WAEC SSCE - Physics - 2007

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To solve this problem, we can use the kinematic equation: v² = u² + 2as Where: v = final velocity (what we want to find) u = initial velocity (in this case, 0 since the body starts from rest) a = acceleration (given as 2 ms^-2) s = distance travelled (given as 9m) Substituting the given values, we get: v² = 0² + 2 x 2 ms^-2 x 9m v² = 36 ms^-1 v = √(36) ms^-1 Therefore, the magnitude of the velocity of the body after travelling 9m with a uniform acceleration of 2ms^-2 is 6.0 ms^-1.

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The observed increase in the loudness of the sound when a tuning fork is brought near the open end of a pipe containing air is due to resonance. Resonance occurs when an object is forced to vibrate at its natural frequency by an external force. In this case, the tuning fork produces sound waves at a specific frequency, which matches the natural frequency of the air column in the pipe. As a result, the air column in the pipe begins to vibrate with greater amplitude, which in turn increases the loudness of the sound. This phenomenon is similar to how pushing a child on a swing at the right time will cause them to swing higher and higher. In both cases, the external force is applied at just the right frequency to match the natural frequency of the object, resulting in increased amplitude. Therefore, the correct option is "resonance."

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The statement that sound waves can be polarized is not correct. Polarization refers to the orientation of the electric field component of a transverse wave. However, sound waves are longitudinal waves, which means that they oscillate in the same direction as the wave propagation. Therefore, sound waves do not have an electric field component and cannot be polarized. On the other hand, sound waves can be reflected, refracted, and diffracted. Reflection occurs when a sound wave bounces off a surface, such as an echo in a room. Refraction occurs when a sound wave bends as it passes through a medium with a different density, such as when sound waves pass through air with different temperatures. Diffraction occurs when a sound wave bends around obstacles in its path, such as when sound waves from a speaker spread out in all directions.

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The operation that does not represent an action of a force field is the "pushing of a wheel-barrow on a level ground". A force field is a region where a force acts on an object, and the object experiences a force because of the interaction with the field. In the case of the pushing of a wheel-barrow, the force is not a result of a field but is applied by the person pushing the wheelbarrow. Therefore, this operation does not represent an action of a force field.

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The total energy consumed by the lamps can be calculated by first finding the total power rating of the lamps, and then multiplying it by the time they were used. Total power = (5 x 80W) + (3 x 100W) = 400W + 300W = 700W Total energy = Power x Time = 700W x 8 hours = 5600 Wh = 5.6 kWh Since 1 unit = 1 kWh, the energy consumed is 5.6 units. The cost of running the lamps can then be calculated by multiplying the energy consumed by the cost per unit of energy. Cost = Energy consumed x Cost per unit = 5.6 units x N5.00 per unit = N28.00 Therefore, the cost of running the lamps is N28.00. Answer is the correct answer.

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A swinging pendulum between the rest position and its maximum displacement possesses both kinetic and potential energy. As the pendulum moves away from its rest position, it gains potential energy due to the increased height above the rest position. As the pendulum swings back towards the rest position, it loses potential energy and gains kinetic energy due to its increased speed. At the rest position, the pendulum has its maximum kinetic energy and minimum potential energy, and at the maximum displacement, it has its maximum potential energy and minimum kinetic energy. Thus, the pendulum continuously converts potential energy to kinetic energy and back again, and possesses both types of energy at any point during its motion.

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When an object is placed at the centre of curvature of a concave mirror, its image is formed at the centre of curvature. The centre of curvature is a point on the principal axis of the mirror, located at a distance equal to the radius of curvature from the mirror's vertex. When light rays from the object fall on the concave mirror, they reflect and converge at the centre of curvature. This convergence of light rays forms a real, inverted image of the object at the centre of curvature. Since the image is formed by the actual convergence of light rays, it is a real image. In summary, when an object is placed at the centre of curvature of a concave mirror, its image is formed at the same location, which is the centre of curvature of the mirror.

