Cambridge A Level Physics 9702 — 2006 May/June Paper 4 · Variant 1

1 The Earth may be considered to be a uniform sphere with its mass M concentrated at its centre. A satellite of mass m orbits the Earth such that the radius of the circular orbit is r. (a) Show that the linear speed v of the satellite is given by the expression ⎛GM⎞ v = . √ ⎝ r ⎠ [2] (b) For this satellite, write down expressions, in terms of G, M, m and r, for (i) its kinetic energy, kinetic energy = …………………………. [1] (ii) its gravitational potential energy, potential energy = …………………………. [1] (iii) its total energy. total energy = …………………………. [2] Use (c) The total energy of the satellite gradually decreases. State and explain the effect of this decrease on (i) the radius r of the orbit, ................................................................................................................................... ................................................................................................................................... .............................................................................................................................. [2] (ii) the linear speed v of the satellite. ................................................................................................................................... ................................................................................................................................... .............................................................................................................................. [2]

Mark scheme: 1 (a) centripetal force is provided by gravitational force B1 mv2 / r = GMm / r2 B1 hence v = √(GM / r) A0 [2] (b) (i) EK (= ½mv2) = GMm / 2r B1 [1] (ii) EP = - GMm / r B1 [1] (iii) ET = - GMm / r + GMm / 2r C1 = - GMm / 2r. A1 [2] (c) (i) if ET decreases then - GMm / 2r becomes more negative or GMm / 2r becomes larger M1 so r decreases A1 [2] (ii) EK = GMm / 2r and r decreases M1 so (EK and) v increases A1 [2]

More questions on Gravitational potential energy and kinetic energy

2 (a) The equation pV = constant × T relates the pressure p and volume V of a gas to its kelvin (thermodynamic) temperature T. State two conditions for the equation to be valid. 1. ..................................................................................................................................... .......................................................................................................................................... 2. ..................................................................................................................................... ..................................................................................................................................... [2] (b) A gas cylinder contains 4.00 ×104cm3 of hydrogen at a pressure of 2.50 ×107Pa and a temperature of 290 K. The cylinder is to be used to fill balloons. Each balloon, when filled, contains 7.24 ×103cm3 of hydrogen at a pressure of 1.85 ×105Pa and a temperature of 290 K. Calculate, assuming that the hydrogen obeys the equation in (a), (i) the total amount of hydrogen in the cylinder, amount = ……………………….. mol [3] (ii) the number of balloons that can be filled from the cylinder. number = ……………………….. [3]

Mark scheme: 2 (a) e.g. fixed mass/ amount of gas ideal gas (any two, 1 each) B2 [2] (b) (i) n = pV / RT C1 = (2.5 × 107 × 4.00 × 104 x 10-6) / (8.31 × 290) C1 = 415 mol A1 [3] (ii) volume of gas at 1.85 × 105 Pa = (2.5 × 107 × 4.00 × 104) / (1.85 × 105) = 5.41 × 106 cm3 C1 so, 5.41 × 106 = 4.00 × 104 + 7.24 × 103 N C1 N = 741 A1 [3] (answer 740 or fails to allow for gas in cylinder, max 2/3)

More questions on Equation of state

3 The electrical resistance of a thermistor is to be used to measure temperatures in the range 12 °C to 24 °C. Fig. 3.1 shows the variation with temperature, measured in degrees Celsius, of the resistance of the thermistor. 2400 2200 resistance / 2000 1800 1600 1400 12 14 16 18 20 22 24 26 temperature / Fig. 3.1 (a) State and explain the feature of Fig. 3.1 which shows that the thermometer has a sensitivity that varies with temperature. .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [2] (b) At one particular temperature, the resistance of the thermistor is 2040 ± 20 Ω. Determine this temperature, in kelvin, to an appropriate number of decimal places. temperature = ……………………… K [3]

Mark scheme: 3 (a) gradient of graph is (a measure of) the sensitivity M1 the gradient varies with temperature A1 [2] (b) 2040 ± 20 Ω corresponds to 15.0 ± 0.2 °C C1 T / K = T / °C + 273.15 (allow 273.2) C1 temperature is 288.2 K A1 [3]

More questions on Temperature scales

4 A piston moves vertically up and down in a cylinder, as illustrated in Fig. 4.1. cylinder pivot piston pivot P wheel Fig. 4.1 The piston is connected to a wheel by means of a rod that is pivoted at the piston and at the wheel. As the piston moves up and down, the wheel is made to rotate. (a) (i) State the number of oscillations made by the piston during one complete rotation of the wheel. number = ………………………. [1] (ii) The wheel makes 2400 revolutions per minute. Determine the frequency of oscillation of the piston. frequency = ………………………. Hz [1] Use (b) The amplitude of the oscillations of the piston is 42 mm. Assuming that these oscillations are simple harmonic, calculate the maximum values for the piston of (i) the linear speed, speed = …………………………. m s–1 [2] (ii) the acceleration. acceleration = …………………………. m s–2 [2] (c) On Fig. 4.1, mark a position of the pivot P for the piston to have (i) maximum speed (mark this position S), [1] (ii) maximum acceleration (mark this position A). [1]

Mark scheme: 4 (a) (i) 1.0 B1 [1] (ii) 40 Hz B1 [1] (b) (i) speed = 2πfa C1 = 2π × 40 × 42 × 10-3 = 10.6 m s-1 A1 [2] (ii) acceleration = 4π2f2 a C1 = (80π)2 × 42 × 10-3 = 2650 m s-2 A1 [2] (c) (i) S marked correctly (on ‘horizontal line through centre of wheel) B1 (ii) A marked correctly (on ‘vertical line’ through centre of wheel) B1 [2] GCE A/AS Level – May/June 2006 9702 04

