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2 2 Answer all the questions. 1 (a) Draw a line from each unit on the left-hand side to the correct equivalent unit on the righthand side. joule (J) kg m s 2 watt (W) N m newton (N) J s 1 (b) This question is about estimating the pressure exerted by a person wearing shoes standing on a floor, see Fig [2] Fig. 1.1 (i) Estimate the weight in newtons of a person. weight =... N [1]

3 (ii) 3 Estimate the total area of contact in square metres between the shoes of this person and the floor. area =... m 2 [1] (iii) Hence estimate the pressure in pascals exerted by this person standing on the floor. pressure =... Pa [1] [Total: 5] Turn over

4 4 2 Fig. 2.1 shows two masses A and B tied to the ends of a length of string. The string passes over a pulley. The mass A is held at rest on the floor. pulley B 1.50 kg floor A 1.20 kg 2.80 m Fig. 2.1 The mass A is 1.20 kg and the mass B is 1.50 kg. (a) Calculate the weight of mass B. weight =... N [1] (b) Mass B is initially at rest at a height of 2.80 m above the floor. Mass A is then released. Mass B has a constant downward acceleration of 1.09 m s 2. Assume that air resistance and the friction between the pulley and the string are negligible. (i) Explain why, in terms of forces, the acceleration of the mass B is less than the acceleration of free fall g [1] (ii) Calculate the time taken for the mass B to fall 1.40 m. time =... s [3]

5 (iii) Calculate the velocity of mass B after falling 1.40 m. 5 velocity =... m s 1 [2] (iv) Mass B hits the floor at a speed of 2.47 m s 1. It rebounds with a speed of 1.50 m s 1. It spends s in contact with the floor. Calculate the magnitude of the average acceleration of mass B during its impact with the floor. acceleration =... m s 2 [2] [Total: 9] Turn over

6 6 3 A lift has a mass of 500 kg. It is designed to carry a maximum of 8 people of total mass 560 kg. The lift is supported by a steel cable of cross-sectional area m 2. The cable is at its maximum length of 140 m when the lift is at ground floor level, as shown in Fig The mass per unit length of the cable is 3.0 kg m 1. P steel cable lift shaft 140 m ground floor Fig. 3.1 (a) Show that the mass of the 140 m long steel cable is 420 kg. [1]

7 (b) (i) 7 The lift with its 8 passengers is stationary at the ground floor level. The initial upward acceleration of the lift and the cable is 1.8 m s 2. Show that the maximum tension in the cable at point P is N. [4] (ii) Calculate the maximum stress in the cable. stress =... Pa [2] [Total: 7] Turn over

8 8 4 (a) An electron in a particle accelerator experiences a constant force. One student thinks that the acceleration of the electron should remain constant because the ratio of force to mass does not change. In fact, experiments show that the acceleration of the electron decreases as its velocity increases. Describe what can be deduced from such experiments about the nature of accelerated electrons.... [2] (b) Fig. 4.1 shows the velocity vector for a particle moving at an angle of 31 to the horizontal. 8.0 m s-1 31 Fig. 4.1 (i) (ii) On Fig. 4.1, show the horizontal (x-direction) and vertical (y-direction) components of the velocity. [2] Calculate the horizontal (x-direction) component of the velocity. velocity =... m s 1 [1]

9 (c) Fig. 4.2 shows a ship S being pulled by two tug-boats. 9 Not to scale S 1.50 kn cable direction of travel of ship S 2.14 kn tug-boat Fig. 4.2 The ship is travelling at a constant velocity. The tensions in the cables and the angles between them and the direction in which the ship travels are shown in Fig (i) Draw a vector triangle and determine the resultant force provided by the two cables. resultant force =... kn [3] (ii) State the value of the drag force acting on the ship S. Explain your answer [2] [Total: 10] Turn over

10 10 5 (a) State the principle of conservation of energy.... [1] (b) Describe one example where elastic potential energy is stored.... [1] (c) Fig. 5.1 shows a simple pendulum with a metal ball attached to the end of a string. string h m P v Fig. 5.1 The ball describes a circular path when it is released from P. The ball has a maximum speed v at the bottom of its swing. The vertical distance between P and bottom of the swing is h. The mass of the ball is m. (i) Write the equation for the change in gravitational potential energy, E p, of the ball as it drops through the height h. Now write the equation for the kinetic energy, E k, of the ball at the bottom of its swing when travelling at speed v. E p = E k = [1] (ii) Use the principle of conservation of energy to derive an equation for the speed v. Assume that there are no energy losses due to air resistance. [2]

11 11 (d) Some countries in the world have frequent thunderstorms. A group of scientists plan to use the energy from the falling rain to generate electricity. A typical thunderstorm deposits rain for 900 s. The water covers an area of m 2 and is m deep. The rain falls from an average height of m. The density of rainwater is kg m 3. About 30% of the gravitational potential energy of the rain can be converted into electrical energy at the ground. (i) Show that the total mass of water deposited in 900 s is kg. [2] (ii) Hence show that the average electrical power available from this thunderstorm is about 2 GW. [3] (iii) Suggest one problem with this scheme of energy production [1] [Total: 11] Turn over

12 12 6 The force against length graph for a spring is shown in Fig force/n length/10 2 m Fig. 6.1 (a) Explain why the graph does not pass through the origin.... [1] (b) State what feature of the graph shows that the spring obeys Hooke s law.... [1] (c) The gradient of the graph is equal to the force constant k of the spring. Determine the force constant of the spring. force constant =... N m 1 [2]

13 13 (d) Calculate the work done on the spring when its length is increased from m to m. work done =... J [2] (e) One end of the spring is fixed and a mass is hung vertically from the other end. The mass is pulled down and then released. The mass oscillates up and down. Fig. 6.2 shows the displacement s against time t graph for the mass. 0.4 s /m t /s -0.4 Fig. 6.2 Explain how you can use Fig. 6.2 to determine the maximum speed of the mass. You are not expected to do the calculations.... [2] [Total: 8] Turn over

14 14 7 (a) Fig. 7.1 shows a length of tape under tension. pull B pull Fig. 7.1 (i) Explain why the tape is most likely to break at point B [1] (ii) Explain what is meant by the statement: the tape has gone beyond its elastic limit [1] (b) Fig. 7.2 shows one possible method for determining the Young modulus of a metal in the form of a wire. wood blocks clamp metal wire marker pulley BENCH TOP masses Fig. 7.2

15 15 Describe how you can use this apparatus to determine the Young modulus of the metal. The sections below should be helpful when writing your answers. The measurements to be taken: In your answer, you should use appropriate technical terms, spelled correctly. The equipment used to take the measurements: In your answer, you should use appropriate technical terms, spelled correctly. How you would determine Young modulus from your measurements: [8] END OF QUESTION PAPER [Total: 10]

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