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The most probable explanation for the phenomenon of a dry plastic comb attracting pieces of paper and dust is that the comb has been electrically charged by friction. When the comb is rubbed against hair, electrons are transferred from the hair to the comb, leaving the comb with a negative charge and the hair with a positive charge. The negative charge on the comb can then attract positively charged pieces of paper and dust. This process is called charging by friction or triboelectric charging. Therefore, "electric charges by friction" is the correct answer.

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Since the object is moving with a constant velocity, its acceleration is zero. This is because acceleration is the rate of change of velocity over time, and if the velocity is constant, there is no change and hence, no acceleration. Therefore, the answer is (a) 0 ms^-2.

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When an object is on an inclined plane, its weight is resolved into two components: one perpendicular to the plane, and the other parallel to the plane. The perpendicular component is counteracted by the normal force of the plane, while the parallel component is responsible for the object's motion along the plane. Since the plane has an efficiency of 50%, it means that only half of the force parallel to the plane is used to move the object up the plane. The other half is lost due to friction and other factors. Therefore, to calculate the required force parallel to the plane, we need to divide the weight of the load by the efficiency: force = (load weight / efficiency) * sin(theta) where theta is the angle of inclination of the plane. Substituting the given values, we get: force = (120 / 0.5) * sin(30) force = 240N * 0.5 force = 120N Therefore, the force required to push the load uniformly up the plane is 120N, which corresponds to.

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According to the kinetic theory of gases, the pressure of a gas can be affected by the collision of gas molecules with the walls of the container. As the gas molecules move randomly, they collide with the walls of the container and exert a force on it. This force per unit area is defined as the pressure of the gas. The more frequent and intense the collisions, the higher the pressure. Therefore, the pressure of a gas can be increased or decreased by changing the number of collisions with the walls of the container. The other options listed (temperature, energy, viscosity) are also properties of gases, but they are not directly affected by collisions with the walls of the container.

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When the number of protons in an element increases by one, it means that a proton has been added to the nucleus of the atom. This can only happen through the emission of a beta particle, which is essentially an electron that is emitted from the nucleus. During beta decay, a neutron in the nucleus of the atom is converted into a proton and an electron. The proton remains in the nucleus, increasing the atomic number by one, while the electron is emitted from the nucleus as a beta particle. Therefore, if the number of protons in an element increases by one, it must have undergone beta decay by emitting a beta particle. Alpha decay involves the emission of an alpha particle, which is made up of two protons and two neutrons. Gamma decay, on the other hand, involves the emission of a gamma ray, which is a high-energy photon. Neutron emission occurs when an unstable nucleus has too many neutrons, but this does not change the atomic number of the element.

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When an object is descending at a steady velocity, the forces acting on it must be balanced. Therefore, the net force on the object must be zero. In this case, the forces acting on the mass are the viscous drag force, F, the upthrust force, U, and the force due to gravity, mg. Using Newton's second law, we know that the net force on an object is equal to its mass times its acceleration. Since the object is descending at a steady velocity, its acceleration is zero, so the net force on the object must also be zero. Therefore, we can write the following equation: U + F - mg = 0 This equation shows that the upthrust force and the viscous drag force must balance the force due to gravity in order for the object to descend at a steady velocity with a parachute. So, the correct expression is: U + F - mg = 0.

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We can use the principle of the thermometer, which states that the volume of the liquid (in this case, mercury) in the bulb and stem of the thermometer changes with temperature, and this change in volume is linearly related to the temperature. Therefore, we can set up a proportion: change in volume of mercury / total length of thermometer stem = change in temperature / temperature interval between ice and steam points Let x be the length of the mercury column when the temperature is at the desired point. Then the change in volume of mercury is 14 - 10 = 4 cm. The total length of the stem is 30 - 10 = 20 cm. The temperature interval between ice and steam points is 100^oC. Substituting these values into the proportion, we get: 4 cm / 20 cm = change in temperature / 100^oC Solving for the change in temperature, we get: change in temperature = (4 cm / 20 cm) * 100^oC = 20^oC To get the actual temperature at the 14 cm mark, we add the change in temperature to the ice point temperature (which is 0^oC): temperature at 14 cm mark = 0^oC + 20^oC = 20^oC Therefore, the answer is 20^oC.

