Physics 9702 · AS & A Level
Elastic and plastic behaviour
100 practice questions on Elastic and plastic behaviour, with worked solutions and instant marking.
A metal wire is extended by a load. The force-extension graph is shown. What does the area beneath the entire graph represent?
Feb/March 2016
A $120\,\text{kN}$ load is applied to the top of a metal column. This causes the column’s length to decrease by $0.25\,\text{mm}$. The column follows Hooke’s law while it is being compressed. How much energy is stored in the compressed column?
Feb/March 2017
A force-extension graph for a metal wire is shown. At which point on the graph does the metal wire cease to obey Hooke’s law?
Feb/March 2018
A spring has a spring constant of $6.0\,\text{N cm}^{-1}$. It is connected to a second spring with spring constant $4.0\,\text{N cm}^{-1}$. An $80\,\text{N}$ load is hung from the composite spring. What extension does this composite spring produce?
Feb/March 2019
The graph illustrates how the extension of a sample of a type of rubber changes as varying loads $F$ are applied and then slowly withdrawn. What is the best estimate of the strain energy in the rubber when a load of $80\,\text{N}$ is applied?
Feb/March 2019
The graph illustrates the non-linear force-extension relationship for a wire made of a new composite material. What is the most suitable estimate of the work done in stretching the wire to point P?
Feb/March 2020
A wire is pulled by applying successively larger forces $F$. For every force value used, the extension $x$ is measured. Using the collected data, a force-extension graph is drawn. Which statement concerning the area beneath the graph must be true?
Feb/March 2021
A force stretches a spring. Figure 3.1 shows how the force $F$ varies with extension $x$.
Feb/March 2021
An object is pulled until it reaches the elastic limit. Which statement has to describe the stress in the object when it is at the elastic limit?
Feb/March 2022
A spring is attached at one end and stretched by a force $F$ applied to the opposite end. Its extension is $x$ and its elastic potential energy is $E_p$. The spring constant is $k$. The spring follows Hooke’s law. Which relationship is correct for this spring?
Feb/March 2024
A force-extension graph is obtained for a metal wire. What does the limit of proportionality of the wire describe?
Feb/March 2024
A spring has a spring constant of $6.0\,\text{N cm}^{-1}$. It is connected to a second spring with a spring constant of $4.0\,\text{N cm}^{-1}$. An $80\,\text{N}$ load is hung from this composite spring. What is the extension of the composite spring?
Feb/March 2024
A wire is stretched by a tensile force, and its deformation remains elastic. What does elastic deformation mean?
Feb/March 2025
The graph illustrates how the force on a compression spring varies with the change in the spring’s length. A spring of this type is fitted at each corner of a horizontal square plate. Each spring is arranged with its axis vertical. Together, the four springs carry a total load of $160\ \text{N}$. Calculate the total elastic potential energy stored in the four springs.
Feb/March 2025
A force compresses a spring. The graph plots the compressing force $F$ against the spring’s length $L$. What is the spring constant of this spring?
May/June 2010
Which graph shows the force-extension relationship for a rubber band when it is stretched very close to breaking?
May/June 2010
An applied force compresses a spring. The graph gives compressing force $F$ as a function of the spring length $L$. What is the spring constant for this spring?
May/June 2010
Which graph shows the force-extension relationship for a rubber band stretched to nearly its breaking point?
May/June 2010
Which graph shows the force-extension relationship for a rubber band stretched almost to the point where it breaks?
May/June 2010
A force compresses a spring. The graph shows the compressive force $F$ against the spring’s length $L$. What is the spring constant of this spring?
May/June 2010
Opposite ends of a copper rod are pulled in tension, causing the rod to extend. Fig. 5.1 shows how the rod’s strain varies with stress.
May/June 2010
A long, narrow metal wire is hung vertically from a fixed support. Masses are attached to its lower end. The load at the lower end is raised from zero and then lowered again until it returns to zero. The diagram illustrates the force-extension graph obtained. Where on the graph would the elastic limit be located?
