Elastic and plastic behaviour
6.2What the syllabus asks of you
- understand and use the terms elastic deformation, plastic deformation and elastic limit
- understand that the area under the force–extension graph represents the work done
- determine the elastic potential energy of a material deformed within its limit of proportionality from the area under the force–extension graph
- recall and use EP = ½Fx = ½kx² for a material deformed within its limit of proportionality
Read the notes first
Chapter 6: Elastic and plastic behaviour
Drill this topic
Every question on Elastic and plastic behaviour, untimed, marked as you go.
Make a worksheet
Choose the years and how many questions, then print it with the answers on separate pages.
94 questions
1May / June 2026 · Paper 11 · Q21Show mark scheme →
A0.0096 N m$^{-1}$
B6.0 N m$^{-1}$
C12 N m$^{-1}$
D24 N m$^{-1}$
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2May / June 2026 · Paper 12 · Q19Show mark scheme →
A30 mm
B50 mm
C60 mm
D110 mm
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3May / June 2026 · Paper 12 · Q20Show mark scheme →
Adeformation for which the elastic potential energy is proportional to the extension
Bdeformation for which the extension is proportional to the tensile force
Cdeformation for which the extension remains constant as the tensile force is removed
Ddeformation for which the extension returns to zero when the tensile force is removed
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4May / June 2026 · Paper 12 · Q21Show mark scheme →
Athe elastic limit of the object
Bthe elastic potential energy stored in the object at an extension of P
Cthe spring constant of the object
Dthe Young modulus of the metal at an extension of P
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5May / June 2026 · Paper 13 · Q20Show mark scheme →
A1 : 1
B1 : 2
C1 : 3
D1 : 4
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6May / June 2026 · Paper 13 · Q22Show mark scheme →
AThe deformation is plastic after the elastic limit has been reached.
BThe deformation is plastic until the elastic limit is reached.
CThe extension is proportional to the tensile force after the elastic limit has been reached.
DThe extension is proportional to the tensile force until the elastic limit is reached.
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7May / June 2026 · Paper 14 · Q20Show mark scheme →
A0.02 J
B0.06 J
C0.08 J
D0.12 J
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8May / June 2026 · Paper 14 · Q21Show mark scheme →
Aelastic potential energy / extension
Bextension / force
Cforce / extension
Dextension / elastic potential energy
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9Oct / Nov 2025 · Paper 11 · Q20Show mark scheme →
A0.12 J
B0.24 J
C0.36 J
D0.60 J
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10Oct / Nov 2025 · Paper 11 · Q23Show mark scheme →
AThe rubber band does not return to its original length when the force is decreased to zero.
BThe rubber band obeys Hooke's law for the extensions shown.
CThe rubber band remains elastic for the extensions shown.
DThe shaded area represents the work done in extending the rubber band.
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11Oct / Nov 2025 · Paper 12 · Q23Show mark scheme →
A60 J
B120 J
C600 J
D1200 J
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12Oct / Nov 2025 · Paper 13 · Q20Show mark scheme →
A0.12 J
B0.24 J
C0.36 J
D0.60 J
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13Oct / Nov 2025 · Paper 13 · Q23Show mark scheme →
AThe rubber band does not return to its original length when the force is decreased to zero.
BThe rubber band obeys Hooke's law for the extensions shown.
CThe rubber band remains elastic for the extensions shown.
DThe shaded area represents the work done in extending the rubber band.
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14Oct / Nov 2025 · Paper 14 · Q21Show mark scheme →
Athe work done as the force is applied
Bthe work done as the force is applied minus the work done as the force is removed
Cthe work done as the force is removed
Dthe work done as the force is removed plus the work done as the force is applied
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15Oct / Nov 2025 · Paper 14 · Q22Show mark scheme →
A1/4 F(y – x)
B1/2 F(y – x)
C1/4 k(y – x)^2
Dk(y – x)^2
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16May / June 2025 · Paper 11 · Q22Show mark scheme →
AAlong the line PQ, the wire obeys Hooke’s law.
BAlong the line RP, the spring constant is equal to extension/force.
CThe wire has elastic deformation at point Q.
DThe work done in stretching the wire to P is equal to (force × extension) at point P.
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17May / June 2025 · Paper 12 · Q22Show mark scheme →
AWhen each spring is given the same extension, the energy stored in Y is 4 times the energy stored in X.
