Time: 2 hours 30 minutes. Care should be taken to give an appropriate number of significant figures in the final answers to calculations.

Transcription

1 C7/SQP367 Physics Advanced Higher (Revised) Specimen Question Paper for use in and after 013 Time: hours 30 minutes NATIONAL QUALIFICATIONS Reference may be made to the Physics Data Booklet. Answer all questions. Any necessary data may be found in the Data Sheet on Page two. Care should be taken to give an appropriate number of significant figures in the final answers to calculations. Square-ruled paper (if used) should be placed inside the front cover of the answer book for return to the Scottish Qualifications Authority. [C7/SQP367] 1

2 DATA SHEET COMMON PHYSICAL QUANTITIES Quantity Symbol Value Quantity Symbol Value Gravitational acceleration on Earth Radius of Earth Mass of Earth Mass of Moon Radius of Moon Mean Radius of Moon Orbit Universal constant of gravitation Hubble s constant Speed of light in vacuum Speed of sound in air Mass of electron g R E M E M M R M G Ho c v m e 9 8 m s m kg kg m m m 3 kg 1 s 3 x s m s m s kg Charge on electron Mass of neutron Mass of proton Mass of alpha particle Charge on alpha particle Planck s constant Permittivity of free space Permeability of free space Solar radius Mass of Sun 1 A.U. Stefan-Boltzmann constant e m n m p m α h e 0 m 0 σ C kg kg kg C J s F m 1 4p 10 7 H m m kg m W m K 4 REFRACTIVE INDICES The refractive indices refer to sodium light of wavelength 589 nm and to substances at a temperature of 73 K. Diamond Glass Ice Perspex Substance Refractive index Substance Refractive index SPECTRAL LINES Glycerol Water Air Magnesium Fluoride Element Wavelength/nm Colour Element Wavelength/nm Colour Hydrogen Sodium Red Blue-green Blue-violet Violet Ultraviolet Ultraviolet Yellow PROPERTIES OF SELECTED MATERIALS Cadmium Lasers Red Green Blue Element Wavelength/nm Colour Carbon dioxide } Infrared Helium-neon 633 Red Substance Density/ kg m 3 Melting Point/ K Boiling Point/K Specific Heat Capacity/ J kg 1 K 1 Specific Latent Heat of Fusion/ J kg 1 Specific Latent Heat of Vaporisation/ J kg 1 Aluminium Copper Glass Ice Glycerol Methanol Sea Water Water Air Hydrogen Nitrogen Oxygen The gas densities refer to a temperature of 73 K and a pressure of Pa. Page two [C7/SQP367]

3 1. A compact disc (CD) stores information on its surface. The information is retrieved by an optical reader, which moves outwoards as the CD rotates as shown in Figure 1. Marks optical reader Figure 1 The part of the CD below the reader must have a constant tangential speed of 1 30 m s 1. (a) The reader starts at a radius of 3 0 mm from the centre of the CD. Calculate the angular velocity of the CD at the start. (b) Explain why the angular velocity of the CD must decrease as the CD plays from start to finish. 1 (c) The CD has an angular displacement of radians when playing from start to finish. The angular velocity when the reader reaches the outside edge is 4 rad s 1. (i) Show that the CD makes a total of revolutions. (ii) Calculate the average angular acceleration of the CD as the disc is played from start to finish. (iii) Calculate the total playing time for the CD. (d) When the reader is at the outside edge of the CD it is switched off and the CD comes to rest in a time of 80 seconds. Calculate the angular acceleration of the CD. 1 (10) [C7/SQP367] 3 Page three

4 . A space station is constructed in the shape of a doughring (hollow toroid) as shown in Figure. The astronauts living quarters are in the outer ring. Marks axis of rotation radial arm outer ring central hub Figure The radius of the space station is 15 0 m. The central hub is connected to the ring by radial arms. The structure has a uniform angular velocity of rad s 1 about an axis through its hub and perpendicular to the plane of the space station. (a) (i) Show that, an astronaut on the outer rim of the living quarters experiences a centripetal acceleration with a value close to that of the gravitational acceleration on Earth. (ii) Calculate the force on an astronaut of mass 80 0 kg at the outer rim. (iii) The rotation provides an artificial gravity. Explain why this is the case. (b) The empty space station has a mass of kg. Most of the mass is located at the outer rim of the station. (i) Calculate the moment of inertia of the empty space station. (ii) The space station houses ten astronauts, each of average mass 80 0 kg. The astronauts are all at the outer rim of the station. Calculate the total angular momentum of the inhabited space station. (iii) The astronauts now move to the central hub. State what effect this has on the space station. Justify your answer. (1) [C7/SQP367] 4 Page four

