PHYSICS A 2824 Forces, Fields and Energy

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2 Data 2 speed of light in free space, c = m s 1 permeability of free space, 0 = 4π 10 7 H m 1 permittivity of free space, 0 = F m 1 elementary charge, the Planck constant, unified atomic mass constant, rest mass of electron, rest mass of proton, e = C h = J s u = kg m e = kg m p = kg molar gas constant, R = 8.31 JK 1 mol 1 the Avogadro constant, N A = mol 1 gravitational constant, G = N m 2 kg 2 acceleration of free fall, g = 9.81 m s 2

3 Formulae 3 uniformly accelerated motion, s = ut at 2 v 2 = u 2 + 2as refractive inde, n = 1 sin C capacitors in series, capacitors in parallel, capacitor discharge, 1 C = 1 C C 2 + C = C 1 + C 2 + = 0 e t/cr pressure of an ideal gas, p = 1 3 Nm V <c 2 > radioactive decay, = 0 e λt t 1 2 = λ critical density of matter in the Universe, ρ 0 = 3H π G relativity factor, = (1 v 2 c 2 ) current, I = nave nuclear radius, r = r 0 A 1/3 sound intensity level, = 10 lg ( I I 0 ) Turn over

4 4 Answer all the questions. 1 This question is about hitting a tennis ball. (a) A player serves a tennis ball of mass 60 g. Fig. 1.1 shows how the force F on the ball varies with the time t of impact between racket and ball. The ball is momentarily at rest before the impact F / N t / m s Fig. 1.1 (i) How can the momentum given to the ball be found from Fig. 1.1? Eplain your answer.... [2] (ii) Use Fig. 1.1 to show that the momentum gained by the ball is about 2.7 N s. Make your reasoning clear. [1] (iii) Eplain why the unit of momentum can be given either as N s or kg m s [1]

5 (iv) Estimate 5 1 the speed v of the ball as it leaves the racket 2 the maimum acceleration a of the ball. v =... m s 1 [1] a =... m s 2 [2] (b) The opponent manages to place his racket in the path of the ball, now travelling at 40 m s 1, so that it is returned at 38 m s 1 in the opposite direction. The contact time between ball and racket is s. Calculate (i) the change in momentum Δp of the ball Δp =... kg m s 1 [1] (ii) the change in kinetic energy ΔE of the ball ΔE =... J [2] (iii) the mean force eerted by the ball on the racket. mean force =... N [2] [Total: 12] Turn over

6 6 2 A gas, which is to be treated as ideal, is trapped in a cylinder by a piston, which is free to move. See Fig Fig. 2.1 (a) The equation of state of an ideal gas is pv = nrt. State the meaning of each term in the equation.. [2] (b) The gas is heated suddenly from 27 C to 627 C. (i) The pressure before heating is atmospheric pressure, p 0. Show that the pressure immediately after heating is 3p 0. Assume that the piston has not had time to move. [2] (ii) The gas then pushes the piston out until the pressure of the gas returns to atmospheric pressure p 0. The volume V 0 of the gas has increased to 2.5 V 0. Calculate the final temperature of the gas in C. temperature =... C [3]

7 (c) (i) 7 The original volume V 0 of gas trapped in the cylinder is m 3. Atmospheric pressure p 0 is Pa. Show that the amount of gas is about mol. [2] (ii) The molar mass M of the gas is kg mol 1. Calculate the mass m of gas present in the cylinder. m =... kg [1] (iii) Calculate the increase in internal energy ΔU of the gas when it is heated suddenly as in (b)(i) from 27 C to 627 C. Take the specific heat capacity of the gas to be 1300 J kg 1 K 1. ΔU =... J [2] [Total: 12] Turn over

8 8 3 (a) Fig. 3.1 shows a car of mass 800 kg travelling at a constant speed of 15 m s 1 around a bend on a level road following a curve of radius 30 m. roadway rear-view mirror Fig. 3.1 Fig. 3.2 (i) (ii) Draw an arrow on Fig. 3.1 to indicate the direction of the resultant horizontal force on the car at the position shown. [1] Calculate the magnitude F of this force. F =... N [3] (iii) A medallion hangs on a string from the shaft of the rear view mirror in the car. Fig. 3.2 shows its position in the vertical plane, perpendicular to the direction of travel in Fig Draw and label arrows on Fig. 3.2 to indicate the forces acting on the medallion. [2] 2 On another occasion the car travels around the bend at 25 m s 1. The angle of the string to the vertical is different. Eplain how and why this is so. You may find it useful to sketch a vector diagram to aid your eplanation.... [3]