BWhen each spring is given the same extension, the energy stored in Y is 8 times the energy stored in X.
CWhen the same force is applied to each spring, the energy stored in Y is 4 times the energy stored in X.
DWhen the same force is applied to each spring, the energy stored in Y is 8 times the energy stored in X.
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18May / June 2025 · Paper 12 · Q23Show mark scheme →
Athe maximum strain below which Hooke's law is obeyed
Bthe maximum strain below which the deformation is plastic
Cthe minimum strain above which Hooke's law is obeyed
Dthe minimum strain above which the deformation is plastic
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19May / June 2025 · Paper 13 · Q21Show mark scheme →
Apower transferred to the wire
Btemperature increase in the wire
Ctime taken for the wire to extend
Dwork done on the wire
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20May / June 2025 · Paper 14 · Q18Show mark scheme →
A0.067 J
B0.13 J
C0.20 J
D0.40 J
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21Feb / March 2025 · Paper 12 · Q19Show mark scheme →
AThe extension of the wire is proportional to the tensile force.
BThe extension of the wire is not proportional to the tensile force.
CWhen the tensile force is removed, the wire does not return to its original length.
DWhen the tensile force is removed, the wire returns to its original length.
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22Feb / March 2025 · Paper 12 · Q21Show mark scheme →
A0.048 J
B0.19 J
C0.38 J
D0.77 J
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23Oct / Nov 2024 · Paper 11 · Q21Show mark scheme →
APoint Q is the elastic limit.
BPoint R is the limit of proportionality.
CThe area under the graph from P to S is the elastic potential energy stored in the wire.
DThe area under the graph from P to S is the work done in stretching the wire.
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24Oct / Nov 2024 · Paper 11 · Q22Show mark scheme →
A8.0 J
B16 J
C40 J
D50 J
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25Oct / Nov 2024 · Paper 12 · Q22Show mark scheme →
Aarea P
Barea Q
Carea P + area Q
Darea Q – area P
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26Oct / Nov 2024 · Paper 13 · Q23Show mark scheme →
Athe elastic potential energy stored in the rubber cord
Bthe thermal energy dissipated in the rubber cord
Cthe work done by the rubber cord during contraction
Dthe work done on the rubber cord during stretching
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27May / June 2024 · Paper 11 · Q23Show mark scheme →
A\frac{1}{2}Ex
BEx
C\frac{1}{2}Fx
DFx
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28May / June 2024 · Paper 12 · Q18Show mark scheme →
Aboth elastic and plastic
Bnot elastic and not plastic
Celastic but not plastic
Dplastic but not elastic
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29May / June 2024 · Paper 13 · Q20Show mark scheme →
AX
BX + Y
CY + Z
DZ
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30May / June 2024 · Paper 13 · Q21Show mark scheme →
AF1 = 2F2
BF1 = 4F2
C2F1 = F2
D4F1 = F2
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31Feb / March 2024 · Paper 12 · Q21Show mark scheme →
AE_P ∝ F
BE_P ∝ x
CE_P ∝ k
DE_P ∝ x²
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32Oct / Nov 2023 · Paper 11 · Q19Show mark scheme →
AGraph A
BGraph B
CGraph C
DGraph D
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33Oct / Nov 2023 · Paper 12 · Q19Show mark scheme →
Alimit of proportionality: X; region of elastic deformation: Y; region of plastic deformation: Z
Blimit of proportionality: Z; region of elastic deformation: Y; region of plastic deformation: X
Climit of proportionality: Y; region of elastic deformation: Z; region of plastic deformation: X
Dlimit of proportionality: Z; region of elastic deformation: X; region of plastic deformation: Y
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34Oct / Nov 2023 · Paper 13 · Q19Show mark scheme →
Aboth elastic and plastic
Belastic only
Cplastic only
Dneither elastic nor plastic
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35May / June 2023 · Paper 11 · Q19Show mark scheme →
Athe area under the graph
Bthe gradient of the graph
Cthe reciprocal of the gradient of the graph
Dtwice the area under the graph
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36May / June 2023 · Paper 12 · Q19Show mark scheme →
A3.8 mJ
B19 mJ
C34 mJ
D38 mJ
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37May / June 2023 · Paper 13 · Q19Show mark scheme →
A1/2 FL₁
B1/2 F(L₁ − L₀)
CFL₁
DF(L₁ − L₀)
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38Feb / March 2023 · Paper 12 · Q19Show mark scheme →
AIt is both elastic and plastic.