5 3. An article in a newspaper describing the launch of a space rocket states: Marks The shuttle blasts off, then comes the tremendous pressure of three G s and the sudden release into weightlessness as the ship leaves the gravitational field behind. Use your knowledge of physics to comment on this statement. (3) 4. Einstein s theory of special relativity is appropriate for inertial frames of reference and his theory of general relativity is appropriate for non-inertial frames of reference. (a) State what is meant by inertial and non-inertial frames of reference. (b) An astronaut on a rocket ship suspends a 3 0 kg mass from a newton balance. The reading on the balance is 9 4 N. The astronaut concludes that the rocket ship is at rest on the Earth s surface. By referring to the Equivalence Principle, what other explanation could there be for the reading on the balance? (c) The rocket ship travels away from Earth and scientists on Earth construct a wordline for the rocket ship s motion, which is shown in Figure 4. Time/s C D B A Space/km Figure 4 Describe the motion of the rocket ship between: (i) A and B; (ii) B and C; (iii) C and D. 3 (7) [C7/SQP367] 5 Page five

6 5. Information about two stars is given in the table. Marks Star A Star B Radius (m) Surface temperature (K) Distance from Earth (ly) 0 0 (a) Which star, if any, appears brighter in the Earth s night sky? Justify your answer. (b) Star A could collapse to form a black hole. Calculate the Schwarzschild radius of this black hole assuming the density of Star A is kg m (6) 6. A report in a newspaper of nd September 011 claimed: The science world has been left in shock after it was announced that CERN scientists had recorded subatomic particles travelling faster than the speed of light in a finding that could overturn a fundamental law of physics. Using your knowledge of physics comment on the implications of this discovery. (3) [C7/SQP367] 6 Page six

7 7. (a) The speed of an electron is measured to be m s 1. (i) Calculate the momentum of the electron. (ii) Calculate the de Broglie wavelength of the electron. (b) The uncertainty in the speed of the electron is ± %. Calculate the uncertainty in determining the position of the electron. Marks 4 (c) Electrons are fired one at a time towards a crystal which behaves like a double slit, as shown in Figure 7. double slit (crystal) screen single electron source Figure 7 Classical physics predicts that each electron will go through one or the other slit. In practice, an interference pattern is observed on the screen. It can be concluded that each electron goes through both slits simultaneously. State what would be observed on the screen if an attempt was made to observe an electron going through either slit. Justify your answer. (10) [C7/SQP367] 7 Page seven

8 8. A motorised mixer in a DIY store is used to mix different coloured paints. Paints are placed in a tin and the tin is clamped to the base as shown in Figure 8A. Marks Figure 8A The oscillation of the tin in the vertical plane closely approximates to simple harmonic motion. (a) State what is meant by simple harmonic motion. 1 [C7/SQP367] 8 Page eight

9 8. (continued) Marks (b) The amplitude of the oscillation is 0 01 m. The mass of the tin of paint is 1 4 kg. Figure 8B shows the graph of the acceleration against displacement for the tin of paint. Acceleration/ms Displacement/m Figure 8B (i) Show that the angular frequency ω of the oscillation is 54 rad s 1. (ii) Write an expression for the displacement y of the tin as a function of time. Include appropriate numerical values. (iii) Derive an expression for the velocity v of the tin as a function of time. Numerical values should again be included. (iv) Calculate the maximum kinetic energy of the tin as it oscillates. (v) Sketch a graph of the potential energy of the oscillating tin against displacement from the tin s central position. Maximum and minimum numerical values are required on both axes. 1 (10) [C7/SQP367] 9 Page nine

10 9. A student sets up a Young s double slit experiment, as shown in Figure 9, to measure the wavelength of laser light. Marks 6 mm double slit screen Laser Figure 9 The student obtains the following results. Separation of 11 fringes Distance to screen from slits Separation of slits (6 ± ) mm (1 94 ± 0 01) m (0 38 ± 0 0) mm (a) Which principle does this experiment illustrate, interference by division of wavefront or by division of amplitude? (b) Calculate the wavelength of the laser light. (c) Calculate the absolute uncertainty in this wavelength. (d) Using the same equipment, suggest an improvement to the experiment that would reduce the uncertainty in the calculated value of the wavelength. You must justify your answer. 1 3 (e) The experiment is now set up under water using the same laser and double slit. The distance to the screen from the slits is kept the same as before at 1 94 m (i) Calculate the wavelength of the laser light in water. (ii) Calculate the separation of 11 fringes as they appear on the screen under water. (1) [C7/SQP367] 10 Page ten

