Stress and strain

The Young modulus of steel is two times that of copper. A $50\,\text{cm}$ length of copper wire with diameter $2.0\,\text{mm}$ is joined onto a $50\,\text{cm}$ length of steel wire with diameter $1.0\,\text{mm}$, forming a combined wire of length $1.0\,\text{m}$, as illustrated. The combined wire is stretched by a weight attached at its end. Both the copper wire and the steel wire obey Hooke’s law. What is the ratio $\frac{\text{extension of steel wire}}{\text{extension of copper wire}}$ ?

Feb/March 2016

Wires X and Y are constructed from different metals. The Young modulus of wire X is twice the Young modulus of wire Y, and the diameter of wire X is half the diameter of wire Y. Both wires undergo the same strain and both obey Hooke’s law. What is the ratio $\dfrac{\text{tension in wire X}}{\text{tension in wire Y}}$?

Feb/March 2017

The diagram depicts a large crane on a construction site raising a cube-shaped load at constant speed. A model of the crane, its load and the cable supporting the load is constructed. The material used for each component of the model is the same as that used for the full-size crane, cable and load. The model is one tenth full-size in every linear dimension. What is the ratio $\dfrac{\text{stress in the cable on the full-size crane}}{\text{stress in the cable on the model crane}}$?

Feb/March 2018

In the deformation of a wire under tension, state what stress means.

Feb/March 2018

A metal wire of length $l$ and cross-sectional area $A$ is secured at one end. When a mass $m$ is attached to the free end, the wire stretches by a distance $e$. What is an expression for the Young modulus $E$ of the metal?

Feb/March 2019

A composite rod is formed by joining a glass-reinforced plastic rod and a nylon rod end to end, as shown. Both rods have the same cross-sectional area, and each rod has a length of $1.00\,\text{m}$. The Young modulus $E_p$ of the plastic is $40\,\text{GPa}$ and the Young modulus $E_n$ of the nylon is $2.0\,\text{GPa}$. The composite rod breaks once its total extension reaches $3.0\,\text{mm}$. What is the maximum tensile stress that can be applied to the composite rod before it breaks?

Feb/March 2020

Which expression gives the stress in a wire?

Feb/March 2021

A metal wire is pulled tight. The wire follows Hooke’s law. Which quantity has a value that remains constant?

Feb/March 2022

Wire X is a thin metal wire with diameter $1.2 \times 10^{-3}\,\text{m}$, and it is used to support a model planet, as illustrated in Fig. 3.1. Fig. 3.2 shows how the stress for wire X changes with strain.

Feb/March 2024

A bolt experiences a tensile force, as illustrated. Its cross-section is circular. At end X, the diameter measures $2d$. At end Y, the diameter measures $d$. What is the value of the ratio $\dfrac{\text{stress at Y}}{\text{stress at X}}$?

Feb/March 2025

In stress–strain tests on metal wires, the stress axis is usually labelled in units of $10^8\,\text{Pa}$, while the strain axis is given as a percentage. This is illustrated for one specific wire in the diagram. Determine the Young modulus for the material of the wire.

May/June 2010

In stress-strain experiments carried out on metal wires, the stress axis is commonly labelled in units of $10^8\,\text{Pa}$, while the strain axis is shown as a percentage. This is illustrated for one specific wire in the diagram. What is the value of the Young modulus for the material of the wire?

May/June 2010

In stress-strain investigations on metal wires, the stress axis is commonly labelled in units of $10^8\,\text{Pa}$, while the strain axis is given as a percentage. The diagram shows this for one particular wire. What is the value of the Young modulus for the material of the wire?

May/June 2010

The Young modulus $E$ can be found from measurements taken when a wire is stretched. Which quantities should be measured in order to determine $E$?

May/June 2011

Stress has SI base units identical to those of

May/June 2011

The way a wire responds when it is stretched can be explained using the Young modulus $E$ of the wire’s material and the force per unit extension $k$ of the wire. For a wire with length $L$ and cross-sectional area $A$, what relationship links $E$ and $k$?

