UNIVERSITY OF MALTA G.F.ABELA JUNIOR COLLEGE FIRST YEAR END-OF-YEAR TEST June Session 2002 Subject: Physics Date: 5 th June 2002 Level: Advanced Time: 09.00hrs 12.00hrs Directions to Candidates You are requested to show your working and write the units where necessary. Answer ALL questions from Section A. Answer any TWO questions from Section B. Answer any TWO questions from Section C. Wherever necessary assume g = 10ms -2.
Section A Attempt ALL eight questions in this section. Each question carries 5 marks. This section carries 40% of the total mark for this paper. 1. Two cars, travelling in the same direction, skid on a patch of smooth, level ice. Car A, of mass 1400kg, skids straight into the back of car B, of mass 1000kg. The two cars become entangled after impact and continue to move in the same straight line. Car A Car B 8m/s Smooth ice Immediately before impact, car B is moving with a velocity of 8m/s. Immediately after impact, both cars move with a velocity of 15m/s. (a)calculate the velocity of car A just before the collision takes place. (2) (b)after the collision, the cars leave the patch of ice and continue skidding along the road. They come to rest in a distance of 20m after leaving the ice. Calculate the average frictional force acting on the cars as they come to rest. (3) 2. The two graphs in figure are load-extension graphs of two different materials X and Y. Each strand is of length 2m and cross-sectional area 1.0mm 2. (a) State which material is ductile and which is brittle. Explain. (1) (b) Calculate the Young s modulus of material X. (2) (c) Deduce the strain energy stored in the strand of material Y for an extension of 2mm. (2)
3. A helicopter with supplies hanging from a rope, circles a lighthouse to deliver them. The load of 80kg is moving in a circular path of radius 20m at 3.3m/s. (a) Explain why the rope cannot be vertical. (2) (b) By considering the tension in the rope and the centripetal force needed, establish the angle of the rope to the horizontal. (3) 4. A tennis player hits a ball at a height of 2.4m. The ball has an initial horizontal velocity. The ball just passes over the net that is 0.6m high and 6m away from her. (Neglect air resistance) 2.4m 0.6m 6.0m (a) Calculate the time required for the ball to reach the net. (2) (b) What was the speed of the ball as it left the racquet? (3) 5. Light enters a layer of glue at the end of an optical fibre as shown in the figure. The refractive index of the glue, η glue is 1.36 and of the core glass η core is 1.58. A ray is incident on the end of the fibre at 10. layer of glue 10 cladding core glass cladding (a) Determine at what angle does it hit the core-cladding boundary? (2) (b) Draw the diagram on your booklet and show, with calculations, what happens to the light once it is incident on the core-cladding boundary. The refractive index of cladding is 1.48. (3)
6. The wavelength of monochromatic light from a lamp is to be determined by means of a double slit experiment. (a) Draw on your booklet a set up of the arrangement that will enable you to determine λ. (1) (b) State what measurements are taken and explain how these measurements are used to calculate the wavelength. (3) (c) Describe the screen pattern that results. (1) 7. Bending and lifting incorrectly often cause back injury. The diagram below shows a man about to lift a box. (a) What is the vertical component T v of the tension in the back muscles in the situation shown in figure. (1) (b) Calculate the tension in the back muscles. (2) (c) Suggest a better way of lifting the box. Explain. (2)
8. The graph below shows the gravitational field strength at various heights above the earth s surface. Gravitational field strength in N/kg Height above the Earth s surface in km (a) Given that the radius of the earth is 6400km show with the aid of the graph that the gravitational field strength varies with distance according to an inverse square law. (2) (b)what is the speed of orbit of a satellite that is 5000km above the earth s surface.(3)
Section B Attempt TWO questions in this section. Each question carries 15marks. This section carries 30% of the total mark of this paper. 9a.State and explain the equation defining simple harmonic motion. (2) b. The graph in figure shows how the acceleration of a mass-spring system undergoing simple harmonic motion varies with time. Deduce from the numerical values given on the graph, the values for this simple harmonic motion of : (i) the period (ii) the frequency (iii) the angular frequency (iv) the amplitude of the oscillation (6) c. Sketch on your booklet a graph which shows how the (i) the displacement varies with time. (ii) the velocity changes with time (4) d. The experiment is repeated using a mass of four times the original mass. Determine the new period and frequency of this mass-spring system. (3) 10a. Distinguish between transverse and longitudinal waves and state an example of each. (4) b. Using diagrams explain what is meant by: (i) an unpolarised wave (ii) a plane-polarised wave. (2) c. Describe the effect of two crossed polaroids (i.e. two polaroids with axis at right angles to each other) on unpolarised light. (2)
