UNIVERSITY OF MALTA G.F. ABELA JUNIOR COLLEGE

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1 UNIVERSITY OF MALTA G.F. ABELA JUNIOR COLLEGE FIRST YEAR END-OF-YEAR TEST RE-SIT SESSION SUBJECT: PHYSICS DATE: September 013 LEVEL: ADVANCED TIME: 09.00h to 1.00h Directions to Candidates Show ALL working. Write units where appropriate. Answer ALL questions in Section A Answer any FOUR questions from Section B You have been provided with two booklets. Use one booklet for Section A, the other for Section B.

2 Formulae Pages The following equations and formulae may be useful in answering some of the questions in the examination. Uniformly accelerated motion: Useful formulae: Mechanics: Newton s second law: Power:P = Fv Momentum: v = u + at 1 s = ut + at v = u + as u + v s = t d( mv) F = dt p = mv Circular motion and rotational dynamics: Angular speed: Angular acceleration: Centripetal force: Torque: d v ω = θ = dt r d a α = ω = dt r mv F = r τ = Iα Work done in rotation: 1 τθ = ( Iω ) Ray optics: Refractive index: n 1 sinθ1 = n sinθ sinθ1 v1 1n = = sinθ v Thin lenses: Magnification: Materials: Hooke's law: Stress: Strain: Young's modulus: n = n. n = + (real is positive) f u v = (Cartesian) f v u v h m = u h m i = (real is positive) v u o h i = = (Cartesian) h o F = k x F σ = A l ε = l σ Y = ε Energy stored in a stretched wire: E = 1 k ( l ) Simple harmonic motion: Displacement: x = x o sin(ωt + φ) Velocity: v = ω x o cos(ωt + φ) Acceleration: Period: Mass on a light spring: o v = ± ω x x a = ω x 1 π T = = f ω T = π m k Stationary waves: Speed of waves on strings: v = T µ Wave motion: Two slit interference: λd s = d Diffraction grating: d sinθ = nλ Single slit diffraction: λ θ = a Diffraction of circular aperture: sinθ θ = 1. λ a - -

3 Fields: F dv Electric field strength: E = = + q dr Uniform field: F E = = + q V d Q1Q Force between point charges: F = 4πε 0r Electric field strength of a point charge: Q E = 4πε r Force between point masses: M 1M F = G r Electric potential: Q V = 4πε 0 r Gravitational potential: GM V G = r Work: W = QV 0 Capacitance: ε A Capacitance of parallel plates: C 0 ε = r d Capacitors in parallel: C = C 1 + C Capacitors in series: = C C C Energy stored: 1 W = CV Charging: t Q Q e RC = 0 1 Discharging: Q = t Q e RC 0 1 The following constants may be useful in answering some of the questions in the examination. Acceleration of free fall on and near the Earth s surface g = 9.81 m s Gravitational field strength on and near the Earth s surface g = 9.81 N kg 1 Boltzmann constant k = J K 1 Molar gas constant R = 8.31 J K 1 mol 1 Avogadro s constant N A = mol 1 Coulomb s law constant k = 1/(4πε o ) = N m C Charge of an electron e = C Mass of an electron m e = kg Electronvolt 1 ev = J Gravitational constant G = N m kg Permittivity of free space ε o = F m 1 Permeability of free space µ o = 4π 10 7 H m 1 Planck constant h = J s Speed of light in a vacuum c = m s 1 Unified atomic mass unit u = kg - 3 -

SECTION A Answer all questions in this section. Please make sure that you write the question number in the margin. Each question carries 10 marks 1.

4 SECTION A Answer all questions in this section. Please make sure that you write the question number in the margin. Each question carries 10 marks 1. The current through a conductor changes with time over a period of 3.0 s as shown. (a) State the essential internal feature that allows a specific material to be a conductor of electricity. [] Calculate the total charge passing through the conductor in this time. [3] Calculate the total number of electrons flowing past a point in the conductor in this time. [] (iii) Calculate the drift velocity of the electrons at t = 1.5 s. Take the crosssectional area of the conductor to be m and the number of free electrons per m 3 to be m -3. [3] - 4 -

. The Silver Carp is a fish that is often seen to jump out of the water and land in the boats of fishermen. [Ignore air resistance throughout this question]..75 m 4.

