WSSS 2007 Prelim P2 ANS

2 Section A Answer all the questions in this section. 1 Fig. 1.1 shows the speed-time graph for a sma ll balloon initially at rest, then falling vertically through the air and then attaining constant speed. (a)(i) Use Fig. 1.1 to determine the time interval over which the balloon is accelerating. 0.4 s [1] [note: 0.5 is also acceptable for this diagram] (ii) Is the acceleration constant ? Explain your answer. No. Since the gradient of the graph is decreasing, the acceleration decreases too. Hence, the acceleration is not constant. [2] (b) Explain, using the forces acting, the motion of the balloon for the first second a f t e r r e l e a s e . As the ballon falls from rest, the air resistance increases gradually and the resultant force decreases. This would result in a decreasing acceleration of the balloon. As the balloon continue falling, the air resistance increases until it balances the weight of the balloon. There is no resultant force and thus no acceleration, which will make the balloon to fall a constant speed. [2] For Examiner’s Use Fig. 1.1

3 (c) The mass of the balloon is 60 g. The gravitational field strength is 10 N/kg. (i) Calculate the weight of the balloon, W = mg = (60/1000) (10) = 0.6 N weight =……………………. [1] (ii) State the value of the air resistance on the balloon 1.0 s after release. Explain y o u r a n s w e r . [ 2 ] 0.6 N. Since the balloon is moving with constanct speed after 1.0 s of release, the forces are balanced (i.e. there is no resultant force). Hence, the air resistance has the same magnitude as the weight of balloon. For Examiner’s Use

4 2 A cyclist, together with his bicycle, has a tota l mass of 90 kg and is travelling with a constant speed of 15 m/s on a flat road at A, as shown in Fig. 2.1. He then goes down a small slope to B so descending 4.0 m. Calculate (a) the kinetic energy at A, Ek = ½ mv2 = ½ (90)(15)2 = 10125 J kinetic energy =……………………. [1] (b) the loss of potential energy between A and B, Ep = mgh = (90)(10)(4) = 3600 J loss of potential energy =……………………. [1] (c) the speed at B, assuming that all the lost potential energy is transformed into kinetic energy of the cyclist and bicycle. Using conservation of energy, Energy at the bottom of slope = Energy at the top of slope ½ (m)(v) 2 = ½ (m)(v)2 + mgh ½ (90)(v) 2 = 10125 + 3600 [2] v 2 = (2)(13725) / 90 v 2 = 305 v = 17.5 m/s [1] speed =……………………. [3] Fig. 2.1 For Examiner’s Use

5 3 Sebastian holds the loose end of a long rope which is fixed to a post. He moves it up and down at a rate of 20 times every 5 seconds. Each time he moves the rope 15 cm up and 15 cm down from its original rest position. Fig. 3.1 shows the wave moving along the rope. (a) Why is the wave that travels along the rope called transverse wave? The direction of vibration of the rope is perpendicular to the direction of travel of the wave. [1] (b) State two other examples of transverse wave. Water wave and radio wave (or any 2 other eletromagnetic waves) [1] (c) State the value of the am plitude of the wave. A = 30/2 = 15 cm amplitude =……………………. [1] (d) Calculate the frequency of the wave. f = 20/5 = 4 Hz frequency =……………………. [1] (e) State the value of the wave length of the wave. λ = 60 cm wavelength =……………………. [1] (f) Calculate the speed of the wave. v = fλ = (4)(0.6) = 2.4 m/s [or 240 cm/s] Speed =……………………. [1] Fig. 3.1 For Examiner’s Use

6 4 Fig. 4.1 shows the virtual image I formed by a converging lens L. (a) By means of a ray diagram, mark and label on Fig. 4.1 the position of the object, O. [3] (b) What happens to the height of the image if the distance of the object from the lens is decreased? [1] The height will decrease. (c) Define the term focal length. [1] The distance from the principal focus (focal point) to the optical center of a lens. (d) Name three characteristics of the image formed if the distance of the object from the lens is equal to 1.7 times the focal length of the lens. [2] Inverted, real and magnified . [1 correct ½ mark, 2 correct 1 mark, 3 correct 2 marks] L F Image, I Fig. 4.1 F For Examiner’s Use Object, O

7 5 An electrically positively charged sphere C is brought near a small uncharged conducting sphere S suspended as shown in Fig. 5.1. S is first attracted towards C until it touches the surface of C and then repelled to the position shown in Fig. 5.2. (a) On Fig. 5.1 draw the charges induced on sphere S. [1] (b) Explain carefully why S is first attracted towards C. [2] Since C is positively charged, it will induce negative charges on the nearer side of S facing C and positive charges on the further side. Since induced negative charges in S are nearer to C, the force of attraction is greater than force of repulsion. Hence, there is a net attractive force. (c) Explain why S is repelled after to uching the surface of C. After touching, electrons from S moves to neutralise some of the positive charges on C. S aquires a net positive charge. C is still positively charged but less in magnitude since it is much bigger than S. As like charges repel, S is repelled from C. [2] Fig. 5.1 Fig. 5.2 For Examiner’s Use

8 6 Fig. 6.1 shows a schematic di agram of the lighting circuit for street lamps. All 60 lamps are connected in parallel to a 240 V a.c. supply. The resistance of each lamp is 50.0 . The wires connecting the lamps have negligible resistance. (a) Calculate the effective resistance of the 60 lamps. R 1 = 1 1 R + 2 1 R + 3 1 R …+ 60 1 R = R 1 x 60 = 0.50 1 x 60 =1.20 R = 0.833  effective resistance =……………………. [2] (b) Calculate the current flowing through one lamp. State the formula you use. V =IR 240 = I x 50.0 I = 4.8 A (2 or 3 s.f.) current =……………………. [2] (c) Calculate the total current flowing out from the power source. Total I = 4.8 x 60 = 288 A total current =……………………. [1] (d) Calculate the power dissipated by one lamp. State the formula you use. P = V 2/ R = 240 2 / 50.0 = 1 152 W power =……………………. [2] 240 V a.c. supply 1st 2nd 60th 59th 50.0 m 50.0 m Fig. 6.1 For Examiner’s Use

9 7 A potential divider circuit is designed with a t hermistor and a fixed resistor as shown in Fig. 7.1. The thermistor has a resistance of 4 kΩ and 6 kΩ when the temperature of the surrounding is 20 oC and 0 oC respectively. This thermistor has resistance that varies linearly with temperature. The alarm sounds when the output voltage (Vout) is 1.0 V or less. (a) Will the alarm sound when the temperature is at 20 oC? Justify your answer by showing clearly the proper calculations. V out = 1/(1+4) x 6 = 1.2 V The alarm will not s ound since output volta