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Infrared radiation can be detected by its heating effect. Infrared radiation is a type of electromagnetic radiation that has longer wavelengths than visible light. When infrared radiation falls on an object, the energy is absorbed by the object, causing the object's temperature to increase. This effect is commonly used in devices such as infrared heaters and thermal imaging cameras, which use infrared radiation to detect the heat signature of objects. Therefore, option D (infrared radiation) is the correct answer to the question.

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Electromagnetic waves are waves that are capable of propagating through a vacuum or through different media. These waves are made up of changing electric and magnetic fields that are perpendicular to each other and to the direction of the wave's propagation. Sound waves, water waves, and tidal waves are all mechanical waves, meaning they require a medium to propagate through. X-rays, on the other hand, are electromagnetic waves, which means they do not require a medium to propagate through and can travel through a vacuum. Therefore, the correct answer is x-rays.

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The quantity of heat released by the body can be calculated using the formula: Q = mcΔT where Q is the quantity of heat, m is the mass of the body, c is the specific heat capacity, and ΔT is the change in temperature. Substituting the given values: m = 200g = 0.2kg c = 0.4Jg^-1k^-1 ΔT = (31 - 37)°C = -6°C Q = (0.2kg) x (0.4Jg^-1k^-1) x (-6°C) = -0.48J The negative sign indicates that the body released heat to the surroundings, which is the expected outcome since the body cooled down. Thus, the correct answer is 0.48J. However, none of the given options match this value exactly. The closest option is 480J, but this is off by a factor of 1000.

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When an object is placed in front of a plane mirror, its image is formed behind the mirror at the same distance as the object is from the mirror. In this case, the object is placed at a distance of 10 cm from the mirror. Therefore, the image will also be formed at a distance of 10 cm behind the mirror. When the object is moved 8 cm farther away from the mirror, its new distance from the mirror will be 18 cm (10 cm + 8 cm). Since the image distance from the mirror is always equal to the object distance from the mirror, the distance of the final image from the mirror will also be 18 cm. Therefore, the correct answer is: 18cm

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Mechanical energy is the energy possessed by an object due to its motion or position. It can be either potential energy or kinetic energy. Potential energy is the energy an object possesses due to its position, shape, or state. Kinetic energy, on the other hand, is the energy an object possesses due to its motion. Therefore, the correct answer is "potential or kinetic."

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A black surface will radiate heat energy best. This is because black surfaces are good absorbers of all wavelengths of light, including infrared radiation, which is the type of radiation associated with heat energy. As a result, they also emit more radiation at these wavelengths, making them better at radiating heat energy compared to surfaces that reflect or transmit more light, such as white, yellow, or red surfaces.

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When a gas is excited by high voltage to produce a discharge and the light is examined in a spectrometer, an emission spectrum is observed. This is because the excited gas atoms emit energy in the form of light of specific wavelengths as they return to their ground state. These emitted wavelengths are characteristic of the element or compound being examined and appear as bright lines in the spectrum. Therefore, the emission spectrum can be used to identify the elements present in the gas being examined.

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The phase angle between two points on a wave is given by the fraction of the wavelength between the points, measured in radians. In this case, the distance between points P and Q is half the wavelength (0.05m is half of 0.10m). Therefore, the phase angle between P and Q is half of the complete wave cycle, which is equal to π radians. So, the answer is: \(\pi\)

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Statement ii and iii distinguish thermal conduction from convection. Thermal conduction refers to the transfer of heat energy through a medium without any actual motion of the medium itself. In conduction, heat is transferred by the transfer of kinetic energy from one molecule to another through collisions. As a result, in conduction, molecules vibrate faster about their mean positions. On the other hand, convection is the transfer of heat energy by the actual movement of a fluid. In convection, hotter and less dense fluids rise while cooler and denser fluids sink, creating a circular motion that transfers heat energy from one place to another. Statement i is incorrect because both conduction and convection require a medium through which heat can be transferred. Statement iii is also incorrect because both thermal conduction and convection can occur in both solids and fluids. Therefore, the correct answer is ii and iii only.

