CAPE Physics Unit 1 · 2007 · Paper 2

55 questions and parts from this paper. Open one to see it in full, then practise it on Quelpr and get it marked against the mark scheme.

1. 1(a)1 markTo find the diameter of the bearings the student lined up 10 identical balls in a row and placed a ruler against them as shown in Figure 1.
2. 1(a)(i)1 markThe positions on the scale were estimated to be: P 1.0 ± 0.2 cm, Q 20.2 ± 0.2 cm. Write down the value for the distance L using the same format.
3. 1(a)(ii)1 markWhat value does this imply for the diameter D of one of the spheres?
4. 1(b)3 marksThe only balance available to the student was a 0 - 500 g instrument whose smallest division is 5 g. Using this balance the student obtained a mass of 30.4 ± 0.3 g for one of the ball bearings. Suggest how the mass of…
5. 1(c)5 marksFind the density of the metal used to make the ball bearings, giving your answer to a suitable number of significant figures together with the error (uncertainty) in the value. (Volume of a sphere = (1/6)πD³)
6. 21 markWhen you blow across the top of a soft-drink bottle as shown in Figure 2, a tone is heard. The pitch of the sound depends on how much drink is left in the bottle. This phenomenon is called cavity resonance. Scientists…
7. 2(a)5 marksComplete Table 1 and then plot a graph of f against 1/√V using the grid opposite. There is no need to start the graph at the origin.
8. 2(b)2 marksFind the gradient of the graph.
9. 2(c)3 marksUse your answer to (b) to determine the velocity of sound in the bottle.
10. 31 markThe data shown in Table 2 was collected by hanging weights (F) on a metal wire and measuring the extension (x) caused. The wire was originally 2.00 m long and had a cross-sectional area of 2.00 x 10⁻⁷ m².
11. 3(a)4 marksPlot a graph of the weight, F, against the extension, x, on the graph grid opposite.
12. 3(b)2 marksBy estimating the area under the graph, find the work done in stretching the wire by 4.0 mm.
13. 3(c)(i)1 markAt what load does the wire cease to obey Hooke's law?
14. 3(c)(ii)3 marksUse the graph to determine the value of Young's Modulus for this metal.
15. 4(a)(i)4 marksDistinguish between scalar and vector quantities and give ONE example of EACH.
16. 4(a)(ii)6 marksThree forces are acting at a point O as shown in Figure 3. Find their resultant and clearly indicate the direction of this resultant force with respect to the positive x-axis.
17. 4(b)(i)4 marksAn extended object (e.g. a uniform wooden plank) is acted upon by several forces. State TWO conditions for the object to remain in equilibrium. Using these two conditions, write TWO equations relating the forces and…
18. 4(b)(ii)6 marksFigure 5 depicts a uniform plank, weight 200 N, leaning against a smooth wall. The foot of the plank is 3 m from the wall and the top of the ladder is 6 m from the ground. Find a) The upward push, R, of the ground on…
19. 5(a)(i)3 marksA body of mass m is accelerated from rest to a speed v by the application of a constant force. Derive the equation E_k = (1/2)mv² for the kinetic energy of the body.
20. 5(a)(ii)1 markA satellite is launched from the ground and placed in an orbit with a height of 900 km. Why does the equation ΔE_p = mgh NOT apply to this situation?
21. 5(a)(iii)5 marksThe car on a roller coaster (Figure 6) is travelling at 12 m s⁻¹ at the top of a hill but a short time later when it reaches the bottom of the hill, 35 m below, it is travelling much faster. Assuming frictional losses…
22. 5(b)(i)1 markWhat was the gain in potential energy of the load?
23. 5(b)(ii)2 marksFind the power output of the winch motor.
24. 5(b)(iii)3 marksThe winch has an efficiency of 70%. How much electrical power is required by the winch's motor?
25. 5(c)(i)1 markSketch graphs to show the variation with time of the drum's displacement and velocity.
26. 5(c)(ii)1 markFind the time taken by the drum to reach the ground.
27. 6(a)(i)2 marksExplain how such a wave may be formed from two progressive waves, CLEARLY indicating any conditions that MUST be fulfilled.