11 10. (a) Figure 10A shows two opposite charges Q 1 and Q separated by a distance of 10 mm. Marks +1 0 nc 10 mm 40 nc Q 1 Figure 10A Q Draw a diagram to show the electric field pattern between these two charges. (b) A third particle, Q 3, of charge 1 0 nc is placed a distance of 50 0 mm to the right of Q as shown in Figure 10B nc 40 nc 1 0 nc 10 mm 50 0 mm Q 1 Q Q 3 Figure 10B Calculate the magnitude and direction of the resultant force acting on Q 3. (c) Charges Q 1 and Q are fixed and particle Q 3 is free to move. Describe the motion of Q (6) [C7/SQP367] 11 Page eleven

12 11. A series CR circuit is set up as shown in Figure 11A. The 0 V d.c. supply has negligible internal resistance. The potential difference across the capacitor is monitored using a data logger. Marks 0 0 V S C 4 7 kω Data logger Initially the capacitor is uncharged. Figure 11A Switch S is closed and the graph shown in Figure 11B is displayed on the data logger V/V t/s Figure 11B (a) Determine the time constant for this circuit. (b) Calculate the capacitance of the capacitor. (4) [C7/SQP367] 1 Page twelve

13 1. A student carrying out research for an investigation, reads that in a series circuit the combined effect of a resistance R and an inductive reactance X L is called the impedance Z. The student reads that Z = R + X L and I is the current in the circuit. Z = V Is where V s is the supply voltage and In the investigation a circuit is setup containing a 50 Ω resistor and an inductor of inductance 0 10 H as shown in Figure 1. Marks Oscilloscope 1 50 Ω variable frequency a.c. supply 0 1 H Oscilloscope Figure 1 The time base on each oscilloscope is switched on to produce a waveform. (a) Explain how the peak current in the circuit can be determined using Oscilloscope 1. (b) The output p.d. of the a.c. supply is kept constant while the frequency is gradually increased. Describe what will be observed on each oscilloscope as the frequency changes. (c) The frequency of the supply is set to 50 Hz. Calculate the impedance Z of the circuit. (d) Using Oscilloscope 1, the student determines that the r.m.s. current in the circuit is 00 ma. Calculate the supply voltage. 3 3 (10) [C7/SQP367] 13 Page thirteen

14 13. A student carried out an experiment to determine g by using a simple pendulum. Details of the experiment are given in the write up below. Marks Aim: Theory: To determine a value for g using a simple pendulum. The equation for the period, T, of a simple pendulum is given by T l = π. g Diagram: Method 1 The apparatus was set up as shown in the diagram. A long, thin piece of thread was attached to a ball bearing and this was placed in a cork with a split down the side so that the length could easily be adjusted. The length of the thread was measured from the pivot point to the top of the ball bearing. This value was measured at the start and end of each run to make sure that the string hadn t stretched. 3 The pendulum was pulled back to the edge of the bench (so that the pendulum would swing from 35 º to the vertical) and the ballbearing was released. 4 Simultaneously the clock was started and timed until the ball bearing had made three complete swings. 5 The time for 3 swings was recorded. 6 This was repeated seven times and then the length of the string was altered. 7 The length of the string was altered by pulling the thread down through the cork attached to the clamp. 8 The experiment was carried out for values between 0 5 m and 00 m 9 The value of g was calculated from the results. (a) State three things that the student could have done to improve the experimental procedure. 3 [C7/SQP367] 14 Page fourteen

15 13. (continued) Marks (b) The student recorded the results in the following table which includes a final column showing calculations for the value of the acceleration due to gravity. length of thread Time for three swings (s) average 3T (av) Random uncertainity in 3T Period (T) Period (T ) g (m) (1) () (3) (4) (5) (6) (7) (s) (s) (s) (s ) (m s ) mean value of g = (i) Comment on the number of significant figures included in the final column. (ii) The student s supervisor suggested that, in addition to omitting scale reading and calibration uncertainties, it is not good practice to determine a final value of g by finding a mean of the calculated values of g in the right hand column. 1 A Explain why this is not good practice. 1 B Explain how the given equation can be used to determine g graphically. [END OF SPECIMEN QUESTION PAPER] (7) [C7/SQP367] 15 Page fifteen