May/June 2011
A long, thin metal wire is hung vertically from a fixed support. Masses are attached to its lower end. The load at the lower end is raised from zero and then reduced again to zero. The diagram shows the force-extension graph that is obtained. Where on the graph is the elastic limit located?
May/June 2011
State Hooke’s Law for a spring.
May/June 2011
Heating white sugar granules makes them melt. If this melt is then cooled rapidly, a brittle solid toffee forms. What change happens to the structure of the sugar?
May/June 2012
What does the gradient of a graph showing force on the vertical axis plotted against extension on the horizontal axis represent?
May/June 2012
This graph plots force against extension for a wire as it is stretched. To two significant figures, how much work must be done by the tensile force to produce an extension of $7.0\,\text{mm}$?
May/June 2012
What does the gradient of a graph with force on the vertical axis and extension on the horizontal axis represent?
May/June 2012
If white sugar granules are heated, they melt. If this molten material is then cooled rapidly, it forms a brittle toffee solid. What change occurs in the structure of the sugar?
May/June 2012
One support holds one end of a spring in place, while a mass is hung from the other end. Fig. 3.1 shows the setup.
May/June 2012
The stress-strain graphs for four different materials are displayed below. Which diagram represents the stress-strain graph of a ductile metal?
May/June 2013
Several identical springs, all with the same spring constant, are connected in four different arrangements. A different load is placed on each arrangement. Which arrangement produces the greatest extension?
May/June 2013
A rubber cord is suspended from a fixed support. A weight attached to its lower end is slowly increased from zero, and then slowly decreased back to zero. The force-extension curve for contraction lies below the force-extension curve for stretching. What does the shaded region between the curves represent?
May/June 2013
A spring with an unextended length of $40\,\text{mm}$ is hung from a fixed point. A load of $16\,\text{N}$ is then placed on the spring’s free end. As a result, the spring stretches until its final length becomes five times its original length. The spring follows Hooke’s Law. What is the energy stored in the spring due to this extension?
May/June 2013
Which graph shows the force-extension relationship for a rubber band when it is stretched to nearly the point of breaking?
May/June 2013
A spring is extended across a range for which elastic deformation takes place. Its spring constant is $3.0\,\text{N cm}^{-1}$. Which row gives the correct extension and strain energy for the stated applied force?
May/June 2013
The graph shown is a load-extension graph for a wire that is being elastically deformed. What amount of work is done on the wire in order to increase the extension from $10\,\text{mm}$ to $20\,\text{mm}$?
May/June 2014
A metal sample is pulled by a force that rises to a peak value and then falls again to zero. The force-extension graph for the sample is shown below. As the sample shortens, it retraces the same force-extension curve that it followed while being stretched. What happens to the metal between X and Y?
May/June 2014
A ball falls onto a horizontal surface and rebounds elastically. What occurs to the ball’s kinetic energy over the very brief interval while it is touching the surface?
May/June 2014
Each of the following cylindrical specimens — steel, glass and rubber — is acted on by a tensile force $F$ that is increased steadily. The extensions $e$ are recorded, and the graphs are drawn as shown below. Which row gives the correct matching between the graphs and the materials?
May/June 2014
A spring is suspended vertically from point $P$, as illustrated in Fig. 4.1. A mass $M$ is fixed to the lower end of the spring. The metre rule reading $x$ is recorded, as shown in Fig. 4.1. Figure 4.2 displays how $x$ varies with $M$.
May/June 2014
Three descriptions of different material types are given below. $1$ a polycrystalline material containing large numbers of tiny crystals $2$ an amorphous material with very little, or no, ordered molecular arrangement $3$ a polymeric material made from long chains of molecules Which row correctly pairs the descriptions with nylon, copper and glass?
May/June 2015
The graph illustrates how the extension of a spring changes as the applied force varies. If no force acts on the spring, its length is $1.0\,\text{cm}$. What increase occurs in the strain energy stored in the spring when its length rises from $2.0\,\text{cm}$ to $3.0\,\text{cm}$?
