17 M00/430/H(2) B3. This question is about an oscillating magnet.

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1 17 M00/430/H(2) B3. This question is about an oscillating magnet. The diagram below shows a magnet M suspended vertically from a spring. When the magnet is in equilibrium its mid-point P coincides with the line C on the adjacent scale. The magnet is pulled down such that P is now opposite E. It is then released. A B C D E P M (a) What conditions must be satisfied by the acceleration of the magnet in order for its motion after release to be simple harmonic? Turn over

2 18 M00/430/H(2) (Question B3 continued) (b) On the diagram below the magnet is moving up at the moment the point P is opposite B. Draw and name the forces acting on the magnet, showing both magnitude and direction. [3] A B C D E P motion On the diagram below draw and name the forces acting on the magnet when the magnet is in the same position but moving downwards. Show the magnitude and direction of the forces. A B P C D E motion

3 19 M00/430/H(2) (Question B3 continued) (c) The graph below shows how the displacement of the magnet varies with time for two oscillations. " # $ % displacement / cm & '!&!%!$!#!" time / s Using information from this graph and the fact that the mass of the magnet is 0.30 kg calculate the value of the spring constant. maximum kinetic energy of the magnet. [3] [4] Turn over

4 20 M00/430/H(2) (Question B3 continued) (d) On the two grids below sketch (You do not need to give any values of energies on either graph.) a graph to show how the kinetic energy of the magnet varies with time for one complete oscillation. kinetic energy a graph to show how the elastic potential energy of the spring varies with time for one complete oscillation. [3] potential energy

5 21 M00/430/H(2) (Question B3 continued) (e) The apparatus is now arranged such that the magnet is suspended inside a coil C that is connected to an electrical circuit as shown in the diagram below. The magnet is again set into oscillation by pushing it down such that point P is opposite D and then releasing it. A B C D E M C P On the grid below sketch a graph to show how you would ideally expect the reading on the voltmeter to vary with time for several complete oscillations of the magnet when the switch S is open. (Note that this is only a sketch graph; you do not need to add values to the axes.) V R S [1] (iii) Label on your sketch graph one point corresponding to a time when the magnet is stationary and one point corresponding to a time when it is moving with maximum velocity. State three factors that determine the maximum reading on the voltmeter when the switch S is open. [3] Turn over

6 22 M00/430/H(2) (Question B3 continued) (f) On the grid below sketch a graph to show how the voltmeter reading varies with time when the switch S is closed. (Again note that this is only a sketch graph, you do not need to add values to the axes.) Explain why this sketch graph is different to the graph you have sketched in (e) above. [3]

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9 20 M09/4/PHYSI/HP2/ENG/TZ1/XX+ B3. This question is in two parts. Part 1 is about simple harmonic motion and waves and Part 2 is about gravitational fields and potential. Part 1 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 E K /J x / m Using the axes above, sketch a graph to show how the potential energy of the particle varies with the displacement x

10 21 M09/4/PHYSI/HP2/ENG/TZ1/XX+ (Question B3, Part 1 (b) continued) 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. [1] Turn over

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13 21 N09/4/PHYSI/HP2/ENG/TZ0/XX+ B3. This question is in two parts. Part 1 is about simple harmonic motion. Part 2 is about thermodynamics. Part 1 Simple harmonic motion (a) (b) In terms of the acceleration, state two conditions necessary for a system to perform simple harmonic motion A tuning fork is sounded and it is assumed that each tip vibrates with simple harmonic motion. d 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. [1] On the axes below, sketch a graph to show how the displacement of one tip of the tuning fork varies with time. [1] displacement 0 0 time (iii) On your graph, label the time period T and the amplitude a Turn over

14 22 N09/4/PHYSI/HP2/ENG/TZ0/XX+ (Question B3, part 1 continued) (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. (d) The sketch graph below shows how the velocity of a tip varies with time. velocity 0 0 time On the axes, sketch a graph to show how the acceleration of the tip varies with time

15 23 N09/4/PHYSI/HP2/ENG/TZ0/XX+ (Question B3, part 1 continued) (e) In practice, the motion of the tips of the tuning fork is damped. Describe what is meant by damped motion. Suggest one reason why the motion of the tips is damped. [1] [1] Turn over

16 12 M10/4/PHYSI/HP2/ENG/TZ2/XX+ B2. This question is in two parts. Part 1 is about oscillations and waves. Part 2 is about gases and thermodynamic processes. Part 1 Oscillations and waves (a) A rectangular piece of wood of length l floats in water with its axis vertical as shown in diagram 1. water surface A x l d d d diagram 1 diagram 2 diagram 3 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 x l [1] Explain why this equation shows that the wood is executing simple harmonic motion

17 13 M10/4/PHYSI/HP2/ENG/TZ2/XX+ (Question B2, part 1 continued) (iii) The period of oscillation of the wood is 1.4 s. Show that the length l of the wood is 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. [1] v 0 t (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. [1] Turn over

18 14 M10/4/PHYSI/HP2/ENG/TZ2/XX+ (Question B2, part 1 continued) (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 from the wood varies with time t. D / cm t / s 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. (iii) ratio of the energy of the wave at t 1.75 s to the energy at t 0.35 s [1]