16 [C7/SQP367] 16

17 C7/SQP367 Physics Advanced Higher (Revised) Specimen Marking Instructions NATIONAL QUALIFICATIONS [C7/SQP367] 17

18 Question Expected Answer/s Max Mark Additional Guidance 1 (a) ω = v/r ω = 1 30/ ω = 56 5 rad s 1 1 mark (b) To maintain a constant tangential velocity the angular velocity must reduce as the radius increases. 1 (c) (i) number of rotations = θ/π number of rotations = /π number of rotations = (ii) ω = ω 0 + αθ 4 = α α = rad s 1 mark (iii) ω = ω 0 + αt 4 = ( ) t t = 4460 s 1 mark (d) ω = ω 0 + αt 0 = 4 + α 80 α = 8 00 rad s (accept 8) 1 mark [C7/SQP367] 18 Page two

19 Question Expected Answer/s Max Mark Additional Guidance (a) (i) a = r ω = 15 (0 810) = 9 84 m s 1 mark (ii) F = ma or use F = mrω = = 787 N 1 mark (iii) Explanation with reference to central force. Reference to force provided by outer rim walls. 1 mark 1 mark (no reference to reaction force) (b) (i) I station = mr = (15 0) = kg m 1 mark (iii) Angular momentum = (I station + I astronauts ) ω = ( ) = kg m s 1 1 mark (iii) L is conserved. I decreases. Hence ω increases 1 mark or by calculation [C7/SQP367] 19 Page three

20 Question Expected Answer/s Max Mark Additional Guidance 3 Open ended question 0 marks The student has demonstrated no understanding of the physics involved. There is no evidence that the student recognised the area of physics involved or has given any statement of a relevant principle. This mark would also be given when a student merely restates the physics given in the question. 1 mark The student has demonstrated a limited understanding of the physics involved and has made some statement(s) which is/are relevant to the situation, showing at least a little of the physics within the problem is understood. marks The student has demonstrated a reasonable understanding of the physics involved and has made some statement(s) which is/are relevant to the situation, showing that the physics within the problem is understood. 3 marks The maximum available mark would be awarded to a student who has demonstrated a good understanding of the physics involved. The student has demonstrated a good comprehension of the physics of the situation and has provided a logically correct answer to the question posed. This type of response might include a statement of the principles involved, a relationship or an equation, and the appropriate application of these to the problem. This does not mean the answer has to be what might be termed excellent or complete. [C7/SQP367] 0 Page four

21 Question Expected Answer/s Max Mark Additional Guidance 4 (a) An inertial frame of reference is one that has a constant velocity (1 mark). A non-inertial frame of reference is one that is accelerating. ( 1 mark) (b) It s impossible to tell the difference between the effects of gravity and acceleration (1 mark). The rocket ship could be accelerating at 9 8 m s (1 mark). which would give the same result. (Could also be a combination of field and acceleration.) (i) A to B constant velocity. 1 (ii) B to C acceleration. 1 (iii) C to D constant velocity (½) but greater than that between A and B. (½) 1 [C7/SQP367] 1 Page five

22 Question Expected Answer/s Max Mark Additional Guidance 5 (a) Star A has surface temperature of star B so star A is 4 or 16 more luminous. 1 mark Star B has 4 radius of star A so star B is 4 or 16 more luminous than star A. Both stars are the same distance from the Earth. Both stars will have same brightness. OR (by calculation) using P = σt 4 and L = P 4pr (or combining L = σt 4 4pr 1 mark star A: L A = σt 4 4πr = (7000) ( 10 9 ) = (W m ) star B: L B = σt 4 4πr = (3500) ( ) = (W m ) same luminosity same distance from Earth same brightness from Earth 3 (b) (mass of star A ) m= ρ V = ρ 4/3πr 3 = / ( ) 3 = (kg) GM r = c = / ( ) = m (1 mark) 3 [C7/SQP367] Page six

23 Question Expected Answer/s Max Mark Additional Guidance 6 Open ended question 0 marks The student has demonstrated no understanding of the physics involved. There is no evidence that the student recognised the area of physics involved or has given any statement of a relevant principle. This mark would also be given when a student merely restates the physics given in the question. 1 mark The student has demonstrated a limited understanding of the physics involved and has made some statement(s) which is/are relevant to the situation, showing at least a little of the physics within the problem is understood. marks The student has demonstrated a reasonable understanding of the physics involved and has made some statement(s) which is/are relevant to the situation, showing that the physics within the problem is understood. 3 marks The maximum available mark would be awarded to a student who has demonstrated a good understanding of the physics involved. The student has demonstrated a good comprehension of the physics of the situation and has provided a logically correct answer to the question posed. This type of response might include a statement of the principles involved, a relationship or an equation, and the appropriate application of these to the problem. This does not mean the answer has to be what might be termed excellent or complete. [C7/SQP367] 3 Page seven