BIt is elastic only.
CIt is neither elastic nor plastic.
DIt is plastic only.
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39Oct / Nov 2022 · Paper 11 · Q16Show mark scheme →
AThe spring gains both gravitational potential energy and elastic potential energy.
BThe spring gains gravitational potential energy and loses elastic potential energy.
CThe spring loses both gravitational potential energy and elastic potential energy.
DThe spring loses gravitational potential energy and gains elastic potential energy.
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40Oct / Nov 2022 · Paper 11 · Q20Show mark scheme →
A3.0 cm
B5.0 cm
C6.0 cm
D8.0 cm
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41Oct / Nov 2022 · Paper 12 · Q21Show mark scheme →
Aelastic potential energy / extension
Bextension / force
Cforce / extension
Dextension / elastic potential energy
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42Oct / Nov 2022 · Paper 13 · Q20Show mark scheme →
Aextension ½x, total elastic potential energy ½E_P
Bextension ½x, total elastic potential energy ¼E_P
Cextension x, total elastic potential energy ½E_P
Dextension x, total elastic potential energy ¼E_P
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43May / June 2022 · Paper 11 · Q20Show mark scheme →
AElastic deformation and plastic deformation are proportional to the applied force.
BElastic deformation and plastic deformation cause no change in volume.
CElastic deformation causes heating of the material but plastic deformation does not.
DElastic deformation is reversible but plastic deformation is not.
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44May / June 2022 · Paper 12 · Q20Show mark scheme →
AThe deformation is plastic after the elastic limit has been reached.
BThe deformation is plastic until the elastic limit is reached.
CThe extension is proportional to the tensile force after the elastic limit has been reached.
DThe extension is proportional to the tensile force until the elastic limit is reached.
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45May / June 2022 · Paper 13 · Q21Show mark scheme →
APoint R is the limit of proportionality.
BThe elastic potential energy of the wire at point S is given by the area under the graph between points T and S.
CThere is no plastic deformation between points Q and P.
DThe wire obeys Hooke's law up to a point between R and Q.
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46Feb / March 2022 · Paper 12 · Q19Show mark scheme →
AIt is the maximum stress for which the object obeys Hooke's law.
BIt is the maximum stress that can be applied to the object before it has elastic deformation.
CIt is the maximum stress that can be applied to the object before it has plastic deformation.
DIt is the maximum stress the object can withstand before it breaks.
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47Oct / Nov 2021 · Paper 11 · Q20Show mark scheme →
A0.060 J
B0.12 J
C0.14 J
D0.24 J
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48Oct / Nov 2021 · Paper 12 · Q22Show mark scheme →
Astrain energy in the wire
Bstrain energy in the wire / cross-sectional area of the wire
Cstrain energy in the wire / original length of the wire
Dstrain energy in the wire / original volume of the wire
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49Oct / Nov 2021 · Paper 13 · Q21Show mark scheme →
AGraph A: elastic region labelled on initial linear part, plastic region labelled on curved part, work done shaded under initial linear region only
BGraph B: plastic region labelled on initial linear part, elastic region labelled on curved part, work done shaded under entire curve
CGraph C: elastic region labelled on initial linear part, plastic region labelled on curved part, work done shaded under entire curve
DGraph D: elastic region labelled on initial linear part, plastic region labelled on curved part, work done shaded under entire curve
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50May / June 2021 · Paper 11 · Q20Show mark scheme →
AGraph A: shaded area under the curve from origin to the extension at the final force
BGraph B: shaded area above the curve from origin to the final force
CGraph C: shaded area above the curve between the extension at P and the final extension
DGraph D: shaded area under the curve between the extension at P and the final extension
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51May / June 2021 · Paper 12 · Q20Show mark scheme →
A4
B2
C$\frac{1}{2}$
D$\frac{1}{4}$
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52May / June 2021 · Paper 13 · Q16Show mark scheme →
Aspring is extended: decreases; spring is compressed: decreases
Bspring is extended: decreases; spring is compressed: increases
Cspring is extended: increases; spring is compressed: decreases
Dspring is extended: increases; spring is compressed: increases
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53May / June 2021 · Paper 13 · Q21Show mark scheme →
AA rubber ball is momentarily compressed every time it hits the ground.
