Summer Holiday Assignment 各位同学： 本学期我们学习了 Newton's 2nd law， Work, Energy and Power, Momentum & Impulse, Circular motion。下学期初我们学习的章节是： SL：Thermal physics HL：Rigid body mechanics (rotational motion) 希望大家好好利用假期，做好预习和复习的工作，温故而知新。 为了帮助大家更好的预复习，我们准备了一份暑假作业，请各位同学自行下载打印后完 成，并请于9月1日下午4点半之前将纸质版递交至402办公室自己的高二物理任课老师处。注意 其中1-15题是SL和HL的同学都必须完成的部分，后面的部分是SL或者HL的同学分别必须完成 的部分，请注意区分。这一份作业的递交时间和完成情况将记入下个学期的平时成绩中，所以 请认真对待。 最后祝大家假期快乐！ 物理组全体老师 1 2 4. 5. 6. 7. 3 8. 9. 10. 4 11. 12. 5 13. 14. 6 15. This question is about an electrostatics experiment to investigate how the force between two charges varies with the distance between them.A small charged sphere S hangs vertically from an insulating thread as shown below. A second identically charged sphere P is brought close to S. S is repelled as shown below. P S force F S r The magnitude of the electrostatic force on sphere S is F. The separation between the two spheres is r. (a) On the axes below draw a sketch graph to show how, based on Coulomb’s law, you would expect F to vary with 1 . r2 F 0 0 1 r2 (2) Values of F are determined for different values of r. The variation with 1 of these values is r2 shown below. The estimated uncertainties in these values are negligible. 7 F / 10- 3 N 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 0.0 (b) (i) 2.0 4.0 6.0 8.0 10.0 12.0 1 /10 3 m- 2 r2 Draw the best-fit line for these data points. (2) (ii) Use the graph to explain whether, in the experiment, there are random errors, systematic errors or both. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (3) (iii) Calculate the gradient of the line drawn in (b) (i). ......................................................................................................................... ......................................................................................................................... (2) (iv) The magnitude of the charge on each sphere is the same. Use your answer to (b) (iii) to calculate this magnitude. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (4) (Total 13 marks) 8 Standard Level Only (Preview: Thermal physics) 1. The physics of cooling (a) Explain what is meant by the temperature of a substance. .............................................................................................................................. .............................................................................................................................. (2) A thermometer is placed in a liquid contained in an open beaker. The reading of the thermometer is recorded at regular intervals. The variation with time t of the temperature is shown below. / C 80 70 60 50 40 30 20 10 0 0 (b) 1000 2000 3000 4000 5000 6000 7000 8000 t/s The temperature of the surroundings is 20˚C. On the graph continue the line to show the variation with time of the temperature for the next 3000 s. (2) (c) By reference to the graph, state and explain the rate of loss of thermal energy from the substance between (i) 0 and 600 s; ................................................................................................................... ................................................................................................................... (2) 9 (ii) 600 and 1800 s. ................................................................................................................... ................................................................................................................... ................................................................................................................... ................................................................................................................... ................................................................................................................... (4) The mass of the liquid is 0.11 kg and the specific heat capacity of the liquid is 1300 J kg–1 K–1. (d) (i) Use the graph to deduce that the rate of loss of thermal energy at time t = 600 s is approximately 4 W. ................................................................................................................... ................................................................................................................... ................................................................................................................... ................................................................................................................... (3) (ii) Calculate the specific latent heat of fusion of the liquid. ................................................................................................................... ................................................................................................................... ................................................................................................................... ................................................................................................................... (3) (Total 16 marks) 10 Higher Level Only (Preview: Rigid body mechanics) 1. A horizontal rigid bar of length 2R is pivoted at its centre. The bar is free to rotate in a horizontal plane about a vertical axis through the pivot. A point particle of mass M is attached to one end of the bar and a container is attached to the other end of the bar. 𝑀 A point particle of mass 3 moving with speed v at right angles to the rod collides with the container and gets stuck in the container. The system then starts to rotate about the vertical axis. The mass of the rod and the container can be neglected. (a) (i) Write down an expression, in terms of M, v and R, for the angular momentum of the system about the vertical axis just before the collision. [1 mark] (ii) Just after the collision the system begins to rotate about the vertical axis with angular velocity 4 ω. Show that the angular momentum of the system is equal to 3 𝑀𝑅 2 𝜔. [1 mark] 𝑣 (iii). Hence, show that 𝜔 = 4𝑅. [1 mark] 11 (iv). Determine in terms of M and v the energy lost during the collision. [3 marks] (b) A torque of 0.010 N m brings the system to rest after a number of revolutions. For this case R = 0.50 m, M = 0.70 kg and v = 2.1 m s–1. (i) Show that the angular deceleration of the system is 0.043 rad s–2. (ii) [1 mark] Calculate the number of revolutions made by the system before it comes to rest. [3 marks] 12 2. A cylindrical space probe of mass 8.00 x 102 kg and diameter 12.0 m is at rest in outer space. Rockets at opposite points on the probe are fired so that the probe rotates about its axis. Each rocket produces a force F = 9.60 x 103 N. The moment of inertia of the probe about its axis is 1.44 x 104 kg m2. (a) (i) Deduce the linear acceleration of the centre of mass of the probe. (ii) Calculate the resultant torque about the axis of the probe. [1 mark] [2 marks] (b) The forces act for 2.00 s. Show that the final angular speed of the probe is about 16 rad s–1. [2 marks] 13 (c) The diagram shows a satellite approaching the rotating probe with negligibly small speed. The satellite is not rotating initially, but after linking to the probe they both rotate together. The moment of inertia of the satellite about its axis is 4.80 x 103 kg m2. The axes of the probe and of the satellite are the same. (i) Determine the final angular speed of the probe–satellite system. [2 marks] (ii) Calculate the loss of rotational kinetic energy due to the linking of the probe with the satellite. [3 marks] 14