1 1 Which of the following correctly defines the terms stress, strain and oung modulus? stress strain oung modulus (force) x (area) (extension) x (original length) (stress) / (strain) (force) x (area) (extension) / (original length) (stress) x (strain) (force) / (area) (extension) / (original length) (stress) / (strain) (force) / (area) (extension) x (original length) (stress) x (strain) icity 2 wire is stretched by 8 mm when a of 6 N is applied. What will be the extension of a wire of the same material having four times the cross-sectional area and twice the original length, when the same is applied? 2 mm 4 mm 8 mm 16 mm 3 The tension in a spring of natural length l is first increased from zero to T 1, causing the length to increase to l 1. The tension is then reduced to T 2, causing the length to decrease to l 2 (as shown). tension T 1 R U M T 2 S V N L Q P l l 2 l 1 length Which area of the graph represents the work done by the spring during this reduction in length? MLP MNQP MNSR MPLU 4 What is the ultimate tensile stress of a material? the stress at which the material becomes ductile the stress at which the material breaks the stress at which the material deforms plastically the stress at which the material reaches its elastic limit
5 suspended copper wire is gradually ed until it is stretched just beyond the elastic limit, and it is then gradually uned. Which graph (with arrows indicating the sequence) best illustrates the variation of the tensile stress with longitudinal strain? 2 stress stress stress stress strain strain strain strain 6 beam, the weight of which may be neglected, is supported by three identical springs. When a weight W is hung from the middle of the beam, the extension of each spring is x. x original position of the beam W The middle spring and the weight are removed. What is the extension when a weight of 2W is hung from the middle of the beam? 3x 4x 2 3 2x 3x 7 Nylon breaks when the stress within it reaches 1 x 1 9 Pa. Which range includes the heaviest that could be lifted by a nylon thread of diameter 1 mm? 2N to 2 N 2 N to 2 N 2 N to 2 N 2 N to 2 N
3 8 The graph shown was plotted in an experiment on a metal wire. The shaded area represents the total strain energy stored in stretching the wire. How should the axes be labelled? force extension mass extension strain energy stress strain 9 number of similar springs, each having the same spring constant, are joined in three arrangements, and Z. The same is applied to each. Z What is the order of increasing extension for these arrangements? smallest largest Z Z Z Z
4 1 ylindrical samples of steel, glass and rubber are each subjected to a gradually increasing tensile force. The extensions e are measured and graphs are plotted as shown below. graph e graph e graph Z e Which row correctly relates the graphs to the materials? steel glass rubber Z Z Z Z 11 Two steel wires P and Q have lengths l and 2l respectively, and cross-sectional areas and 2 respectively. oth wires obey Hooke s law. What is the ratio tension in P tension in Q when both wires are stretched to the same extension? 1 1 2 4 4 2 1 1 12 In describing the behaviour of a spring, the spring constant is used. ifferent s are used to extend the spring by different amounts. To find the spring constant, which quantities are required? the elastic limit and the s the elastic limit, extensions and the length of the spring the s and the extensions of the spring the s and the length of the spring
5 13 The force-extension graph of a particular sample of rubber as a is applied and then removed is shown. force extension What does the shaded area represent? the energy transformed into heat during the complete cycle the recoverable elastic potential energy stored at maximum extension the work done on the sample while ing the work done on the sample while uning 14 The graph shows the behaviour of a sample of a metal when it is stretched until it starts to undergo plastic deformation. force / N 55 5 1. 12. extension / mm What is the total work done in stretching the sample from zero extension to 12. mm? Simplify the calculation by treating the region as a straight line. 3.3 J 3.55 J 3.6 J 6.6 J
15 spring of unextended length.5 m is stretched by a force of 2. N to a new length of.9 m. The variation of its length with tension is as shown. 6 2. tension / N.5.9 length / m How much strain energy is stored in the spring?.4 J.8 J.9 J 1.8 J 16 simple crane consists of a rigid vertical pillar supporting a horizontal beam. Z W weight W is lifted by a rope at the end of the beam. What are the forces at points, and Z due to the weight W? force at force at force at Z tension compression tension tension tension compression compression tension compression compression compression compression