28. 6(a)(ii)3 marksCompare the amplitudes of particle vibrations at A, B and C and the phases at B and C.
29. 6(a)(iii)3 marksGive the THREE subjective sensations of sound and state what objective quantities are associated with them.
30. 6(b)(i)3 marksCalculate the wavelength of the waves emitted by the loudspeaker.
31. 6(b)(ii)3 marksWhat is the intensity level at 20 m?
32. 6(b)(iii)6 marksGiven that the intensity (in W m⁻²) of the sound is inversely proportional to the distance, x, from the speaker (I ∝ 1/x²), find the distance at which the intensity level will be at the pain threshold of 120 dB.…
33. 7(a)(i)1 markDefine the term 'refractive index' of a medium as it applies to light waves.
34. 7(a)(ii)2 marksDraw a diagram showing the refraction of waves moving from one medium to another in which the velocity is slower.
35. 7(a)(iii)3 marksDerive the law of refraction, n₁ sin θ₁ = n₂ sin θ₂, for waves moving from one medium to another.
36. 7(a)(iv)2 marksState the relationship between the frequencies of the waves in the two media and the relationship between wavelengths in the two media.
37. 7(b)(i)6 marksWhat is the speed of EACH of these colours of light in the glass?
38. 7(b)(ii)6 marksA mixture of red and blue light is incident on the prism as shown in Figure 8. What is the angle between the two emergent rays?
39. 7(c)6 marksA larger dispersion of the two colours of light may be produced by using a diffraction grating. What is the angle between rays of the two colours if a grating with 1200 lines per millimetre is used? The wavelength of…
40. 8(a)(i)2 marksState ONE situation in which a constant volume gas thermometer would be used in preference to other types of thermometers. Give a reason for your choice.
41. 8(a)(ii)4 marksState, with a reason, the type of thermometer you would use to a) locate the hottest part of a Bunsen burner flame b) record the mean temperature of the gases emerging from the exhaust pipe of a car.
42. 8(a)(iii)2 marksState TWO ways in which the behaviour of a thermistor differs from that of a platinum coil when used as a resistance thermometer.
43. 8(b)(i)12 marksCalculate the values of R₀ and B.
44. 8(b)(ii)12 marksDetermine the temperature, in degrees Celsius, when the thermistor resistance is 2200 Ω.
45. 8(b)(iii)a)12 marksIf an empirical temperature scale were used, what temperature would this resistance of 2200 Ω give?
46. 8(b)(iii)b)12 marksExplain why this scale is NOT suitable for determining the value of the temperature from resistance.
47. 9(a)(i)a)3 marksUse the kinetic theory of gases to explain how the molecules inside a gas cylinder containing oxygen are able to exert a pressure.
48. 9(a)(i)b)1 markUse the kinetic theory of gases to explain why pumping in more oxygen increases the pressure inside it.
49. 9(a)(i)c)2 marksUse the kinetic theory of gases to explain why the pressure would increase if the cylinder were left in the sun for a long time.
50. 9(a)(ii)4 marksA cylinder contains 2.8 mol of oxygen at room temperature, 27°C, and the pressure inside the cylinder is 4.5 x 10⁵ Pa. The temperature rises to 47 °C when another 3.9 mol of oxygen is pumped into the cylinder. Find the…
51. 9(b)(i)2 marksWrite an equation representing the first law of thermodynamics and state CLEARLY the meaning of EACH term.
52. 9(b)(ii)3 marksHow much thermal energy would be required to raise the temperature of 6.2 mol of a gas from 25°C to 50°C while the volume remained constant if C_v = 12.5 J K⁻¹ mol⁻¹?
53. 9(b)(iii)1 markBy HOW MUCH would the internal energy of the gas change?
54. 9(b)(iv)2 marksIf instead, the gas were heated at constant pressure from 25°C to 50°C the thermal energy required would be 3200 J. How much work would be done by the gas in this case?
55. 9(b)(v)2 marksDeduce the value of C_p, the molar heat capacity of the gas, at constant pressure.