AHL 9.1 Energy transformation 17.1.2018 1. [1 mark] A pendulum oscillating near the surface of the Earth swings with a time period T. What is the time period of the same pendulum near the surface of the planet Mercury where the gravitational field strength is 0.4g? A. 0.4T B. 0.6T C. 1.6T D. 2.5T 2. [1 mark] A mass oscillates with simple harmonic motion (SHM) of amplitude x o. Its total energy is 16 J. What is the kinetic energy of the mass when its displacement is? A. 4 J B. 8 J C. 12 J D. 16 J 3. [1 mark] A particle is oscillating with simple harmonic motion (shm) of amplitude x 0 and maximum kinetic energy E k. What is the potential energy of the system when the particle is a distance 0.20x 0 from its maximum displacement? A. 0.20E k B. 0.36E k C. 0.64E k D. 0.80E k 4. [1 mark] 1
A mass is connected to a spring on a frictionless horizontal surface as shown. The spring is extended beyond its equilibrium length and the mass executes simple harmonic motion (SHM). Which of the following is independent of the initial displacement of the spring? A. The angular frequency of the oscillation B. The total energy of the mass C. The average speed of the mass D. The maximum kinetic energy of the mass 5. [1 mark] The period of a particle undergoing simple harmonic motion (SHM) is. The ratio is proportional to A.. B.. C.. D. 6. [1 mark] A particle of mass oscillates with simple harmonic motion (SHM) of angular frequency. The amplitude of the SHM is. What is the kinetic energy of the particle when it is half way between the equilibrium position and one extreme of the motion? A. 2
B. C. D. 7. [1 mark] The bob of a pendulum has an initial displacement 0 to the right. The bob is released and allowed to oscillate. The graph shows how the displacement varies with time. At which point is the velocity of the bob at maximum towards the right? 8. [1 mark] A particle undergoes simple harmonic motion (SHM) of maximum kinetic energy E max and amplitude x 0. The particle is released from rest at its maximum displacement amplitude. What is the change in the kinetic energy when the particle has travelled a distance of? A. B. 3
C. D. 9. [1 mark] A body moves with simple harmonic motion (SHM) with period T and total energy E T. What is the total energy when the period of the motion is changed to 5T and the amplitude of the motion remains constant? A. 0.04 E T B. 0.2 E T C. 5 E T D. 25 E T 10. [1 mark] A small point mass m is placed at the same distance from two identical fixed spherical masses far from any other masses. The point mass is released from rest. The point mass will A. move upwards. B. stay where it is. C. move towards P and stop there. D. oscillate about point P. 4
11. [1 mark] A particle P executes simple harmonic motion (SHM) about its equilibrium position Y. The amplitude of the motion is XY. At which of the positions shown on the diagram is the acceleration of P equal to zero and the kinetic energy of P equal to zero? 12. [1 mark] Which graph shows how velocity v varies with displacement x of a system moving with simple harmonic motion? 5
13. [1 mark] An object undergoes simple harmonic motion. Which graph shows the relationship between the acceleration a and the displacement x from the equilibrium position? 14. [1 mark] An object undergoes simple harmonic motion (SHM). The total energy of the object is proportional to A. the amplitude of the oscillations. B. the time period of the oscillations. C. the frequency of the oscillations. D. the mass of the object. 6
15. [1 mark] A particle is undergoing simple harmonic motion (SHM) in a horizontal plane. The total mechanical energy of the system is E. Which of the following correctly gives the kinetic energy of the particle at the positions of maximum displacement and equilibrium? 16. [1 mark] The equation for the velocity of an object performing simple harmonic motion is of the following is a correct alternative form of the equation?. Which A. B. C. D. 7
17a. [2 marks] This question is about simple harmonic motion (SHM). The graph shows the variation with time of the acceleration of an object X undergoing simple harmonic motion (SHM). Define simple harmonic motion (SHM). 8
17b. [1 mark] X has a mass of 0.28 kg. Calculate the maximum force acting on X. 17c. [4 marks] Determine the maximum displacement of X. Give your answer to an appropriate number of significant figures. 9
17d. [2 marks] A second object Y oscillates with the same frequency as X but with a phase difference of using the graph opposite, how the acceleration of object Y varies with.. Sketch, 18a. [2 marks] This question is about simple harmonic motion (SHM). An object is placed on a frictionless surface. The object is attached by a spring fixed at one end and oscillates at the end of the spring with simple harmonic motion (SHM). The tension F in the spring is given by F = k x where x is the extension of the spring and k is a constant. Show that. 10
18b. [3 marks] One cycle of the variation of displacement with time is shown for two separate mass spring systems, A and B. (i) Calculate the frequency of the oscillation of A. (ii) The springs used in A and B are identical. Show that the mass in A is equal to the mass in B. 11
18c. [5 marks] The graph shows the variation of the potential energy of A with displacement. On the axes, (i) draw a graph to show the variation of kinetic energy with displacement for the mass in A. Label this A. (ii) sketch a graph to show the variation of kinetic energy with displacement for the mass in B. Label this B. 12
19a. [3 marks] This question is about the oscillation of a mass. A mass of 0.80 kg rests on a frictionless surface and is connected to two identical springs both of which are fixed at their other ends. A force of 0.030 N is required to extend or compress each spring by 1.0 mm. When the mass is at rest in the centre of the arrangement, the springs are not extended. The mass is displaced to the right by 60 mm and released. Determine the acceleration of the mass at the moment of release. 13
19b. [2 marks] Outline why the mass subsequently performs simple harmonic motion (SHM). 19c. [2 marks] Calculate the period of oscillation of the mass. 14
19d. [2 marks] The motion of an ion in a crystal lattice can be modelled using the mass spring arrangement. The interatomic forces may be modelled as forces due to springs as in the arrangement shown. The frequency of vibration of a particular ion is and the mass of the ion is. The amplitude of vibration of the ion is. Estimate the maximum kinetic energy of the ion. 19e. [3 marks] On the axes, draw a graph to show the variation with time of the kinetic energy of mass and the elastic potential energy stored in the springs. You should add appropriate values to the axes, showing the variation over one period. 15
19f. [1 mark] Calculate the wavelength of an infrared wave with a frequency equal to that of the model in (b). Printed for Jyvaskylan Lyseon lukio International Baccalaureate Organization 2018 International Baccalaureate - Baccalauréat International - Bachillerato Internacional 16