d. A biologist is studying the effect of different colours of light on a sample of chlorophyll. He sets up the apparatus shown below, using a diffraction grating with 6.0 x 10 5 lines per metre to produce a first order spectrum of sunlight. ray of sunlight θ A diffraction grating 1 st order spectrum X a sample of chlorophyll Y (i) The wavelength of the light at the end X of the spectrum is 410nm. Calculate the value of the angle θ. (2) (ii) The angle A in the diagram is 9. Calculate the wavelength at end Y of the spectrum. (3) (iii) The biologist now uses a triangular prism to produce a continuous spectrum from a ray of sunlight. State two differences between this spectrum and the spectrum produced by the grating. (2) 11. A photocell has a cathode coated with a material, which emits electrons when visible light shines on it. a. When light of wavelength 550nm shines on the cathode, electrons are just emitted. (i) What is the threshold frequency of this material? (ii) What is the work function, φ, of the metal in joules? (5) b. The wavelength of the light is changed to 400nm at the same intensity. (i) What is the maximum possible K.E. of an ejected electron? (ii) How does this change of frequency affect the number of electrons emitted each second? (5) c. The intensity is then increased. What is the effect on: (i) the KE of the ejected electrons (ii) the number of electrons emitted per second? (5) (c = 3.0 x 10 8 m/s, h = 6.6 x 10-34 Js)
Section C Attempt TWO questions in this section. Each question carries 15marks. This section carries 30% of the total mark of this paper. 12. The figure shows a Ferris wheel, at a fun fair, which rotates in a vertical plane about a horizontal axis. Below is data on the Ferris wheel. Moment of inertia of the wheel empty = 8.8 x 10 5 kgm 2 Maximum passenger mass per chair = 200kg Number of chairs = 16 Radius of the wheel = 10m With each chair carrying its maximum load, the Ferris wheel is found to rotate 7 times in 30s, when rotating at its maximum angular speed. (a) Determine the moment of inertia of the loaded wheel (2) (b) Find the angular velocity of the wheel (2) (c) Calculate the rotational KE of the loaded wheel at this speed. (2) (d) With the driver motor switched off and with no application of the brakes, the system decelerates uniformly to rest from its maximum speed in 20 revolutions. Calculate the frictional torque that causes this deceleration. (3) (e) The wheel takes 50s, from rest to reach its maximum angular speed. Calculate its angular acceleration. (2) (f) Calculate the torque of the driver motor which would produce this acceleration of the loaded Ferris wheel. (4)
13. An electron is projected into an evacuated space between two charged plates of length 5cm as shown in figure. The electric field strength E is 3.5 x 10 4 NC -1. The velocity of the electron, v, is 3.2 x 10 7 m/s. Neglect any gravitational effects. (a) State whether the quantity electric field strength is a vector or a scalar quantity? (1) (b) What is the size and direction of the electric force on the electron? (3) (c) What is the horizontal velocity of the electron as it leaves the uniform field? (1) (d) How long does it take to pass between the plates? (2) (e) What is the vertical acceleration of the electron? (2) (f) What is the vertical velocity on leaving the plates? (4) (g) What is the size and direction of the final velocity? (3) (electronic charge e = 1.6 x 10-19 C, mass of electron m e = 9.1 x 10-31 kg) 14. a. Define the capacitance of a capacitor. (1) b. The figure shows a circuit diagram of three capacitors, of capacitance 10µF, 5µF and 25µF respectively, connected in a network with a battery of e.m.f. 12V. (i) Which capacitors are in parallel? (1) (ii) Calculate the capacitance of the single capacitor, connected across the battery, which is equivalent to the network of three capacitors. (3) (iii) Calculate the energy stored in the network of capacitors. (3)
c. The figure is a diagram of a circuit containing a resistor R and a capacitor C, together with a two-way switch S and a battery of e.m.f. 10V. When the switch is in position A the capacitor and resistor are connected in series with the battery; when the switch is in position B the capacitor discharges through the resistor. (i) With switch S in position A, what is the maximum possible potential difference across the capacitor C? (1) When the capacitor C is fully charged, the switch S is moved from position A to position B at t=0s. The graph in figure shows the potential difference V across the capacitor C as a function of time t in the range from 0 to 12s. (ii) Estimate the time constant of the circuit from the graph. (2) (iii) If the capacitance of C is 20µF, what is the value of the resistance R? (2) (iv) Calculate the current flowing in the circuit, 1s after switching on. (2)