May/June 2015
A long, thin metal wire is hung vertically from a fixed support. Masses are attached to its lower end. The load at the lower end is raised from zero and then reduced again to zero. The diagram shows the force-extension graph obtained. At what point on the graph would the elastic limit be located?
May/June 2015
The graph illustrates the non-linear force-extension curve for a wire formed from a new composite material. What might be the strain energy stored in the wire when it is extended elastically to point $P$?
May/June 2015
As shown in Fig. 4.1, the spring is held horizontally by connection to points A and B. Point A is attached to a movable slider, while point B is attached to a fixed support. A cart of mass $1.7\,\text{kg}$ moves towards the slider with horizontal velocity $v$. The cart then collides with the slider. As the cart is brought to rest, the spring becomes compressed. Fig. 4.2 shows how the compression $x$ of the spring varies with the force $F$ applied to the spring. Fig. 4.2 gives the spring compression for $F = 1.5\,\text{N}$ to $F = 4.5\,\text{N}$. The cart is at rest when $F = 4.5\,\text{N}$.
May/June 2015
Several identical springs are connected in four different arrangements. Which arrangement has the same spring constant as one spring?
May/June 2016
A sample of material is pulled by a tensile force until it has moved past its elastic limit. The tensile force is then reduced to zero. The graph of force against extension is shown. Which area shows the net work done on the sample?
May/June 2016
A metal wire has one end secured to a fixed point, while a load is suspended from the opposite end so that the wire hangs straight down. The load is then raised from zero to $20\,\text{N}$. As a result, the wire undergoes an elastic extension of $5.0\,\text{mm}$. Next, the load is lowered to $12\,\text{N}$, and the extension falls to $3.0\,\text{mm}$. How much strain energy is released as the wire is unloaded?
May/June 2016
The graph illustrates the force-extension relationship for a sample of material. The sample is stretched and then goes back to its starting length. Which area shows the work done in stretching the sample?
May/June 2016
What does elastic potential energy mean?
May/June 2016
A cable in a suspension bridge carries a load of $19.3 \times 10^5\,\text{N}$. Under this load, the cable extends by $47\,\text{mm}$. When a lorry then travels across the bridge, the force on the cable rises to $23.3 \times 10^5\,\text{N}$. The force-extension graph for the cable is shown. What is the increase in strain energy in the cable when the lorry is crossing the bridge?
May/June 2017
A rubber band is pulled out and then allowed to return to its original length. The diagram gives the force-extension graph for this sequence. When the force is increased, the graph goes along OPQ to extension $e$. When the force is decreased, the graph goes along QRO to come back to zero extension. The area marked $X$ lies between the curves OPQ and QRO. The area marked $Y$ is enclosed by the curve QRO and the horizontal axis. Which statement about the process is correct?
May/June 2017
Two springs $X$ and $Y$ undergo elastic extension. The graphs illustrate how the force $F$ applied to each spring changes with extension $x$. Which of the following statements is correct?
May/June 2017
The diagram illustrates the force-extension graph for a steel wire, right up to the point at which it breaks. What is the best estimate of the work done in breaking the wire?
May/June 2017
The spring is fixed so that it hangs down vertically, as shown in Fig. 4.1. Various masses are then hung from the bottom end of the spring. For each mass $M$, the extension $x$ of the spring is measured. The way $M$ changes with $x$ is plotted in Fig. 4.2.
May/June 2017
The graph plots how the length of a spring changes as the load applied to it increases. What is the spring constant of the spring?
May/June 2018
The graph illustrates how a spring’s extension changes with the force applied to stretch it. What is the strain energy stored in the spring when the extension is $4.0\,\text{cm}$?
May/June 2018
A spring with an initial length of $100\ \text{mm}$ is being shortened by a force. The graph illustrates how the compressive force $F$ changes with the spring length $L$. How much energy is stored in the spring when the length is $70\ \text{mm}$?
May/June 2019
A force stretches wire X and gives it elastic potential energy $E$. The same force is then applied to wire Y, which is made of the same material and has the same starting length as wire X, but its diameter is twice that of wire X. Both wires follow Hooke’s law. What is the increase in elastic potential energy of wire Y?