More questions on Simple harmonic oscillations

5 An isolated conducting sphere of radius r is placed in air. It is given a charge +Q. This charge may be assumed to act as a point charge situated at the centre of the sphere. (a) (i) Define electric field strength. ................................................................................................................................... .............................................................................................................................. [1] (ii) State a formula for the electric field strength E at the surface of the sphere. Also, state the meaning of any other symbols used. ................................................................................................................................... ................................................................................................................................... .............................................................................................................................. [2] (b) The maximum field strength at the surface of the sphere before electrical breakdown (sparking) occurs is 2.0 ×106 V m–1. The sphere has a radius r of 0.35 m. Calculate the maximum values of (i) the charge that can be stored on the sphere, charge = ………...……………… C [2] (ii) the potential at the surface of the sphere. potential = ………...……………… V [2] Use (c) Suggest the effect of the electric field on a single atom near the sphere’s surface as electrical breakdown of the air occurs. .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [2]

Mark scheme: 5 (a) (i) force per unit positive charge (ratio idea essential) B1 [1] (ii) E = Q / 4πε0r2 M1 ε0 being the permittivity of free space A1 [2] (b) (i) 2.0 × 106 = Q / (4π × 8.85 × 10-12 × 0.352) C1 Q = 2.7 × 10-5 C A1 [2] (ii) V = (2.7 × 10-5) / (4π × 8.85 × 10-12 × 0.35) C1 = 7.0 × 105 V A1 [2] (c) electrons are stripped off the atoms B1 electrons and positive ions move in opposite directions, (giving rise to a current) B1 [2]

More questions on Electric field of a point charge

6 Two long, straight, current-carrying conductors, PQ and XY, are held a constant distance apart, as shown in Fig. 6.1. Q Y I I P X Fig. 6.1 The conductors each carry the same magnitude current in the same direction. A plan view from above the conductors is shown in Fig. 6.2. current out current out of paper of paper Q Y Fig. 6.2 (a) On Fig. 6.2 draw arrows, one in each case, to show the direction of (i) the magnetic field at Q due to the current in wire XY (label this arrow B), [1] (ii) the force at Q as a result of the magnetic field due to the current in wire XY (label this arrow F). [1] Use (b) (i) State Newton’s third law of motion. ................................................................................................................................... ................................................................................................................................... .............................................................................................................................. [1] (ii) Use this law and your answer in (a)(ii) to state the direction of the force on wire XY. ................................................................................................................................... .............................................................................................................................. [1] (c) The magnetic flux density B at a distance d from a long straight wire carrying a current I is given by I B = 2.0 × 10–7 × . d Use this expression to explain why, under normal circumstances, wires carrying alternating current are not seen to vibrate. Make reasonable estimates of the magnitudes of the quantities involved. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [4]

Mark scheme: 6 (a) (i) arrow B in correct direction (down the page) B1 (ii) arrow F in correct direction (towards Y) B1 [2] (b) (i) When two bodies interact, force on one body is equal but opposite in direction to force on the other body. B1 [1] (ii) direction opposite to that in (a)(ii) B1 [1] (c) suggested reasonable values of I and d B1 mention of expression F = BIL B1 force between wires is small M1 compared to weight of wire A1 [4]

More questions on Momentum and Newton’s laws of motion

7 A parallel beam of electrons, all travelling at the same speed, is incident normally on a carbon film. The scattering of the electrons by the film is observed on a fluorescent screen, as illustrated in Fig. 7.1. glass envelope fluorescent screen carbon film beam of electrons vacuum Fig. 7.1 (a) Assuming that the electrons behave as particles, predict what would be seen on the screen. .......................................................................................................................................... ..................................................................................................................................... [1] (b) In this experiment, the electrons do not behave as particles. Describe briefly the pattern that is actually observed on the screen. You may draw a sketch if you wish. .......................................................................................................................................... ..................................................................................................................................... [1] Use (c) The speed of the electrons is gradually increased. State and explain what change, if any, is observed in the pattern on the screen. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [3] QUESTION 8 IS ON THE NEXT PAGE

Mark scheme: 7 (a) ‘uniform’ distribution B1 [1] (b) concentric rings B1 [1] (c) higher speed, more momentum M1 λ = h / p M1 so λ decreases and ring diameter decreases A1 [3]

More questions on Wave-particle duality

8 A proton is moving with constant velocity v. It enters a uniform magnetic field that is normal to the initial direction of motion of the proton, as shown in Fig. 8.1. proton velocity v uniform magnetic field into plane of paper Fig. 8.1 A uniform electric field is applied in the same region as the magnetic field so that the proton passes undeviated through the fields. (a) On Fig. 8.1, draw an arrow labelled E to show the direction of the electric field. [1] (b) The proton is replaced by other particles. The electric and magnetic fields remain unchanged. State and explain the deviation, if any, of the following particles in the region of the fields. (i) an α-particle with initial velocity v ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... .............................................................................................................................. [3] (ii) an electron with initial velocity 2v ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... .............................................................................................................................. [3]

Mark scheme: 8 (a) arrow labelled E pointing down the page B1 [1] (b) (i) Bqv = qE M1 forces are independent of mass and charge ‘cancels’ M1 so no deviation A1 [3] (ii) magnetic force > electric force M1 so deflects M1 ‘downwards’ A1 [3]

More questions on Force on a moving charge