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The formula for calculating electrical energy is given by: E = P x t Where E is the energy in joules, P is the power in watts, and t is the time in seconds. Firstly, we need to convert the time of 30 minutes to seconds. 30 minutes = 30 x 60 seconds = 1800 seconds The power of the bulb is given as 40W, and the voltage is given as 240V. We can use these values to calculate the current (I) flowing through the bulb: Power (P) = Voltage (V) x Current (I) Current (I) = Power (P) / Voltage (V) Current (I) = 40 / 240 = 0.1667 A (to 4 decimal places) Now we can use the formula for energy to calculate the heat generated: E = P x t E = 40 x 1800 E = 72000 J Therefore, the answer is 72000J. So, the correct option is 4) 72000J.

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The observation that is not an effect of surface tension is "water flowing out more easily than engine oil from a container." Surface tension is the cohesive force that exists between molecules at the surface of a liquid, which causes the surface to behave like an elastic film. This property of liquids has several effects, such as the formation of droplets, the spherical shape of mercury droplets, and the ability of small insects to walk on the surface of water. However, the flow rate of a liquid out of a container is not directly related to surface tension. It is primarily determined by the viscosity of the liquid, which is a measure of its resistance to flow. Engine oil is more viscous than water, so it flows more slowly out of a container. This difference in viscosity is why engine oil is thicker and more sluggish than water. In summary, the rate of flow of a liquid out of a container is determined by its viscosity and not surface tension, which only affects the surface properties of the liquid.

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The statement "There is always an uncertainty involved in any attempt to measure the position and momentum of an electron simultaneously" is known as the Heisenberg uncertainty principle. It states that it is impossible to simultaneously determine the precise position and momentum of a subatomic particle such as an electron. The more precisely we know the position of an electron, the less precisely we can know its momentum, and vice versa. This principle is a fundamental concept in quantum mechanics and has important implications for our understanding of the behavior of particles at the subatomic level.

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The change in the speed of the particle can be calculated using the formula: Δv = FΔt/m Where Δv is the change in velocity (speed), F is the external force applied, Δt is the time for which the force is applied, and m is the mass of the particle. Substituting the given values, we get: Δv = (100N) x (0.03s) / 0.15kg Δv = 20ms^-1 Therefore, the change in the speed of the particle is 20ms^-1. This means that the speed of the particle increased by 20 meters per second during the time when the external force was applied.

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In a nuclear reactor, chain reactions result from the release of neutrons. A nuclear chain reaction occurs when a neutron collides with a nucleus of a fissile material, such as uranium-235 or plutonium-239, which then splits into two smaller nuclei, releasing energy in the form of heat and more neutrons. These newly released neutrons can then collide with other fissile nuclei, causing them to split and release more neutrons, which continue the chain reaction. This chain reaction is carefully controlled in a nuclear reactor to produce a steady supply of heat that is used to generate electricity.

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The term "rectilinear acceleration" refers to the rate of change or increase in velocity along a straight-line path in a unit time. It is also known as linear acceleration or simply acceleration. Therefore, the correct option is: velocity along a straight-line path in a unit time.

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The phenomenon that is not a direct consequence of rectilinear propagation of light is diffraction of light. Rectilinear propagation of light means that light travels in a straight line in a uniform medium. Lunar and solar eclipses, images of objects in a pinhole camera, and shadows of opaque objects can all be explained by the principle of rectilinear propagation of light. However, diffraction of light is a bending of light waves around obstacles or through narrow slits, and it cannot be explained by the principle of rectilinear propagation of light. Diffraction is a result of the wave nature of light and occurs when light waves encounter obstacles that are comparable in size to the wavelength of light.