May/June 2011

The diagram illustrates the structure of part of a mattress. The manufacturer wants to produce a softer mattress, meaning one that will compress more under the same load. Which change would not produce the required effect?

May/June 2011

The Young modulus $E$ may be found using measurements taken while a wire is under tension. Which quantities need to be measured in order to determine $E$?

May/June 2011

Define stress for a wire.

May/June 2011

A student determines the Young modulus of a metal wire.

May/June 2011

Which property of a metal wire is determined by its Young modulus?

May/June 2012

In the diagram, a wire with diameter $D$ and length $L$ is held tightly at one end between two blocks of wood. A load is then placed on the wire, making it increase in length by $x$. If the same load is applied to a wire of the same material with diameter $2D$ and length $3L$, what extension would it produce?

May/June 2012

A wire extends by $8\,\text{mm}$ when a load of $60\,\text{N}$ is applied. A second wire, made from the same material, has half the diameter and one quarter of the original length of the first wire, and the same load is applied to it. Assuming that Hooke’s law is obeyed, what is the extension of this wire?

May/June 2012

The diagram depicts a wire with diameter $D$ and length $L$, held securely at one end between two pieces of wood. A load is then placed on the wire, making it lengthen by an amount $x$. When the same load is applied to a wire made of the same material but with diameter $2D$ and length $3L$, by what amount will it lengthen?

May/June 2012

Which characteristic of a metal wire is determined by its Young modulus?

May/June 2012

Define the Young modulus in terms of stress and strain.

May/June 2012

Which unit is used for the Young modulus?

May/June 2013

The diagram depicts a large crane at a construction site raising a cube-shaped load. A scale model is constructed of the crane, the load and the cable that supports the load. Each part of the model is made from the same material as the corresponding part of the full-size crane, cable and load. The model is one tenth full-size in every linear dimension. What is the ratio $\dfrac{\text{stress in the cable on the full-size crane}}{\text{stress in the cable on the model crane}}$?

May/June 2013

The diagram depicts a large construction-site crane raising a cube-shaped load. A scale model is formed of the crane, the load and the cable that holds the load. Each part of the model is made from the same material as the corresponding part in the actual crane, cable and load. In the model, every linear dimension is one tenth of the full-size version. What is the ratio $\frac{\text{extension of the cable on the full-size crane}}{\text{extension of the cable on the model crane}}$?

May/June 2013

Elastic potential energy is stored in a metal wire when it has been stretched elastically.

May/June 2013

Define what stress is.

May/June 2013

Stress-strain graphs for three different materials are shown; they are not plotted to the same scale. These materials are copper, rubber and glass. Which material corresponds to each graph?

May/June 2014

The graph illustrates how the length of a spring changes when a larger load is applied and it is stretched. What is the spring constant?

May/June 2014

A composite rod is produced by joining, end to end, a glass-reinforced plastic rod and a nylon rod, as shown. The rods each have the same cross-sectional area, and every rod is $1.00\,\text{m}$ long. The Young modulus $E_p$ of the plastic is $40\,\text{GPa}$, and the Young modulus $E_n$ of the nylon is $2.0\,\text{GPa}$. The composite rod breaks once its total extension reaches $3.0\,\text{mm}$. What is the maximum tensile stress that can be applied to the composite rod before it breaks?

May/June 2014

For an elastic material with Young modulus $E$, a tensile stress $S$ is applied. Hooke’s Law holds. What expression gives the elastic energy stored per unit volume of the material?

May/June 2014

Define the Young modulus in words.

May/June 2014

The graph below was drawn from an experiment using a metal wire. The shaded region shows the total strain energy stored when the wire is stretched. What labels should be used for the axes?

May/June 2015

To find the Young modulus of a wire, a number of readings are recorded. In which row is it not possible to make the measurement directly using the apparatus given?

May/June 2015

The diagram shows a steel tube whose wall thickness $w$ is tiny compared with the tube’s diameter. A force $T$, acting parallel to the tube’s axis, puts the tube in tension. In order to lower the stress in the tube material, the wall is to be made thicker. If the tube diameter and the tension stay unchanged, which wall thickness gives half the stress?

