A body is displaced from equilibrium. State the two conditions necessary for the body to execute simple harmonic motion

Transcription

1 1. Simple harmonic motion and the greenhouse effect (a) A body is displaced from equilibrium. State the two conditions necessary for the body to execute simple harmonic motion (b) In a simple model of a methane molecule, a hydrogen atom and the carbon atom can be regarded as two masses attached by a spring. A hydrogen atom is much less massive than the carbon atom such that any displacement of the carbon atom may be ignored. The graph below shows the variation with time t of the displacement x from its equilibrium position of a hydrogen atom in a molecule of methane. The mass of hydrogen atom is kg. Use data from the graph above to determine its amplitude of oscillation. to show that the frequency of its oscillation is Hz. IB Questionbank Physics 1

2 (iii) to show that the maximum kinetic energy of the hydrogen atom is J. (c) Assuming that the motion of the hydrogen atom is simple harmonic, its frequency of oscillation f is given by the expression f 1 2 k m p, where k is the force per unit displacement between a hydrogen atom and the carbon atom and m p is the mass of a proton. Show that the value of k is approximately 560 N m 1. Estimate, using your answer to (c), the maximum acceleration of the hydrogen atom. IB Questionbank Physics 2

3 (d) Methane is classified as a greenhouse gas. Describe what is meant by a greenhouse gas. Electromagnetic radiation of frequency Hz is in the infrared region of the electromagnetic spectrum. Suggest, based on the information given in (b), why methane is classified as a greenhouse gas. (Total 14 marks) IB Questionbank Physics 3

4 2. This question is about oscillations and waves. (a) A rectangular piece of wood of length l floats in water with its axis vertical as shown in diagram 1. The length of wood below the surface is d. The wood is pushed vertically downwards a distance A such that a length of wood is still above the water surface as shown in diagram 2. The wood is then released and oscillates vertically. At the instant shown in diagram 3, the wood is moving downwards and the length of wood beneath the surface is d + x. On diagram 3, draw an arrow to show the direction of the acceleration of the wood. The acceleration a of the wood (in m s 2 ) is related to x (in m) by the following equation. a = 14 l x Explain why this equation shows that the wood is executing simple harmonic motion. (iii) The period of oscillation of the wood is 1.4 s. Show that the length l of the wood is IB Questionbank Physics 4

5 0.70 m. (3) (b) The wood in (a), as shown in diagram 2, is released at time t = 0. On the axes below, sketch a graph to show how the velocity v of the wood varies with time over one period of oscillation. (c) The distance A that the wood is initially pushed down is 0.12 m. Calculate the magnitude of the maximum acceleration of the wood. On your sketch graph in (b) label with the letter P one point where the magnitude of the acceleration is a maximum. (d) The oscillations of the wood generate waves in the water of wavelength 0.45 m. The graph shows how the displacement D, of the water surface at a particular distance IB Questionbank Physics 5

6 from the wood varies with time t. Using the graph, calculate the speed of the waves. ratio of the displacement at t = 1.75 s to the displacement at t = 0.35 s. IB Questionbank Physics 6

7 (iii) ratio of the energy of the wave at t = 1.75 s to the energy at t = 0.35 s (Total 15 marks) 3. This question is about a simple pendulum. (a) A pendulum consists of a bob suspended by a light inextensible string from a rigid support. The pendulum bob is moved to one side and then released. The sketch graph shows how the displacement of the pendulum bob undergoing simple harmonic motion varies with time over one time period. On the sketch graph above, label with the letter A a point at which the acceleration of the pendulum bob is a maximum. label with the letter V a point at which the speed of the pendulum bob is a maximum. IB Questionbank Physics 7

8 (b) Explain why the magnitude of the tension in the string at the midpoint of the oscillation is greater than the weight of the pendulum bob (3) (c) The pendulum bob is moved to one side until its centre is 25 mm above its rest position and then released. Show that the speed of the pendulum bob at the midpoint of the oscillation is 0.70 m s 1. IB Questionbank Physics 8

9 The mass of the pendulum bob is kg. The centre of the pendulum bob is 0.80 m below the support. Calculate the magnitude of the tension in the string when the pendulum bob is vertically below the point of suspension. (3) (d) The point of suspension of the pendulum bob is moved from side to side with a small amplitude and at a variable driving frequency f. For each value of the driving frequency a steady constant amplitude A is reached. The oscillations of the pendulum bob are lightly damped. IB Questionbank Physics 9

10 On the axes below, sketch a graph to show the variation of A with f. Explain, with reference to the graph in (d), what is meant by resonance. (e) The pendulum bob is now immersed in water and the variable frequency driving force in (d) is again applied. Suggest the effect this immersion of the pendulum bob will have on the shape of your graph in (d) (Total 16 marks) IB Questionbank Physics 10

11 4. This question is about simple harmonic motion and waves. (a) A particle of mass m that is attached to a light spring is executing simple harmonic motion in a horizontal direction. State the condition relating to the net force acting on the particle that is necessary for it to execute simple harmonic motion (b) The graph shows how the kinetic energy E K of the particle in (a) varies with the displacement x of the particle from equilibrium. Using the axes above, sketch a graph to show how the potential energy of the particle varies with the displacement x. IB Questionbank Physics 11

12 The mass of the particle is 0.30 kg. Use data from the graph to show that the frequency f of oscillation of the particle is 2.0 Hz. (4) (c) The particles of a medium M 1 through which a transverse wave is travelling, oscillate with the same frequency and amplitude as that of the particle in (b). Describe, with reference to the propagation of energy through the medium, what is meant by a transverse wave. The speed of the wave is 0.80 m s 1. Calculate the wavelength of the wave. IB Questionbank Physics 12

13 (d) The diagram shows wavefronts of the waves in (c) incident on a boundary XY between medium M 1 and another medium M 2. The angle between the normal, and the direction of travel of the wavefronts is 30. The speed of the wave in M 1 is 0.80 m s 1. The speed of the waves in M 2 is 1.2 m s 1. Calculate the angle between the direction of travel of the wavefronts in M 2 and the normal. (3) On the diagram, sketch the wavefronts in M 2. (Total 15 marks) IB Questionbank Physics 13

14 5. This question is about simple harmonic motion and waves. An object is vibrating in air. The variation with displacement x of the acceleration a of the object is shown below. IB Questionbank Physics 14

15 (a) State and explain two reasons why the graph opposite indicates that the object is executing simple harmonic motion (4) (b) Use data from the graph to show that the frequency of oscillation is 350 Hz (4) (c) State the amplitude of the vibrations.... (d) The motion of the object gives rise to a longitudinal progressive (travelling) sound wave. State what is meant by a longitudinal progressive wave. IB Questionbank Physics 15

16 The speed of the wave is 330 m s 1. Using the answer in (b), calculate the wavelength of the wave. (Total 13 marks) 6. This question is about simple harmonic motion. (a) In terms of the acceleration, state two conditions necessary for a system to perform simple harmonic motion (b) A tuning fork is sounded and it is assumed that each tip vibrates with simple harmonic motion. The extreme positions of the oscillating tip of one fork are separated by a distance d. State, in terms of d, the amplitude of vibration. IB Questionbank Physics 16

17 On the axes below, sketch a graph to show how the displacement of one tip of the tuning fork varies with time. (iii) On your graph, label the time period T and the amplitude a. (c) The frequency of oscillation of the tips is 440 Hz and the amplitude of oscillation of each tip is 1.2 mm. Determine the maximum linear speed of a tip. acceleration of a tip. (Total 10 marks) IB Questionbank Physics 17