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The equation that relates initial velocity, final velocity, acceleration, time and distance is given by s = ut + 0.5at^2 + \(\frac{1}{2}\) at^2. We are given that the body is moving with an initial velocity U and attains a final velocity V within time t. Hence, the acceleration of the body can be calculated using the equation: a = (V - U) / t. Now, substituting the value of acceleration in the above equation, we get: s = Ut + \(\frac{1}{2}\)(V - U)t = \(\frac{V+U}{2}\)t Therefore, the expression for the distance, s covered by the body is s = (\(\frac{V+U}{2}\))t. Hence, option (C) is the correct answer.

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A capacitor is the component used for storing electric charges. A capacitor consists of two conductors separated by an insulator, called a dielectric. When a potential difference is applied across the conductors, electrons accumulate on one conductor and are depleted from the other, resulting in an electric field between the conductors. The insulator prevents the electrons from flowing between the conductors, so the charge is stored on the conductors, effectively storing electric charges. The ability of a capacitor to store charge is measured in farads, and capacitors are commonly used in electronic circuits for a variety of applications, including filtering, timing, and power storage.

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(a)(i) Mode of operation of a modern (Coolidge) X-ray tube

The tube is a highly evacuated glass envelope carrying a tungsten filament (cathode) at one end and a target-anode at the other, as shown in the labelled diagram below.

A low-voltage supply heats the tungsten filament, which by thermionic emission releases electrons. A concave focusing cup gathers these electrons into a narrow beam and directs them toward the target. A very high potential difference (the E.H.T., tens of kilovolts) is applied between the cathode and the anode, with the anode positive; this accelerates the electrons to a very high speed across the evacuated tube.

The fast electron beam strikes a small tungsten target embedded in a massive copper anode. On being suddenly stopped, the electrons give up their kinetic energy: only about 1 % is emitted as X-rays, which leave the tube through the window, while the greater part appears as heat. The copper anode and its cooling fins (aided in practice by circulating oil or water) conduct this heat away and prevent the target from melting.

The hardness (penetrating power) of the X-rays is controlled by the accelerating voltage across the tube, while the intensity (quantity of X-rays) is controlled by the filament heating current, which fixes the number of electrons produced.

(a)(ii) Energy transformations

\[\text{Electrical energy}\;\rightarrow\;\text{kinetic energy of the accelerated electrons}\;\rightarrow\;\text{X-ray (electromagnetic) energy}\;+\;\text{heat (thermal) energy at the target.}\]

(b) Definitions (as applied to X-rays)

(i) Hardness: the penetrating power of the X-rays. Hard X-rays have short wavelength and high frequency and penetrate deeply; the hardness increases with the accelerating potential difference across the tube.

(ii) Intensity: the energy radiated per unit area per unit time, i.e. the number of X-ray photons arriving per second on unit area. It depends on the number of electrons striking the target, and hence on the filament heating current.

(c)(i) Four uses of X-rays

1. Medical diagnosis (radiography) to reveal fractured bones and the condition of internal organs.
2. Radiotherapy, to destroy cancerous cells and tumours.
3. Detection of hidden flaws, cracks and air bubbles in metals and welded joints (industrial radiography).
4. Security screening of luggage at airports, and the study of crystal structure by X-ray crystallography.

(c)(ii) One hazard of over-exposure

Over-exposure to X-rays destroys living body cells, causing skin burns and cancer (for example leukaemia), as well as tissue damage, cataracts, sterility and genetic mutation.

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None

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(a) Two factors that affect the rate of diffusion:

• Temperature (higher temperature gives faster diffusion).
• The mass/size of the diffusing molecules (lighter molecules diffuse faster). The concentration gradient is also acceptable.

(b) Two examples illustrating the effects of surface tension:

• Small liquid drops (e.g. water or mercury) take up a spherical shape.
• A dry steel needle or a small insect can rest on the surface of water without sinking. (Capillary rise of liquid in a narrow tube is also acceptable.)