5 . The Silver Carp is a fish that is often seen to jump out of the water and land in the boats of fishermen. [Ignore air resistance throughout this question]..75 m 4.50 m (a) A fisherman makes the following estimations about the trajectory of a particular Carp: Horizontal distance travelled by the Carp = 4.50 m Time of flight = 1.50 s Maximum height =.75 m Use this information to calculate the horizontal component of the velocity of the Carp, [] the initial vertical velocity of the Carp, [] (iii) the magnitude of the velocity with which the Carp actually jumped out of the water. [] Assume the Carp had a mass of 6kg. What was its kinetic energy at its topmost point of its trajectory? [] gain in potential energy at its topmost point of its trajectory? [] 3. The drum of a washing machine is a hollow perforated cylinder with an inside radius of 0.15m. On its spin cycle it rotates (about the axis of the cylinder) at a rate of 400 revolutions per minute. (a) Calculate the angular velocity of the drum in radians per second. [] Apart from angular velocity, the angular momentum of the rotating drum depends on its moment of inertia. Discuss the factors that affect the moment of inertia of a rotating body. [] - 5 -

6 Calculate the acceleration of a point on the inside of the drum. [] Hence explain why gravity has little effect on the spin-drying operation. [1] (c) Calculate the resultant force that must act on a wet sock of mass 80g in contact with the cylinder wall. [] State the direction of this force. [1] 4. Just over two hundred years ago Thomas Young demonstrated the interference of light by illuminating two closely spaced narrow slits with light from a single light source. (a) What did this suggest to Young about the nature of light? [] The demonstration can be carried out more conveniently with a laser. A laser produces coherent, monochromatic light. State what is meant by monochromatic. [] State what is meant by coherent. [] (c) The figure below shows the maxima of a two slit interference pattern produced on a screen when a laser was used as a monochromatic light source. The slit spacing = 0.30mm. The distance from the slits to the screen = 10.0 m. Use the details given in the figure to calculate the wavelength of the light that produced the pattern. [4] 5. It has been predicted that in the future large offshore wind turbines may have a power output ten times that of the largest ones currently in use. These turbines could have a blade length of 100 m or more. A turbine such as this is shown in the diagram overleaf

7 wind turbine (a) At a wind speed of 11m s 1 the volume of air passing through the blades each second is m 3. Show that the mass of air that would pass through the blades each second is about kg. The density of air is 1. kgm 3. [] Calculate the kinetic energy of the air that would enter the turbine each second. [] (c) Hence state the wind power input to the turbine. [1] (d) (e) It has been predicted that the turbine would produce an electrical power output of 10 MW in these wind conditions. Calculate the percentage efficiency of the turbine in converting this kinetic energy into electrical energy. [3] Explain why the velocity of the air is reduced after it has passed through the turbine. [] 6. A rubber cord is used to provide mechanical resistance when performing fitness exercises. A scientist decided to test the properties of the cord to find out how effective it was for this purpose. (a) State two ways in which the behaviour of a rubber cord differs from that of a steel wire of similar dimensions when both are subjected to a stretching force. [] - 7 -

8 The graph of load against extension for a 0.50 m length of the cord was plotted. Curve A shows the extension variation during loading while curve B shows the extension variation during unloading of the cord. State which feature of this graph confirms that the rubber cord is elastic. [] What is the physical significance of the area enclosed by curves A and B i.e. the area of the loop? [] (c) Assuming that line A is linear up to an extension of 0.04 m, calculate the Young modulus of the rubber for small strains. The cross-sectional area of the cord = 5.0 x 10-6 m The unstretched length of the cord = 0.50m [3] What does the size of the Young Modulus indicate about the elastic behaviour of a material? [1] 7. (a) Explain why the homogeneity of a physical equation does not necessarily guarantee the correctness of the equation. [] The root mean square speed for gas molecules is given the symbol c rms - 8 -

9 and has the same units as speed. It is found to be related to mass per mole, M, of the gas through the equation C rms = 3RT M where R is the so-called molar gas constant and T is the absolute temperature. What are the SI units of T? [1] What are the units of M? [] (iii) Hence work out the base units of R. [5] 8. The helicopter shown in the figure is moving horizontally to the left through still air. The lift force from the helicopter s blades is labelled A. Two other forces, B and C, act on the helicopter in such a way that the three forces (A, B and C) form a closed triangle of forces as shown. (a) State Newton s first law of motion. [] Name the two other forces i.e. B and C, that act on the helicopter. [] (c) (d) How can you conclude that the helicopter is moving with constant velocity? [] If the lift force is equal to 9.5 kn and acts at an angle of 74 o as shown, determine the magnitudes of B and C respectively. [4] - 9 -