7 17 sample of metal is subjected to a force which increases to a maximum value and then decreases back to zero. force-extension graph for the sample is shown. force extension When the sample contracts it follows the same force-extension curve as when it was being stretched. What is the behaviour of the metal between and? both elastic and plastic elastic but not plastic plastic but not elastic not elastic and not plastic 18 spring of original length 1 mm is compressed by a force. The graph shows the variation of the length L of the spring with the compressing force. 12 / N 1 8 6 4 2 4 5 6 7 8 9 1 What is the energy stored in the spring when the length is 7 mm?.9 J.21 J.27 J.63 J L / mm
19 The oung modulus of steel is determined using a length of steel wire and is found to have the value E. nother experiment is carried out using a wire of the same steel, but of twice the length and half the diameter. What value is obtained for the oung modulus in the second experiment? 1 4 E 1 2 E E 2E 8 2 piece of copper is drawn into a continuous wire. What behaviour is the copper exhibiting? brittle only elastic only plastic only both brittle and elastic 21 Two springs P and Q both obey Hooke s law. They have spring constants 2k and k respectively. The springs are stretched, separately, by a force that is gradually increased from zero up to a certain maximum value, the same for each spring. The work done in stretching spring P is W P, and the work done in stretching spring Q is W Q. How is W P related to W Q? W P = W Q W P = W Q W P =2W Q W P =4W Q 22 The graph shows how the extension of a spring varies with the force used to stretch it. extension/cm 4. 2. What is the strain energy stored in the spring when the extension is 4. cm? 6 J 12 J 6 J 12 J 1 2 3 force/kn
9 23 What is the oung modulus of a metal? extension / force force / extension strain / stress stress / strain 24 ductile material is stretched by a tensile force to a point beyond its elastic limit. The tensile force is then reduced to zero. The graph of force against extension is shown below. force Z extension Which area represents the net work done on the sample? + + Z Z 25 The variation of the extension x of a spring with applied force is shown. x Which shaded area represents the work done when the extension is increased from x 1 to x 2? x 1 x 2 x x 1 x 2 x x 1 x 2 x x 1 x 2 x
1 26 The force required to extend a sample of rubber by a distance x is found to vary as shown. / N 4 3 2 1 1 2 3 4 5 x / m The energy stored in the rubber for an extension of 5m is less than 1 J. 1 J. between 1 J and 2 J. more than 2 J. 27 The table shows a applied to four wires and the cross-sectional area of each. Which of the wires is subjected to the greatest stress? / N cross-sectional area / mm 2 15.25 2 1. 3.56 5 2.3 28 What is the unit of the oung modulus? N m 1 N m N m 2 N m 2 29 or a wire, Hooke s law is obeyed for a tension and extension x. The oung modulus for the material of the wire is E. Which expression represents the elastic strain energy stored in the wire? 1 E x E x 1 x x 2 2
11 3 wire stretches 8 mm under a of 6 N. second wire of the same material, with half the diameter and a quarter of the original length of the first wire, is stretched by the same. ssuming that Hooke s law is obeyed, what is the extension of this wire? 1 mm 4 mm 8 mm 16 mm 31 What is represented by the gradient of a graph of force (vertical axis) against extension (horizontal axis)? elastic limit spring constant stress the oung modulus 32 The graph shows how the length of a particular rubber cord varies as force is applied..4 length / m.2 force / N 25 What is the maximum strain energy in this deformed rubber cord? 2.5 J 5. J 7.5 J 1 J 33 Which properties best describe modelling clay? brittle and ductile ductile and elastic elastic and plastic plastic and ductile
12 34 What is plastic deformation? Plastic deformation occurs when strain is not proportional to stress but when the is removed the material returns to its original length. Plastic deformation occurs if, when the is removed, the material contracts but a permanent stretching has occurred. Plastic deformation occurs until the extension is no longer proportional to the. Plastic deformation occurs when the material extends so that strain is directly proportional to stress. 35 number of similar springs, each having the same spring constant, are joined in four arrangements. The same is applied to each. Which arrangement gives the greatest extension? 36 The graphs show how force varies with extension and stress varies with strain for the ing of a metal wire. force stress extension strain The oung modulus for this wire is equal to the gradient of the force-extension graph. the area between the force-extension graph and the extension axis. the gradient of the stress-strain graph. the area between the stress-strain graph and the strain axis.