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C11.1 Density AQA AS Physics P11 Materials Kerboodle Answers: Page No. 185

1.Ans- a its volume, 8.0 x 10-4 m3 b its density. 3.1 x 103 kgm-3 2.ANS- a the mass, 6.3kg b the volume, 2.0x 10-3 m3 c the density of the paint in the tin. 3.1×103 kgm-3 3.Ans- a its volume in rn3, 9.6 x 10-6 m3 b its mass in kg. The density of steel = 7800 kg m-3 7.5 x 10-2 kg 4.Ans- a the mass of i aluminium, 0.29kg ii magnesium in the tube, 0.12kg b the density of the alloy. The density of aluminium = 2700 kg m-3 The density of magnesium = 1700 kg m-3 2.3 x 103 kg m-3

11.2 Springs AQA AS Physics P11 Materials Kerboodle Answers: Page No. 188

1. a the extension of the spring when the tension in it is equal to ION 0.40m b the tension in the spring when it is extended by 0.50m from its unstretched length. 12.5N 2.a the tension in each spring 20N b the extension of each spring 100mm c the spring constant of each spring. 200Nm-1 3.a 40N b for the two springs in series and vertical. 200mm 4.a the spring constant 12.3Nm-1 b the energy stored in the spring 8.8 x 10-2 J c the weight that needs to be added to extend the spring to 600 mm. 2.2 N

11.3 Deformation of solids AQA AS Physics P11 Materials Kerboodle Answers: Page No. 191

1.1.0 x 109 Pa 2. 1.3 x 1011 Pa 3.a the tensile stress in the wire 9.4 x 108 Pa b the extension of the wire. The Young modulus of steel 2.1 x 1011 Pa. 1.1 x 10-2m

11.4 More about stress and strain AQA AS Physics P11 Materials Kerboodle Answers : Page No. 193

1.a the tensile stress in the cable, 3.3 x 106 Pa b the extension of the cable, 2.8 x 10-4 m c the elastic energy stored in the cable, assuming its elastic limit has not been reached. 0.21 J 2. 2.3mm b the elastic energy stored in the wire. 1.7 x 10-2 J 3. a the compressive force exerted on the bar, 470kN b the work done to Compress it. 47J 4. a the work done to stretch the rubber band to an extension of 0.40 m, 10.0J b the internal energy retained by the rubber band when it unstretched. 4.2J Banner 8

Practice questions: Page No. 194-195

1. (a) The density of a material is the mass per unit volume (b) Density of copper 8.9 x 103 kg m-3 Density of zinc 7.1 x 103 kg m-3 (i) Volume of copper = 0.70 × 0.80 × 10-3 = 0.56 × 10-3 m3 Mass of copper = ρCVC = 8.9 × 103 × 0.56 × 10-3 = 5.0 kg Mass of zinc = ρZVZ = 7.1 × 103 × 0.30 × 0.80 × 10-3 = 1.7 kg (ii) Force applied to spring = weight of lorry = mg = 1.2 × 103 × 9.81 = 1.18 × 104 N 3 (a) (i) Material X obeys Hooke’s law until it fractures because stress is proportional to strain over the whole line (ii) is the weaker material Y is the weaker material because its breaking stress is lower than that of X (iii) is ductile material Y is ductile because it exhibits plastic behaviour (iv) has the greater elastic strain energy for a given tensile stress (8 marks) Material Y has the greater strain energy for a given tensile stress because the area under its graph is greater for a given tensile stress (b) (i) cross-sectional area = 0.64 mm2 = 0.64 × 10−6 m2 (ii)Energy stored in cord 4. (a)Graph plotted to include: • At least 9 points plotted correctly • All 12 points plotted correctly • correct graph for increasing loads, linear up to about 80 N and with curved part for higher loads >80 N • Correct linear graph for decreasing loads, with permanent extension for zero load (b).Relevant points include: • Initially the wire obeys Hooke’s law (or behaves elastically) • This continues up to the limit of proportionality • The elastic limit is reached beyond the limit of proportionality • The wire then undergoes plastic deformation • Which produces a permanent extension • Extension varies linearly with load as the load is decreased (c). 5. (i) (ii) (iii) The cross-seasonal area 01 each wire is I .4 x 10*’ and the unstretched length is 1.5 m. Determine the extension produced in either wire. (3 marks) AQA, 2005 Banner 9

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