10 Section B. Answer any FOUR questions from this section. USE THE OTHER BOOKLET FOR THIS SECTION. DO NOT forget to write the question number in the margin. Each question carries 5 marks 9 (a) Deep space probes often carry modules which may be ejected from them by an explosion. A space probe of total mass 500 kg is travelling in a straight line through free space at 160 m s 1 when it ejects a capsule of mass 150 kg. Immediately after the explosion, the probe, now of mass 350 kg, continues to travel in the original straight line but at an increased velocity of 40 m s 1, as shown below. State the law of conservation of momentum, including any condition under which it holds. [] The law of conservation of momentum is derived from two other laws in Physics. Identify, without stating, these two particular laws. [] (iii) Determine the maximum velocity with which the capsule could have possibly been ejected. [3] In the 1969 Moon landing, the Lunar Module separated from the Command Module above the surface of the Moon when it was travelling at a horizontal speed of 040 m s 1. In order to descend to the Moon s surface the Lunar Module needed to reduce its speed using its rocket as shown

11 How does firing a rocket in the direction of motion (i.e. hot gases are propelled out in the direction of motion) help in reducing the speed of the Lunar Module? [] The average thrust from the rocket was 30 kn and the mass of the Lunar Module was kg. Calculate the horizontal deceleration of the Lunar Module. [3] (iii) Calculate the time for the Lunar Module to slow to the required horizontal velocity of 150 m s 1. Assume the mass remained constant. [3] (c) The rocket was then used to control the velocity of descent so that the Lunar Module descended vertically with a constant velocity as shown below. Due to the use of fuel during the previous deceleration, the mass of the Lunar Module had fallen by 53%. Determine the weight of the Lunar Module given that the gravitational field strength near the Moon s surface is 1.61 N kg 1. [3] What thrust was needed from the rocket in order to maintain the descent of the Module at a constant speed? Explain. [] (iii) When the Lunar Module was 1. m from the lunar surface, the rocket was switched off. At this point the vertical velocity was 0.80 m s 1. Show that the Lunar Module hits the lunar surface at a speed of.1 m s 1. [3] (iv) How does a soft patch of lunar surface assist in keeping the impact force, experienced by the Module on landing, reasonably small? []

$10 (a) Waves are often said to undergo diffraction under the right conditions. Explain what you understand by the term diffraction as applied to the behaviour of waves.$

12 10 (a) Waves are often said to undergo diffraction under the right conditions. Explain what you understand by the term diffraction as applied to the behaviour of waves. [] In the picture shown, the street cleaner cannot see the radio around the corner but he can hear the sound coming from it. Explain. [4] When light passes through a single slit, a pattern similar to the one shown in the picture below is obtained on a screen, placed at some distance behind the slit. Sketch a graph to show how the intensity varies with angle of diffraction on either side of the centre of the pattern. [3] Sketch another graph to show how the intensity would vary if the single slit had been replaced by two close slits of similar width as the first single-slit. [3] (iii) How would the intensity pattern for the two slits have changed, if the two slits had been closer to each other? [] (c) A diffraction grating is mounted on the table of a spectrometer. The grating has lines per metre and is illuminated with a narrow parallel beam of white light. White light comprises wavelengths in the range 400nm 750nm. Identify the colour of light having a wavelength of 750nm. [] What is the angular separation between the first-order images of the 400nm and 750nm wavelengths respectively? [5] (iii) Show that the red image in the second-order spectrum will appear beyond the violet image in the third-order spectrum. [4] - 1 -

13 11 (a) A body of mass m is placed in a gravitational field. State the relationship, in equation form, between the gravitational potential energy, Ep, and the gravitational potential, V, for this body. [3] What is the effect, if any, on the values of Ep and V if the mass m is doubled? [] The figure shows two of the orbits, A and B, that could be occupied by a satellite in circular orbit around the Earth, E of mass M = kg. The gravitational potential due to the Earth of each of these orbits is: orbit A 1.0 MJ kg 1 orbit B 36.0 MJ kg 1. A B E Calculate the radius, from the centre of the Earth, of orbit A. [3] Show that the radius of orbit B is approximately km. [3] (iii) Calculate the centripetal acceleration of a satellite in orbit B. [3] (iv) Show that the gravitational potential energy of a 330 kg satellite decreases by about 8 GJ when it moves from orbit A to orbit B. [3] (c) (d) Explain why it is not possible to use the equation ΔEp = mgδh when determining the change in the gravitational potential energy of a satellite as it moves between these orbits. [] Show that the escape velocity v with which an object may be kicked out out of the Earth s gravitational field is about 11. km s 1. Show the entire reasoning. The radius R of the Earth is 6378km. [6]

