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# Worksheet 08

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• 1. 8 Worksheet (AS)Data needed to answer questions can be found in the Data, formulae and relationships sheet.1 Two springs X and Y have spring constants k and 2k respectively. Spring X is stretched by a force F and spring Y is stretched by a force 2F. Each spring obeys Hooke’s law during the extension. The work done in stretching spring X is WX and the work done in stretching spring Y is WY. What is the relationship between WX and WY? [1] 1 A WY = WX 2 B WY = WX C WY = 2WX D WY = 4WX2 Four wires A, B, C and D have diameters, lengths and are stretched by forces as shown. All the wires are made of the same material. Which wire has the smallest extension? [1] A B C D l d 2d d 2d 2l F 2F F 2F3 The force on a sample of a material is slowly increased and then slowly decreased. The force–extension graph is shown in the diagram. Which area represents the net work done on the sample during the complete process? [1] A P+Q B Q+R C P+Q–R D P+Q+RAS and A Level Physics Original material © Cambridge University Press 2010 1
• 2. 8 Worksheet4 Which statement is true about rubber, a polymeric material? [1] A A normal rubber band breaks when the strain is greater than 1. B A normal rubber band breaks when the strain is less than 10%. C When a small amount of sulfur is added, to provide cross-links between molecules in rubber, the elastic limit is reduced. D When a small amount of sulfur is added, to provide cross-links between molecules in rubber, the ultimate tensile stress is reduced.5 What is equal to the Young modulus? [1] A The area between a force–extension graph and the extension axis. B The area between a stress–strain graph and the stress axis. C The gradient of a force–extension graph. D The gradient of a stress–strain graph.6 Springs and wires obey Hooke’s law. State Hooke’s law. [1]7 A spring has a natural length of 2.5 cm. A force of 4.0 N extends the spring to a length of 6.2 cm. a What is the extension of the spring? [1] b Determine the force (spring) constant k for the spring in N m−1. [3] c Calculate the extension of the spring when a tensile force of 6.0 N is applied. You may assume that the spring has not exceeded its elastic limit. [2]8 The diagram shows the stress–strain graphs for two wires A and B made from different materials. The wires have the same length and cross-sectional area. Explain which of the materials is: a brittle [1] b stiffer [1] c stronger. [1]AS and A Level Physics Original material © Cambridge University Press 2010 2
• 3. 8 Worksheet9 A graph of force F against extension x is shown for a spring. a Use the graph to determine the force (spring) constant k of the spring. [2] b Calculate the energy stored (elastic potential energy) in the spring when its extension is 5.0 cm. [3]10 A length of cable of diameter 1.2 mm is under a tension of 150 N. Calculate the stress in the cable. [3]11 A metal wire of diameter 0.68 mm and natural length 1.5 m is fixed firmly to the ceiling at one end. When a 6.8 kg mass is hung from the free end, the wire extends by 2.8 mm. Calculate: a the stress in the wire [3] b the Young modulus of the material of the wire. [4]12 The diagram shows two springs X and Y connected in series and supporting a weight of 8.0 N. The force constants of the springs are shown on the diagram. a Calculate the extension of each spring. [2] b Determine the force (spring) constant for the combination. [2] c According to a student, the force constant for the springs in series is the sum of the force constants of the individual springs. Is the student correct? [1]AS and A Level Physics Original material © Cambridge University Press 2010 3
• 4. 8 Worksheet13 A 180 g trolley is placed on a frictionless air track. One end of the trolley is attached to a spring of force constant 50 N m−1. The trolley is pushed against a fixed support so that the compression of the spring is 8.0 cm. The trolley is then released. a What is the initial acceleration of the trolley when it is released? [3] b What is the initial energy stored in the spring? [3] c Calculate the final speed of the trolley along the air track. You may assume that there is 100% transfer of energy from the spring to the trolley. [2]14 The force–extension graph for a length of metal wire is shown below. a The gradient of the graph is equal to the force constant k of the wire. Show that the force constant k is given by: EA k= l where E is the Young modulus of the metal, A is the cross-sectional area of the wire and l is the natural length of the wire. [4] b Explain how the gradient of the force–extension graph would change for a wire of the same material but: i twice the length [1] ii twice the radius. [1] Total: Score: % 49AS and A Level Physics Original material © Cambridge University Press 2010 4