Materials Flashcards
Define density and give the relevant equation for it including units
The density of a substance is its mass per unit volume
ρ (kgm⁻3)= m (kg) / v (m³)
State Hooke’s Law and give the formula
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)
What happens to a spring when the force applied has been removed beyond its elastic limit?
It does not regain its initial length when the force applied is removed
Give an expression for Hooke’s law for 2 springs in parallel
W = Fp + Fq = kpΔL + kq∆L = kΔL
Where k = kp + kq
Give the equation for tensile stress and give its units
Stress (Pa) = Tension / Cross-sectional area
σ = T / A
(Where 1Pa = 1Nm⁻³)
State the equation for tensile strain and give its units
Strain = Extension / Length
ε = L / ΔL
(Strain is a ratio and has no units)
How would you measure the diameter of a wire accurately?
By using a micrometer in different places along the wire and taking a mean value
Give the formula for the Young modulus
E = σ / ε = TL / AΔL
How many gcm⁻³ in 1000kgm⁻³?
1000kgm⁻³ = 1gcm⁻³
Describe how you would measure the density of a regular solid
Measuring its dimensions and its mass and using the equation ρ = m / v
Describe how you would measure the density of an irregular solid
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
Describe how you would measure the density of a liquid
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
Define an alloy and give an example
An alloy is a solid mixture of two or more metals
Example: brass is an alloy of copper and zinc
Derive the equation to calculate the density of an alloy of volume V, consisting of metals A and B
- 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)
Define tension in a spring
- 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
Define elastic limit
If a spring is stretched beyond its elastic limit, it does not regain its initial length when the force applied to it is removed
Define spring constant and give its units
The spring constant is a measure of a spring’s stiffness
Units: Nm⁻¹
Describe a Force vs. Extension graph
The graph of F against ΔL is a straight line with gradient k which passes through the origin
Describe how you would measure the spring constant of a spring
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
Give an expression for Hooke’s law for 2 springs (spring A and spring B) in series supporting a weight W
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
State the equation for the energy stored in a stretched spring
Elastic Potential, Eᴘ = ½FΔL = ½kΔL²
State how you would find the elastic potential of a spring from a graph of force vs. extension
Eᴘ = ½FΔL
The area under the line = ½FΔL
Define tensile
Deformation that stretches the object
Define compressive
Deformation that compresses an object
Define elasticity
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
Describe the shape of the graph of extension vs weight for:
i) a steel spring
ii) a rubber band
iii) a polyethene strip
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
State the apparatus used to measure the extension of a wire under tension
Searle’s Apparatus (or similar apparatus with a vernier scale)
Describe how you would measure the extension of a wire under tension
- 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
Define tensile stress and give the units
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
Define tensile stain and give the units
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
For a wire of uniform diameter d, give its cross-sectional area
A = πd² / 4
Describe the stages on a graph of stress vs. strain
- 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.
Define Young’s modulus
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
Describe how you would compare the stiffness of materials
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
Define strength (of a material)
The strength of a material is its ultimate tensile strength (UTS) which is its maximum stress
Describe a brittle material
A brittle material snaps without any noticeable yield
Describe a ductile material
A ductile material can be drawn into a wire
Describe the loading and unloading curve for a metal when:
i) Its elastic limit is not exceeded
ii) Its elastic limit is exceeded
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
Describe the loading and unloading curve for a rubber band
- 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
Define limit of proportionality
The limit of proportionality is the is the point beyond which Hooke’s law is no longer true when stretching a material
Describe the loading and unloading curve for a polyethene strip
- 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
Define strain energy
The work done to deform an object
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
Work done = ½TΔL
For a metal wire, give the equation for the elastic energy stored in the stretched wire, provided that the elastic limit is not reached
Work done is stored as elastic energy in wire, therefore:
Elastic energy stored = ½TΔL
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
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
Describe the significance in the difference between the areas under the loading and unloading curve of a rubber band
- 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
Describe the significance of the difference between the areas under the loading and unloading curve for a poyethene strip
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
Explain why polyethene deforms permanently when stretched but rubber does not, even though they are both polymers
- 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