May/June 2015

A steel rod with a circular cross-section is subjected to tension $T$, as illustrated. The diameter of the wider section is twice the diameter of the narrower section. What is the value of $\dfrac{\text{stress in the wide portion}}{\text{stress in the narrow portion}}$?

May/June 2015

The diagram illustrates the stress-strain graph for bone. What value does the Young modulus of bone have?

May/June 2015

Fig. 4.1 presents the results from an experiment carried out to determine the Young modulus $E$ of a metal wire.

May/June 2015

A lift is held up by two steel cables, each with length $10\,\text{m}$ and diameter $0.5\,\text{cm}$. When a man with mass $80\,\text{kg}$ gets into the lift, the cables lengthen by $1\,\text{mm}$. What is the best estimate for the Young modulus of the steel?

May/June 2016

A spring balance is made from a spring that has an initial length of $20.0\,\text{cm}$ and a hook fixed to it. When a fish with mass $3.0\,\text{kg}$ is hung from the hook, the spring’s length increases to $27.0\,\text{cm}$. What is the spring constant of the spring?

May/June 2016

The stress $\sigma$ required to break a certain solid is described by $\sigma = k \sqrt{\frac{\gamma E}{d}}$, where $E$ represents the Young modulus, $d$ is the separation between atomic planes, and $k$ is a constant with no units. What are the SI base units of $\gamma$?

May/June 2016

A metal wire with cross-sectional area $0.20\,\text{mm}^2$ is suspended vertically from a fixed point. An $84\,\text{N}$ load is then added to its lower end. The wire follows Hooke’s law and its length increases by $0.30\%$. What is the Young modulus of the metal in the wire?

May/June 2016

Define Young modulus in terms of stress and strain.

May/June 2016

A wire with diameter $d$ and length $l$ is suspended vertically from a fixed support. By attaching a mass $M$ to its lower end, the wire is stretched. The Young modulus of the wire is $E$. The acceleration of free fall is $g$. Which equation is used to find the extension $x$ of the wire?

May/June 2017

What units are used for stress, strain and the Young modulus?

May/June 2017

There are two wires that have the same Young modulus $E$ and cross-sectional area $A$, although their lengths $L$ are different, and each wire is acted on by a different tensile force $F$. The extension $e$ of both wires is equal. The table headings list four separate quantities. Which of these quantities have equal values, and which have unequal values, for the two wires?

May/June 2017

Determine the SI base units used for stress. Show your working.

May/June 2017

The Young modulus for the wire’s material can be measured with the apparatus shown in Fig. 3.1. One end of the wire is held at C, and a marker is fixed to the wire above scale S. Masses are added to the other end to apply a stretching force. The reading X from the marker on scale S is measured for a range of forces F acting at the wire’s end. Fig. 3.2 shows the relationship between X and F.

May/June 2017

What unit is used for stress?

May/June 2018

The diagram represents a wire with diameter $D$ and length $L$, fixed securely at one end between two blocks of wood. A load is then hung from the wire, causing it to increase in length by $x$. A second wire is made from the same material, but has diameter $2D$ and length $3L$. Both wires obey Hooke’s law. What is the extension of the second wire when the same load is applied?

May/June 2018

In an experiment, two wires are stretched, one brass and the other steel. During this experiment, both wires obey Hooke’s law. The Young modulus for brass is smaller than the Young modulus for steel. Which graph shows the way stress changes with strain for both wires in this experiment?

May/June 2018

For an elastic material with Young modulus $E$, a tensile stress $S$ is applied. Hooke’s law is obeyed. What is the expression for the elastic energy stored per unit volume of the material?

May/June 2018

The following data relate to a steel wire on an electric guitar. Diameter $= 5.0 \times 10^{-4}\,\text{m}$ Young modulus $= 2.0 \times 10^{11}\,\text{Pa}$ Tension $= 20\,\text{N}$ The wire breaks and then contracts elastically. Assume that Hooke’s law applies to the wire. By what percentage does the length $l$ of a section of the wire shorten?