24 Question Expected Answer/s Max Mark Additional Guidance 7 (a) (i) p = mv = = kg m s 1 1 mark (ii) λ =h/p = / = m 1 mark (b) Percentage uncertainty in speed is the percentage uncertainty in momentum (treating mass of electron as an exact number) 1 mark Absolute uncertainty in momentum is = kg m s 1 1 mark x p h x π 31 x π 34 x = m 1 mark 4 (c) Interference pattern will collapse or single spot where electron hits or two spots where electrons from each slit hit screen 1 mark Electrons cannot simultaneously be observed as particles and waves. 1 mark or As soon as electron is observed, it behaves like a particle (probability function collapses not required) or similar. [C7/SQP367] 4 Page eight

25 Question Expected Answer/s Max Mark Additional Guidance 8 (a) Force ( acceleration) is proportional to displacement and/but in opposite direction 1 (b) (i) a = ω y (ii) 35 = ω 0 01 or 35 = ω ( 0 010) (ω = 54 rad s 1 ) y = 0 01 sin 54t or y = 0 01 cos 54t 1 mark (sin or cos) (A) (ω) (iii) dy d( 0 01sin 54t) v = or dt dt v = (+) 0 65 cos 54t OR v = 0 65 sin 54t 1s (iv) E k = ½ m ω (A y ) OR = ½ = 0 9 J 1 mark E k = ½ m ω = ½ = 0 30 J 1 mark 4 (v) Potential energy/j 0 9 / 0 30 shape labels/units min/max disp Displacement/m min/max E [C7/SQP367] 5 Page nine

26 Question Expected Answer/s Max Mark 9 (a) Division of wavefront 1 Additional Guidance (b) λ = d x/d x = /10 = m λ = ( )/1 94 λ = m (accept 509 nm or 510 nm) 1 mark (c) % uncert in fringe separation = ( 100)/6 = 7 7% (d) % uncert in distance to screen = ( )/1 94 = 0 5% % uncert in slit separation = ( )/0 38 = 5 3% Overall % uncert = ( ) = 9 4% (+0 5 not strictly necessary) Absolute uncert in λ = 9 4% of m = m 1 mark 3 Increase the distance to the screen which would result in greater fringe separation (1 mark) allowing a smaller uncertainty in this quantity (1 mark). (no justification = 0 marks) (e) n = λ air /λ water n water = 1 33 from data sheet = λ water λ water = m 1 mark (f) 7 λd 38 x = = = d x = = m 3 m 1 mark 1 mark [C7/SQP367] 6 Page ten

27 Question Expected Answer/s 10 (a) Field lines from one charge to other skewed/non-symmetrical 1 mark Max Mark Additional Guidance +1 nc Q 1 4 nc Q Fields lines to show direction from positive to negative () (b) F QQ 1 = 4πε0r Force on Q 3 from Q = π = N (to left) Force on Q 3 from Q 9 9 = π = N (to right) Resultant force = N to right 1 mark 3 (c) Q 3 has a decreasing acceleration to the right 1 mark 1 [C7/SQP367] 7 Page eleven

28 Question Expected Answer/s Max Mark Additional Guidance 11 (a) Time constant is time for V i = 0 63 V supply = = 1 6 (V) From graph, time = 0 10 s Allow suitable tolerance. 1 mark (b) t = RC 0 1 = C C = F 1 mark [C7/SQP367] 8 Page twelve

29 Question Expected Answer/s Max Mark Additional Guidance 1 (a) Measure amplitude of trace Read off y gain to determine V Use I = V/R 1 mark (b) Spacing between peaks on both oscilloscopes will decrease as frequency is increased. 1 mark Height of trace on Oscilloscope will increase as f is increased. 1 mark Height of trace on Oscilloscope 1 will decrease as f is increased. 1 mark 3 (c) X L = π fl = π = 31 4 Ω 1 mark Z = R + X L = = 59 Ω 1 mark 3 (d) V = Z I V = V = 1 V 1 mark accept 11 8 V [C7/SQP367] 9 Page thirteen

30 Question Expected Answer/s Max Mark Additional Guidance 13 (a) 1 mark for each of the following: Measure length of string to centre of ball Reduce angle of swing Record for more than 3 times 3 (b) (i) Number of significant figures should be three 1 (ii) A Finding the mean gives equal emphasis to all the values of g. B Plot graph of T against l. 1 mark Find gradient of line Gradient is π/g [END OF SPECIMEN MARKING INSTRUCTIONS] [C7/SQP367] 30 Page fourteen