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6.1.3Work, energy, power and deformation

The Young Modulus

5 min read 9 parts Lesson 13 of 17 1 quiz

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Lesson summary

6.1.3 The Young Modulus — AS PHYSICS 9702 notes: Define stress, strain and the Young modulus and describe the experiment to measure it for a wire.Tensile stress — the applied force per unit cross-sectional area of a material.Equation — σ = F/A.What the symbols mean: σ = stress (P…

  • Ultimate tensile stress
  • Elastic check
  • Force–extension gradient
  • Micrometer screw gauge
  • Compression
  • Spring constant

Section 1 of 9Stress

Tensile stress
  • Tensile stress the applied force per unit cross-sectional area of a material.
Equation
  • σ = F/A.
    What the symbols mean: σ = stress (Pa) · F = tensile force (N) · A = cross-sectional area (m2)
  • σ is stress in Pa.
  • F is the applied force in N.
  • A is the cross-sectional area in m2.
Ultimate tensile stress
  • Ultimate tensile stress the maximum force per original cross-sectional area a wire can support at the point it breaks.

Section 2 of 9Strain

Strain
  • Strain the extension per unit length, the deformation of a solid due to stress.
Equation
  • ε = x/L.
    What the symbols mean: ε = strain (no unit) · x or ΔL = extension (m) · L = original length (m)
  • x is the extension in m.
  • L is the original length in m.
No unit
  • No unit strain is a ratio of lengths and has no unit.

Section 3 of 9The Young modulus

Meaning
  • Meaning a measure of the ability of a material to withstand changes in length when a load is added.
Equation
  • E = σ/ε = FL/(Ax).
    What the symbols mean: E = Young modulus (Pa) · σ = stress (Pa) · ε = strain · F = force (N) · L = original length (m) · A = cross-sectional area (m2) · ΔL = extension (m)
Unit
  • Unit pascal (Pa), the same as stress, because strain has no unit.
Graph
  • Graph for elastic behaviour stress is proportional to strain, and the gradient of the linear section of a stress–strain graph is E.
Stiffness
  • Stiffness a stiffer material has a larger Young modulus.

Section 4 of 9Young modulus experiment — set-up

Apparatus
  • Apparatus the wire is clamped and passed over a pulley, with a tape marker moving along a ruler to show the extension.
  • This assumes the wire stretches the same amount at all points along its length.
Variables
  • Variables the independent variable is the load, and the dependent variable is the extension.

Section 5 of 9Young modulus experiment — method

1
Measure the original length of the wire with a metre ruler and mark the reference point with tape.
2
Measure the diameter with a micrometer screw gauge or digital callipers.
3
Add the first mass and calculate the weight.
4
Record the total length from the reference point on the ruler.
5
Add more mass and record the new total length.
6
Subtract the original length from each total length to obtain the extension.
7
Plot a graph of force against extension with a line of best fit and find its gradient.
8
Calculate the area A = πd2/4 using the average diameter.
9
Calculate E = gradient × L/A.

Section 6 of 9Improving the experiment

Diameter
  • Diameter measure it in several places along the wire and take an average to reduce uncertainty in the area.
Elastic check
  • Elastic check remove the load after each reading and check that the wire returns to its original length.
Repeats
  • Repeats take several readings with each load and find the average extension.
Extension
  • Extension use a vernier scale to measure the extension and use a longer wire.

Section 7 of 9More from the specification

1Tensile forces and elastic limit
  • Tensile forces and elastic limit applied tensile forces stretch structural materials elastically until stress exceeds the proportional elastic limit.
2Compressive forces and material deformation
  • Compressive forces and material deformation axial compressive forces squeeze cylindrical specimens,
    • reducing axial length while increasing lateral cross-sectional area under load.
3Constant
  • Not changing.
4Compression
  • Decrease in length under a squashing force.
5Spring constant
  • Stiffness k in N/m.
6Compressive force
  • Force that squashes a body and causes compression.
7Natural length
  • Length with no force acting.
8Directly proportional
  • Two quantities increase together in a constant ratio, giving a straight line through the origin.
9F = kx
What the symbols mean: F = force (N) · k = spring constant (N m−1) · x or e = extension (m)
10Force–extension gradient
  • Force–extension gradient it is neither stress nor strain, but with the wire's length and cross-sectional area it gives the Young modulus.

Section 8 of 9Key terms

TermMeaning
StressForce per unit cross-sectional area, σ = F/A.
StrainExtension per unit original length, ε = x/L.
Young modulusRatio of stress to strain, E = σ/ε = FL/(Ax), in Pa.
Ultimate tensile stressMaximum force per original cross-sectional area a wire supports before breaking.
Micrometer screw gaugeInstrument for measuring the diameter of a wire accurately.

Section 9 of 9Exam technique

1
Using the diameter instead of the radius in the area — use A = πd²/4.
2
Giving strain a unit — it is a ratio.
3
Using the extended length for strain — use the original length.
4
Thinking the gradient of a force–extension graph is E — it equals EA/L.
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