May/June 2018

In an investigation to find the Young modulus $E$ of the material in a wire, the measurements recorded are shown below. Mass suspended from the wire end: $m = 2.300 \pm 0.002\,\text{kg}$ Initial length of wire: $l = 2.864 \pm 0.005\,\text{m}$ Wire diameter: $d = 0.82 \pm 0.01\,\text{mm}$ Wire extension: $e = 7.6 \pm 0.2\,\text{mm}$ The Young modulus is found from $E = \dfrac{4mgl}{\pi d^2 e}$ where $g$ represents the acceleration of free fall. The obtained value of $E$ is $1.61 \times 10^{10}\,\text{N m}^{-2}$. In what form should the value of $E$ and its uncertainty be written?

May/June 2018

Define the Young modulus of a material.

May/June 2018

A $0.80\ \text{m}$ steel wire and a $1.4\ \text{m}$ brass wire are connected end to end. The joined wires are hung from a fixed support, and a force of $40\ \text{N}$ is exerted on them, as illustrated. The Young modulus of steel is $2.0 \times 10^{11}\ \text{Pa}$. The Young modulus of brass is $1.0 \times 10^{11}\ \text{Pa}$. The cross-sectional area of each wire is $2.4 \times 10^{-6}\ \text{m}^2$. Both wires obey Hooke’s law. Determine the total extension. Neglect the weight of the wires.

May/June 2019

An object of weight $10\,\text{kN}$ is supported equally by four solid steel rods, each with length $2.0\,\text{m}$ and cross-sectional area $250\,\text{mm}^2$. As a result of the object's weight, the rods shorten by $0.10\,\text{mm}$. Assume the rods follow Hooke’s law. What is the Young modulus of steel?

May/June 2019

An elastic cord has an unstretched total length of $16.0\,\text{cm}$ and a cross-sectional area of $2.0 \times 10^{-6}\,\text{m}^2$. It is kept horizontal by two smooth pins that are $8.0\,\text{cm}$ apart. The cord follows Hooke’s law. A load with mass $0.40\,\text{kg}$ is hung at the centre of the cord. The angle between the two sections of cord supporting the load is $60^\circ$. Determine the Young modulus of the cord material.

May/June 2020

A student is examining the mechanical properties of a metal. He loads a long, thin wire with a range of weights up to the point at which it breaks, and records the extension of the wire for every load. He then draws a graph of stress against strain. The student repeats the experiment using a wire made of the same metal, but with twice the initial length and half the diameter. Which graph is obtained?

May/June 2020

The diagram depicts a simplified building model containing four identical heavy floors. The gap from the ground to the bottom floor is twice the separation between neighbouring floors. Between successive floors are equal numbers of vertical steel support rods whose mass is negligible compared with that of the floors. The rods have different diameters so that the stress in every rod is the same. What is the ratio $\dfrac{\text{diameter of bottom rods}}{\text{diameter of top rods}}$?

May/June 2020

One end of the wire is fixed at a point. A force $F$ is applied so that the wire extends by $x$. Figure 5.1 shows how $x$ varies with $F$. The wire’s cross-sectional area is $4.1 \times 10^{-7}\,\text{m}^2$ and it is made from a metal with Young modulus $1.7 \times 10^{11}\,\text{Pa}$. Assume that the cross-sectional area stays constant while the wire is stretched.

May/June 2020

As illustrated, a steel bar with a circular cross-section is being pulled by tension $T$. The diameter of the wider section is twice the diameter of the narrower section. Determine the value of $\frac{\text{stress in the wide portion}}{\text{stress in the narrow portion}}$?

May/June 2021

Two guitar strings are subjected to tensile forces. String X experiences a tensile force $F$, producing an extension $x$. String Y experiences a tensile force $2F$, producing an extension $2x$. The strings follow Hooke’s law. What is the ratio $\frac{\text{strain energy in stretched string X}}{\text{strain energy in stretched string Y}}$?