May/June 2019
The stress-strain graphs for loading and unloading four different materials are displayed. Which material shows purely elastic behaviour?
May/June 2019
One end of a wire is fastened to a fixed point. At the opposite end, a tensile force $F$ is applied, making the wire extend. The graph labels this stage as line OSP. The force $F$ is then reduced gradually to zero, after which the wire contracts. The graph labels this stage as line PQ. Which area on the graph represents the work done by the wire during contraction?
May/June 2019
The vibration frequency $f$ of a mass $m$ held by a spring of spring constant $k$ is described by $f = C m^p k^q$ where $C$ is a constant with no units. State the values of $p$ and $q$?
May/June 2020
A tensile force is applied to stretch a sample of a material, then the force is taken away. The graph shows how the applied stress changes with strain. Which point on the graph could be the elastic limit for the material?
May/June 2020
A tensile force is applied to a rubber band that has not yet been stretched, so that it extends. The tensile force is then taken away. Which statement about the rubber band must be true?
May/June 2020
One end of a spring is fastened to a fixed point. A mass is then suspended from the spring’s other end. When the system is in equilibrium, the spring has an extension $x$. The graph shows how the tension in the spring varies with its extension. Which of the following statements is correct?
May/June 2020
Which statement explains the meaning of plastic deformation of a material?
May/June 2020
When a rabbit jumps, the Achilles tendon in its leg is extended. The graph shows how the tendon’s length changes with tension. Calculate the strain energy in the tendon when the tension is $400\,\text{N}$?
May/June 2020
The spring constants of four springs are obtained by plotting the graphs below of force $F$ against extension $x$. Which sequence of graphs shows the spring constants in decreasing order?
May/June 2021
A rod is stretched by forces acting at its two ends, causing it to lengthen. The graph shows how the rod’s extension $e$ varies with force $F$. Point P marks the elastic limit. Which shaded region shows the work done during the plastic deformation of the rod?
May/June 2021
A spring starts off with no compression and no extension. A force may be applied to it so that it becomes shorter by compression or longer by extension. What is the change in the elastic potential energy stored in the spring when it is extended and when it is compressed?
May/June 2021
Give one example of plastic deformation.
May/June 2021
Which of the following statements about elastic and plastic deformation has to be correct?
May/June 2022
A wire is under a tensile force that is stretching it. Which statement about the elastic limit has to be true?
May/June 2022
The extension of a copper wire is recorded for several different forces acting on the wire. A graph is drawn to illustrate how the force on the wire changes with extension. The greatest force is applied at point P. Which statement must be true?
May/June 2022
One end of a spring hangs from a fixed support, and a vertical force is applied to the opposite end, as shown in Fig. 4.1. Fig. 4.2 shows how the applied force $F$ varies with the spring length $L$.
May/June 2022
A force-extension graph for a spring is displayed. Which quantity corresponds to the work done when the spring is extended?
May/June 2023
What does the term spring constant of a spring mean?
May/June 2023
A child is holding a slim metal wire that is fastened to a kite. The graph illustrates how the wire’s extension changes as its tension changes. A gust of wind raises the tension from $100\,\text{N}$ to $150\,\text{N}$. What is the increase in the elastic potential energy of the wire caused by the gust of wind?
May/June 2023
The graph indicates how the spring’s length changes with the force exerted on it. The spring has unstretched length $L_0$. If a force $F$ is applied, the spring then has length $L_1$. What is the work done in extending the spring to length $L_1$?
May/June 2023
One end of a spring hangs from a fixed point. A vertical force is then applied to the opposite end, causing the spring to stretch. Figure 4.1 shows how the applied force $F$ varies with the spring length $L$.
May/June 2023
A force of $0.80\,\text{N}$ stretches a spring to a length of $90\,\text{mm}$. The same spring has a length of $115\,\text{mm}$ when a force of $1.30\,\text{N}$ is applied. The spring obeys Hooke’s law. Determine the spring constant of the spring.