BA spoon stirring some coffee in a ceramic mug hits its surface and makes a clinking sound.
CA toolbox is left on a horizontal plank. When the toolbox is removed, the plank is no longer straight.
DThe spring in some bathroom weighing scales is compressed by a person standing on the scales.
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54Feb / March 2021 · Paper 12 · Q20Show mark scheme →
AIt can be calculated as \frac{1}{2}Fx.
BIt is the elastic potential energy stored in the stretched sample.
CIt is the work done in stretching the sample.
DIt would be the same for any wire of the same material.
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55Oct / Nov 2020 · Paper 11 · Q20Show mark scheme →
Athe elastic energy stored in the rubber cord
Bthe energy that causes plastic deformation
Cthe energy dissipated as heat
Dthe work done to extend the rubber cord
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56Oct / Nov 2020 · Paper 12 · Q21Show mark scheme →
A0.040 J
B0.090 J
C0.16 J
D0.25 J
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57Oct / Nov 2020 · Paper 13 · Q21Show mark scheme →
A17.5 J
B35.0 J
C17.5 kJ
D35.0 kJ
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58May / June 2020 · Paper 11 · Q20Show mark scheme →
A
B
C
D
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59May / June 2020 · Paper 11 · Q21Show mark scheme →
AIf the rubber band stretches elastically and plastically, all the work done by the force is converted to thermal energy in the rubber.
BIf the rubber band stretches elastically, it obeys Hooke's law.
CIf the rubber band stretches elastically, the gradient of the force–extension graph represents the work done by the force.
DIf the rubber band stretches plastically, the rubber band will be longer after the force is removed than it was before the force is applied.
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60May / June 2020 · Paper 12 · Q16Show mark scheme →
AArea SPR represents the energy stored in the spring which cannot be recovered.
BArea SPQR represents the energy stored in the spring which can be recovered.
CArea SPQ represents the loss of gravitational potential energy of the mass due to the extension of the spring.
DArea SQR represents the elastic potential energy stored in the spring.
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61May / June 2020 · Paper 12 · Q20Show mark scheme →
AIt always obeys Hooke's law.
BIt does not return to its original length when the extending force is removed.
CIt never obeys Hooke's law.
DIt returns to its original length when the extending force is removed.
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62May / June 2020 · Paper 13 · Q21Show mark scheme →
A0.40 J
B0.80 J
C2.4 J
D7.4 J
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63Feb / March 2020 · Paper 12 · Q20Show mark scheme →
A0.09 J
B0.10 J
C0.11 J
D0.20 J
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64Oct / Nov 2019 · Paper 11 · Q20Show mark scheme →
AORQ
BOQRS
CORS
DTMRS
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65Oct / Nov 2019 · Paper 12 · Q19Show mark scheme →
Athe elastic potential energy stored in the rubber cord
Bthe thermal energy dissipated in the rubber cord
Cthe work done on the rubber cord during stretching
Dthe work done by the rubber cord during contraction
Mark scheme
66Oct / Nov 2019 · Paper 13 · Q20Show mark scheme →
AThe rubber band does not return to its original length when the force is decreased to zero.
BThe rubber band obeys Hooke’s law for the extensions shown.
CThe rubber band remains elastic for the extensions shown.
DThe shaded area represents the work done in extending the rubber band.
Mark scheme
67May / June 2019 · Paper 11 · Q20Show mark scheme →
A0.090 J
B0.21 J
C0.27 J
D0.63 J
Mark scheme
68May / June 2019 · Paper 12 · Q20Show mark scheme →
A0.25E
B0.5E
C2E
D4E
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69May / June 2019 · Paper 12 · Q22Show mark scheme →
AGraph A
BGraph B
CGraph C
DGraph D
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70May / June 2019 · Paper 13 · Q20Show mark scheme →
AOSTO
BOSPRO
CQPRQ
DOSPQO
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71Feb / March 2019 · Paper 12 · Q21Show mark scheme →
A0.40 J
B0.64 J
C0.88 J
D1.3 J
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72Oct / Nov 2018 · Paper 11 · Q16Show mark scheme →
A0.04 J
B0.08 J
C0.16 J
D0.32 J
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73Oct / Nov 2018 · Paper 11 · Q20Show mark scheme →
AGraph A: shaded area under the curve from origin to L
BGraph B: shaded area above the curve from origin to L
CGraph C: shaded area above the curve from P to L
DGraph D: shaded area under the curve from P to L
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74Oct / Nov 2018 · Paper 12 · Q21Show mark scheme →
AP
BQ
CQ + R
DR
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75Oct / Nov 2018 · Paper 13 · Q20Show mark scheme →
AThe area under the graph from P to R is the strain energy stored in the material.