May/June 2021

Stress $\sigma$ in a material is defined by the equation $\sigma = \dfrac{F}{A}$. Strain $\varepsilon$ in the same material is defined by the equation $\varepsilon = \dfrac{x}{L}$. Which expression gives the Young modulus of the material?

May/June 2021

Wires P and Q are each made from the same metal and are suspended vertically from a steel support beam. Wire Q is half the length of wire P and has twice the diameter of wire P. The same masses are hung from the lower end of each wire. As the masses stretch the wires, both wires obey Hooke’s law. What is the value of $\frac{\text{extension of wire P}}{\text{extension of wire Q}}$?

May/June 2022

A metal wire follows Hooke’s law and has a Young modulus of $2.0 \times 10^{11}\,\text{Pa}$. Its initial length is $1.6\,\text{m}$ and its diameter is $0.48 \times 10^{-3}\,\text{m}$. Determine the spring constant of the wire.

May/June 2022

A steel wire measures $300\,\text{cm}$ in length and has a cross-sectional area of $0.50\,\text{mm}^2$. Its Young modulus is $2.0 \times 10^{11}\,\text{Pa}$. One end of the wire is fastened to a fixed point, and a load of $10\,\text{N}$ is suspended from the other end. The wire follows Hooke’s law. Determine the extension of the wire.

May/June 2022

A lamp hangs in equilibrium from a fixed support, held by three long identical wires. The lamp’s weight makes each wire extend by $0.40\,\text{cm}$. The height $h$ of the lamp above the floor is then measured. The centre wire suddenly snaps, and the lamp drops a short distance while the extensions of the other two wires increase. The wires obey Hooke’s law. When the lamp is again in equilibrium, the height $h$ of the lamp above the floor is measured once more. What is the difference between the two values of $h$?

May/June 2023

A metal wire is $5.2\,\text{m}$ long and has a diameter of $1.0\,\text{mm}$. Its Young modulus is $360\,\text{GPa}$. One end of the wire is held fixed, and a force is exerted on the other end. This force produces an extension of $7.2\,\text{mm}$ in the wire. Assume Hooke’s law applies. What is the force applied to the wire?

May/June 2023

Define the term Young modulus.

May/June 2023

A metal wire is used in an experiment to see how it responds as the tensile force applied to it is varied. The wire has a constant cross-sectional area. Which graph has a gradient equal to the Young modulus of the metal?

May/June 2024

For a wire, Hooke’s law is obeyed for a tension $F$ and extension $x$. The Young modulus for the material of the wire is $E$. Which expression gives the elastic potential energy stored in the wire?

May/June 2024

Two wires, P and Q, are made from the same material and are pulled with a force that increases steadily. A graph is drawn to show how the extension of each wire varies with force. Both wires have the same original length, but their diameters are different. Determine the ratio $\frac{\text{diameter of wire Q}}{\text{diameter of wire P}}$?

May/June 2024

In an experiment, two wires are pulled tight: one is brass and the other is steel. Throughout the experiment, both wires follow Hooke’s law. The Young modulus of brass is lower than the Young modulus of steel. Which graph shows the way stress changes with strain for both wires in this experiment?

May/June 2024

The Young modulus of the material used for a wire is to be determined. The Young modulus $E$ is defined by the equation shown. $E=\dfrac{4FL}{\pi d^2 x}$ A known force is used to extend the wire, and these measurements are taken. Which measurement has the greatest effect on the uncertainty in the calculated value of the Young modulus?

May/June 2024

Define the term strain.

May/June 2024

State what Hooke’s law says.

May/June 2024

A metal wire of uniform cross-section, with length $L$ and diameter $d$, has spring constant $k$. What is the Young modulus of the metal?

May/June 2025

A student has one copper wire and one steel wire that are the same length and have the same cross-sectional area. The student applies identical loads to both wires. The two wires extend by different amounts. The student works out the stress, strain and Young modulus for each wire. Which row shows with a tick (✓) the calculated quantities that are the same for both wires?