14 1 (a) A body is in a state of equilibrium. In mechanics, what do we mean when we say that a body is in equilibrium? [] State the two conditions needed for a rigid body to be in equilibrium. [4] (iii) Which condition listed in above would no longer be applicable if the rigid body were to be replaced by a point object? Explain. [] rod A metal block of volume V is hung at a distance x from the centre of a uniform rod that is pivoted at its centre of gravity. The rod is kept in equilibrium, in a horizontal position, by a mass m attached at a distance d 1 from the centre on the other side as the metal block. Express the mass of the metal block, M, in terms of x, d 1 and m. [] The metal block is now immersed in a beaker of water but its distance x from the pivot is unchanged. The density of water is ρ. The mass m is moved to a new distance d to restore equilibrium. rod metal block Explain, with reference to Archimedes s principle, why the downward pull of the metal block on the rod is now smaller. [3]

15 (iii) Give an expression for the upthrust on the metal block in terms of V. [1] (iv) By applying the principle of moments in this new situation, show that the new distance d is given by: d = d 1 ρ V x / m [4] (c) The figure below shows a uniform rod being acted upon by two equal and opposite forces as shown. The beam is 1m long. 4N 4N Give one word that describes two equal and opposite forces whose lines of action do not coincide. [1] What torque is exerted on the rod by these two forces? [1] (iii) In which direction will the rod rotate as a result of this torque? [1] (iv) A frictional torque of 3 Nm acts on the rod during rotation and the moment of inertia of the rod is 0.0 kg m. Determine the angular acceleration of the rod. [] (v) What angular velocity would the rod attain after rotating through an angle of 70 o? [] 13 (a). Two point charges are found to exert a force F on each other. State the law which determines how F varies with the separation and size of these charges. [] In what way is this force similar to the gravitational force between two point masses and in what way is it different? [,] (iii) Two ions, each of positive charge C, are in water and at one instant come within a distance of m of each other. What electrostatic force do these ions experience given that water has a relative permittivity (dielectric constant) of 80? [3] (iv) The two ions are momentarily at rest at their closest separation of m. What is their electrical potential energy at this instant? []

16 (v) The two ions then repel each other and move off in opposite directions. If both ions are of the same mass, which principle in Physics predicts that they would move off with equal and opposite velocities? Explain. [3] Two parallel metal plates are charged by connecting them to a battery. The left plate is positively charged while the right plate is negatively charged. Draw a sketch of the two charged plates and mark the electrical field lines between the plates. [] How does your sketch show that the field between the plates is uniform? [1] (iii) If the voltage V (potential difference) across the plates was 9 V and the separation d between the plates was 10 cm, calculate the electric field strength between the plates. [] (iv) State an alternative unit of electric field strength to the one given in (iii). [1] (v) A dust particle, carrying a charge of C happens to be exactly midway between the two plates. What size of electric force would act on this dust particle? [] (vi) Would it have mattered had the dust particle been at any point between the plates other than exactly midway? Explain. [] (vii) The right hand plate was moved so that the distance d was doubled i.e. d = 0cm. State how this affects the size of the force on the dust particle. [1] 14 (a) The diagram shows monochromatic light that is incident on a glass block of refractive index 1.5 and width 10.0 cm. What does a refractive index of 1.5 indicate about the behaviour light as it enters the glass block? [1]

17 If monochromatic light of a different colour is incident on the glass block, would the refractive index of the glass change or would it stay fixed at 1.5? Explain. [] 40 o 10.0 cm (iii) Find the angle of refraction inside the glass block. [] (iv) Hence find the distance travelled by the light inside the block and the time it takes to emerge from the block. [,3] An illuminated object is placed 35.0cm in front of a convex lens of focal length 0.0cm and an image is formed on a screen, placed on the other side of the lens. Calculate the image distance. [3] What is the magnification m of the image? [] (iii) The distance between object and screen are kept fixed and the lens is moved between them until a second image appears on the screen. State the respective object and image distances at which this will happen. [] (c) A converging lens, in a slide projector, is used to magnify a square-shaped slide, of area 4cm, to an image covering a total area of 6400 cm on the projector screen. Find the linear magnification of the image. [3] Hence, calculate the focal length of this lens if the screen is 8cm away from the slide. [5]

UNIVERSITY OF MALTA G.F. ABELA JUNIOR COLLEGE

UNIVERSITY OF MALTA G.F. ABELA JUNIOR COLLEGE FIRST YEAR END-OF-YEAR TEST SUBJECT: PHYSICS DATE: Tuesday 9 th June 015 LEVEL: ADVANCED TIME: 09.00h to 1.00h Directions to Candidates Show ALL working. Write