limit of proportionality

Answer 40

The limit of proportionality is the is the point beyond which Hooke’s law is no longer true when stretching a material

Question 41

Describe the loading and unloading curve for a polyethene strip

Answer 41

• The extension during unloading is greater than during loading, but, the strip does not return to the same initial length when completely unloaded.
• The polyethene strip has a low limit of proportionality and suffers plastic deformation

Question 42

Define strain energy

Answer 42

The work done to deform an object

Question 43

For a metal wire or spring, provided the limit of proportionality is not exceeded, give the equation for the work done to stretch the wire to extension ΔL

Answer 43

Work done = ½TΔL

Question 44

For a metal wire, give the equation for the elastic energy stored in the stretched wire, provided that the elastic limit is not reached

Answer 44

Work done is stored as elastic energy in wire, therefore:

Elastic energy stored = ½TΔL

Question 45

For a graph showing the loading and unloading curve of a rubber band, state how you would find:

i) The work done on the rubber band
ii) The work done by the rubber band

Answer 45

i) The work done to stretch the rubber band is represented by the area under the loading curve
ii) The work done by the rubber band when it is unloaded is represented by the area under the unloading curve

Question 46

Describe the significance in the difference between the areas under the loading and unloading curve of a rubber band

Answer 46

• The area between the loading and unloading curve represents the useful energy stored in the rubber band when it is stretched, and the useful energy recovered from it when it is unstretched.
• The difference occurs because some of the energy stored in the rubber band becomes internal energy of the molecules when the rubber band unstretches

Question 47

Describe the significance of the difference between the areas under the loading and unloading curve for a poyethene strip

Answer 47

As it doesn’t regain its initial length, the area between the loading and unloading curves represents the work done to deform the material permanently, as well as the internal energy retained by the polyethene when it unstretches

Question 48

Explain why polyethene deforms permanently when stretched but rubber does not, even though they are both polymers

Answer 48

• When polyethene is being stretched, the intermolecular bonds between polymer molecules break. New intermolecular bonds between the polymer molecules form when stress is still placed on the polymer but there is no change in extension.
• When the force that stretched polyethene is released, the polymer chains hardly move at all due to the new intermolecular forces formed
• Rubbers’ molecules are curled up and tangled together when in an unstretched state. When placed under tension, its molecules straighten out. When the tension is removed, its molecules curl up again and it regains its initial length