May/June 2024
A sample of metal is put under a force that rises to a maximum value and then falls again to zero. The force-extension graph for the sample is shown. As the sample shortens, it follows the same force-extension curve as when it was being stretched. What is the behaviour of the metal between X and Y?
May/June 2024
A graph showing extension against force for a spring is shown. What is the spring constant of the spring?
May/June 2024
A specimen of material is pulled with a tensile force until it has been taken past its elastic limit. The tensile force is then brought down to zero. The force-extension graph is displayed. Which area shows the net work done on the specimen?
May/June 2024
A wire is secured at one end and a force $F_1$ is applied at the other end so that the wire stretches. In this situation, the wire stores $0.15\,\text{J}$ of elastic potential energy. The applied force is then replaced by a force $F_2$. The wire then stores $0.60\,\text{J}$ of elastic potential energy. The wire obeys Hooke’s law. What is the relationship between $F_1$ and $F_2$?
May/June 2024
A student carries out an investigation on a spring. The graph shows how the length of the spring changes with the force acting on the spring. What is the spring constant of the spring?
May/June 2025
The graph illustrates how the extension of a wire changes as the force varies. The force is increased little by little to a peak at Q and then reduced gradually back to zero at R. Which of the following statements is correct?
May/June 2025
Springs X and Y undergo elastic extension. The graphs illustrate how the applied force $F$ varies with extension $x$ for each spring. Which statement is correct?
May/June 2025
A force-extension graph for a metal wire is shown. What quantity does the area beneath the graph represent?
May/June 2025
A wire with length $L$ is stretched so that its limit of proportionality can be found. The graph illustrates how the extension $x$ changes as the force $F$ applied to the wire changes. On the graph, point $P$ marks the limit of proportionality. The test is then carried out again using a different wire of length $2L$, made from the same material and having the same diameter as the first wire. Which point on the graph indicates the limit of proportionality for the new wire?
May/June 2025
A spring with an unextended length of $0.10\,\text{m}$ hangs in a vertical position from a support. When a weight of $2.0\,\text{N}$ is hung from the lower end of the spring, its length becomes $0.15\,\text{m}$. A further weight of $4.0\,\text{N}$ is then attached to the spring’s lower end. The spring follows Hooke’s law. What extra elastic potential energy is stored in the spring as a result of adding the $4.0\,\text{N}$ weight?
May/June 2025
The graph indicates the relationship between force and extension for a particular spring. What is the energy stored in the spring when the extension is $30\,\text{mm}$?
Oct/Nov 2010
Which set of materials includes two polymers?
Oct/Nov 2010
To measure the mass of food in a pan, a balance is needed that is very sensitive for small masses but less sensitive for large masses. To achieve this, two springs are employed, each with a different spring constant $k$. One spring has a small spring constant, while the other has a large spring constant. Which spring arrangement would be appropriate?
Oct/Nov 2010
The graph illustrates the way force varies with extension for a particular spring. How much energy is stored in the spring when the extension is $30\,\text{mm}$?
Oct/Nov 2010
A metal wire has spring constant $k$. Forces are applied to the ends of the wire so that it extends while remaining within Hooke’s law. Show that, for an extension $x$, the strain energy $E$ stored in the wire is $E = \frac{1}{2}kx^2$.
Oct/Nov 2010
Briefly describe the structural features of crystalline solids, polymers and amorphous materials.
Oct/Nov 2010
A rubber band is stretched and then allowed to return to its original length. The diagram displays the force-extension graph for this process. As the force rises, the curve traces the route OPQ to extension $e$. As the force falls, the curve follows QRO to go back to zero extension. The region marked X lies between the curves OPQ and QRO. The region marked Y is enclosed by the curve QRO and the horizontal axis. Which statement about the process is correct?
Oct/Nov 2011
When explaining how a spring behaves, the spring constant is used. Different loads are applied to stretch the spring by varying amounts. To determine the spring constant, which quantities are needed?
Oct/Nov 2011