May/June 2025

What phrase is used to describe the strain at the elastic limit on a stress-strain graph?

May/June 2025

What units are used for stress, strain and the Young modulus?

May/June 2025

A wire with original length $L_0$ is fixed at one end. A tensile force is then exerted on the other end, causing the wire to stretch to a new length $L_1$. What is the strain of the wire?

May/June 2025

What does the term strain mean?

May/June 2025

State the definition of Young modulus.

May/June 2025

A wire is made from a $3.0\,\text{m}$ section of metal X connected to a $1.0\,\text{m}$ section of metal Y, and its cross-sectional area is constant throughout. When a load is suspended from the wire, metal X increases in length by $1.5\,\text{mm}$ and metal Y increases in length by $1.0\,\text{mm}$. Next, the same load is suspended from a second wire with the same cross-sectional area, but this one contains $1.0\,\text{m}$ of metal X and $3.0\,\text{m}$ of metal Y. What is the overall extension of this second wire?

Oct/Nov 2010

Two wires P and Q are produced from the same material. Wire P starts with a diameter that is twice that of wire Q and a length that is twice that of wire Q. The same force is applied to each wire, so both wires extend elastically. What is the ratio of the extension of P to the extension of Q?

Oct/Nov 2010

A wire is made from a $3.0\,\text{m}$ section of metal X connected to a $1.0\,\text{m}$ section of metal Y. Its cross-sectional area is constant throughout. When a load is attached to this wire, metal X extends by $1.5\,\text{mm}$ and metal Y extends by $1.0\,\text{mm}$. The same load is then attached to a second wire with the same cross-sectional area, but this time it contains $1.0\,\text{m}$ of metal X and $3.0\,\text{m}$ of metal Y. What is the overall extension of the second wire?

Oct/Nov 2010

A uniform wire has length $L$ and a constant cross-sectional area $A$. The material of the wire has Young modulus $E$ and resistivity $\rho$. A tension $F$ in the wire causes its length to increase by $\Delta L$. For this wire, state expressions, in terms of $L$, $A$, $F$, $\Delta L$ and $\rho$ for:

Oct/Nov 2010

The Young modulus of steel is measured with a steel wire of length and is found to be $E$. A second experiment is then done with a wire made from the same steel, but with half the length and half the diameter. What value is obtained for the Young modulus in the second experiment?

Oct/Nov 2011

A metal cube with side $l$ is held in a vice and compressed elastically by two opposing forces $F$. What relationship will $\Delta l$, the amount of compression, have with $l$?

Oct/Nov 2011

The Young modulus for the material of a wire is to be determined. The Young modulus $E$ is given by the equation below. $E = \frac{4Fl}{\pi d^2 x}$ A known force is used to extend the wire, and the measurements below are obtained. Which measurement has the greatest effect on the uncertainty in the value of the Young modulus calculated?

Oct/Nov 2011

The graph illustrates how stress varies with strain for three wires that have identical linear dimensions but are made from different materials. Which of the following statements are correct? 1. For the same stress, the extension of P is approximately twice the extension of Q. 2. The ratio of the Young modulus of P to that of Q is approximately two. 3. When strain is less than $0.1$, R obeys Hooke’s law.

Oct/Nov 2011

A steel wire of a certain length is used to determine the Young modulus of steel, and the result is found to be $E$. A second experiment is then performed with a wire of the same steel, but with half the length and half the diameter. What value is obtained for the Young modulus in this second experiment?

Oct/Nov 2011

A metal cube with side $l$ is held in a vice and undergoes elastic compression due to two opposing forces $F$. What is the relationship between $\Delta l$, the amount of compression, and $l$?

Oct/Nov 2011

The Young modulus of the material in a wire is to be determined. The Young modulus $E$ is given by the equation $E = \frac{4Fl}{\pi d^{2} x}$. A known force is applied to stretch the wire and the following measurements are taken. Which measurement contributes the greatest effect to the uncertainty in the calculated Young modulus?

Oct/Nov 2011

Define power.

Oct/Nov 2011