9 9 (b) Each wheel assembly of the car is mounted on a suspension spring. In a garage test, one wheel assembly is suspended off the ground by its spring with the damper disconnected. Fig. 3.3 shows a graph of the vertical motion of the wheel assembly against time when it is given a small displacement and released. displacement / cm t / s Fig. 3.3 (i) Use the graph to find the natural frequency f 0 of oscillation of the wheel. f 0 =... Hz [2] (ii) When the car is travelling along a ridged concrete road at a speed of 20 m s 1 the driver notices that the car bounces significantly. The ridges in the road are equally spaced 6.2 m apart. 1 Calculate the frequency f of the bounce. f =... Hz [1] 2 State and eplain the phenomenon which is occurring.... [3] [Total: 15] Turn over

10 10 4 This question is about changing the motion of a beam of electrons travelling in a vacuum. Fig. 4.1 shows a simple device for accelerating or decelerating electrons. It consists of two parallel conducting plates, labelled P and Q, each with a hole at its centre. beam of electrons P Q 0 V 36 V Fig. 4.1 (a) On Fig. 4.1 draw at least si arrowed lines to represent the electric field between the plates. [2] (b) The electrons, all travelling at m s 1, pass through the holes in P and Q. The plates, a distance of 8.0 mm apart, are maintained at 0 V and 36 V as shown in Fig Calculate (i) the electric field strength E between the plates E =... N C 1 [1] (ii) the magnitude F of the force on an electron when between the plates F =... N [1] (iii) the loss of kinetic energy Δε of each electron between P and Q (iv) the decrease in velocity Δv of each electron between P and Q. Δε =... J [1] Δv =... m s 1 [3]

11 11 (c) The plates are rotated through 90. Fig. 4.2 shows the same beam of electrons, travelling at m s 1, entering the region between the plates, but now parallel to the plates. A uniform magnetic field is applied into the paper in the region between the plates. P 0 V beam of electrons magnetic field into paper Q 36 V Fig. 4.2 (i) State the direction in which the force due to the magnetic field acts on the electrons as they enter the field.... [1] (ii) Eplain why, by adjusting the strength of the magnetic field, the electrons can pass undeflected between the plates.... [2] (iii) Calculate the magnitude B of the magnetic field density needed for these electrons to pass undeflected between the plates. Give a unit with your answer. B =... unit... [4] [Total: 15] Turn over

12 12 5 Fig. 5.1 shows two capacitors of capacitance 150 μf and 300 μf connected in parallel to a 9.0 V d.c. supply. Fig. 5.2 shows them connected in series to the supply. 150 μf 300 μf 150 μf 9.0 V 9.0 V 300 μf Fig. 5.1 Fig. 5.2 (a) Determine the voltage V across the 300 μf capacitor in the circuit of (i) Fig. 5.1 (ii) Fig V =... V [1] V =... V [2] (b) Calculate the charge Q in μc stored in the 150 μf capacitor in the circuit of (i) Fig. 5.1 (ii) Fig Q =... μc [2] Q =... μc [1]

13 (c) Calculate the ratio f where f = 13 the total energy stored in the capacitors in Fig. 5.1 the total energy stored in the capacitors in Fig f =... [4] [Total: 10] Turn over

14 6 (a) Define the terms nuclide and nucleon. 14. [2] (b) Fig. 6.1 shows a small region of the chart of nucleon number against proton number. A radioactive nuclide Bi decays by either α or β-emission. The nucleon and proton numbers for this nuclide are plotted on the chart at the dot marked with the letter X X nucleon number proton number Fig. 6.1 (i) (ii) (iii) Mark with a dot and the letter A the position on the chart for the daughter nuclide created Bi emits an α-particle. [2] when Mark with a dot and the letter B the position on the chart for the daughter nuclide created Bi emits a β-particle. [1] when Eplain why it is not possible to represent a γ-decay on this chart.... [1]

15 (c) (i) 15 Complete the table below for the three types of ionising radiation. radiation range in air range in a solid α 0.2 mm paper β γ several km [2] (ii) Describe briefly with the aid of a sketch an absorption eperiment to distinguish between the three radiations listed in (i).... [3] [Total: 11] Turn over

16 7 In this question, four marks are available for the quality of written communication. 16 Many laws of physics can be described using mathematical functions and relationships and displayed graphically. (a) y Fig. 7.1 Show that the graph of Fig. 7.1 displays an inverse square relationship between the variables and y. Choose one law of physics which follows an inverse square relationship. State the law in both word and mathematical forms. Indicate which physical quantities would be represented by and y in Fig Describe any physical conditions necessary for the law to be obeyed.. [6]

17 17 (b) y Fig. 7.2 Show that the graph of Fig. 7.2 displays an eponential relationship between the variables and y. Choose one law of physics which follows an eponential relationship. State the law in both word and mathematical forms. Indicate which physical quantities would be represented by and y in Fig [5] END OF QUESTION PAPER Quality of Written Communication [4] [Total: 15]

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