BThe area under the graph from P to R is the work done in stretching the material.
CThe material stretches elastically from Q to R.
DThe material stretches plastically from P to Q.
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76May / June 2018 · Paper 12 · Q20Show mark scheme →
AE / (2S²)
B2E / S²
CS² / E
DS² / (2E)
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77May / June 2018 · Paper 13 · Q19Show mark scheme →
A60 J
B120 J
C600 J
D1200 J
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78Oct / Nov 2017 · Paper 11 · Q20Show mark scheme →
Aboth elastic and plastic deformation
Belastic deformation only
Cneither elastic nor plastic deformation
Dplastic deformation only
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79Oct / Nov 2017 · Paper 11 · Q21Show mark scheme →
A10 kJ m–3
B100 kJ m–3
C1.0 MJ m–3
D10 MJ m–3
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80Oct / Nov 2017 · Paper 13 · Q20Show mark scheme →
Aboth elastic and plastic
Bnot elastic and not plastic
Cplastic but not elastic
Delastic but not plastic
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81Oct / Nov 2017 · Paper 13 · Q21Show mark scheme →
A16 J
B32 J
C1.0 kJ
D2.0 kJ
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82May / June 2017 · Paper 11 · Q21Show mark scheme →
A0.16 J
B0.32 J
C16 J
D32 J
Mark scheme
83May / June 2017 · Paper 12 · Q19Show mark scheme →
A21 kJ
B23 kJ
C45 kJ
D66 kJ
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84May / June 2017 · Paper 12 · Q21Show mark scheme →
AArea X is the energy which heats the band as it is stretched to extension e.
B(Area X + area Y) is the minimum energy required to stretch the band to extension e.
CArea X is the elastic potential energy stored in the band when it is stretched to extension e.
D(Area Y – area X) is the net work done on the band during the process.
Mark scheme
85May / June 2017 · Paper 13 · Q19Show mark scheme →
AWhen each spring is given the same extension, the energy stored in Y is 4 times the energy stored in X.
BWhen each spring is given the same extension, the energy stored in Y is 8 times the energy stored in X.
CWhen the same force is applied to each spring, the energy stored in Y is 4 times the energy stored in X.
DWhen the same force is applied to each spring, the energy stored in Y is 8 times the energy stored in X.
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86May / June 2017 · Paper 13 · Q20Show mark scheme →
A2.1 J
B2.3 J
C2.4 J
D2.5 J
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87Feb / March 2017 · Paper 12 · Q21Show mark scheme →
A15 J
B30 J
C15 kJ
D30 kJ
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88Oct / Nov 2016 · Paper 11 · Q21Show mark scheme →
AGraph A
BGraph B
CGraph C
DGraph D
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89Oct / Nov 2016 · Paper 12 · Q21Show mark scheme →
Agraph A
Bgraph B
Cgraph C
Dgraph D
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90Oct / Nov 2016 · Paper 13 · Q21Show mark scheme →
AGraph A
BGraph B
CGraph C
DGraph D
Mark scheme
91May / June 2016 · Paper 11 · Q21Show mark scheme →
AX
BX + Y
CY + Z
DZ
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92May / June 2016 · Paper 12 · Q21Show mark scheme →
A0.8 × 10⁻² J
B1.8 × 10⁻² J
C2.4 × 10⁻² J
D3.2 × 10⁻² J
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93May / June 2016 · Paper 13 · Q20Show mark scheme →
AP + Q
BP only
CQ + R
DR only
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94Feb / March 2016 · Paper 12 · Q18Show mark scheme →
Athe change in gravitational potential energy of the wire
Bthe energy that would be released from the wire if the final load was removed
Cthe energy transferred into heat energy in the wire
Dthe work done in stretching the wire
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