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(a) Boiling point of a liquid

The boiling point of a liquid is the constant temperature at which the liquid changes into vapour throughout its bulk, that is, the temperature at which the saturated vapour pressure of the liquid becomes equal to the external (atmospheric) pressure.

(b) Experiment to determine the boiling point of a small quantity of a liquid

Place the small quantity of the liquid in a clean ignition (test) tube and lower it into a beaker of water so that the liquid is well below the water surface. Support a thermometer with its bulb immersed in the liquid, and place a stirrer in the surrounding water. Stand the beaker on a wire gauze and tripod above a Bunsen burner.

Heat the water bath gently and stir the water continuously so that the heat reaches the small tube evenly. Watch the thermometer: its reading rises steadily and then becomes constant while the liquid is boiling vigorously. Record this steady temperature. The constant temperature at which the thermometer reading remains fixed while the liquid boils is the boiling point of the liquid.

(c) Mass of water that boils away

Data: mass of copper \(m_{Cu}=300\,\text{g}=0.300\,\text{kg}\), specific heat capacity of copper \(c_{Cu}=4.0\times10^{2}\,\text{J kg}^{-1}\text{K}^{-1}\), mass of water \(m_w=250\,\text{g}=0.250\,\text{kg}\), specific heat capacity of water \(c_w=4.2\times10^{3}\,\text{J kg}^{-1}\text{K}^{-1}\), specific latent heat of vaporization \(L=2.26\times10^{6}\,\text{J kg}^{-1}\).

Heat lost by the copper as it cools from \(950^{\circ}\text{C}\) to the final temperature \(100^{\circ}\text{C}\):

Heat needed to raise the \(250\,\text{g}\) of water from \(25^{\circ}\text{C}\) to \(100^{\circ}\text{C}\):

By conservation of energy, the heat remaining after warming the water is used to boil some of it into steam:

If \(m_v\) is the mass of water boiled away, then \(Q_{2}=m_v L\):

The mass of water that boils away is about \(10.3\,\text{g}\) (\(1.03\times10^{-2}\,\text{kg}\)).

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(a)(i) Wave motion. A wave motion is a disturbance that travels through a medium (or through space) transferring energy from one point to another without any net transfer of the particles of the medium.

(a)(ii) Two differences between a radio wave and a sound wave.

(b)(i) Experiment to determine the frequency of a note (resonance method using a burette).

The burette is clamped vertically and filled with water, so that the water and the tube walls enclose a short column of air at the open top. The vibrating tuning fork is held horizontally, with its prongs just above (not touching) the open mouth of the burette, as shown below.

The tap of the burette is opened so that water runs out slowly, gradually lengthening the air column. As the length increases, a position is reached where the sound suddenly becomes loudest; this is the first resonance. The length of the air column from the water surface to the open mouth is measured and recorded as \(L_1\).

Water is run out further, keeping the fork sounding over the mouth, until the sound is again loudest; this is the second resonance. This longer air column is measured and recorded as \(L_2\). The whole procedure is repeated a few times and the mean values of \(L_1\) and \(L_2\) taken.

Between the first and second resonances the air column has increased by exactly half a wavelength, so end-correction is eliminated:

The frequency of the note is then obtained from \(f=\dfrac{v}{\lambda}\), giving

where \(v\) is the known velocity of sound in air.

(b)(ii) Two precautions.

• The tuning fork should be struck gently on a soft rubber pad (not on a hard surface) and held with its prongs just above the mouth of the burette without touching it.
• The resonance lengths should be read at the position of loudest sound with the eye level with the water meniscus to avoid parallax error; the readings should be repeated and averaged.

(c) Fundamental frequency of a pipe closed at one end.

For a pipe closed at one end, the fundamental note has an air column equal to a quarter of a wavelength: \(L=\dfrac{\lambda}{4}\), so \(\lambda=4L\). With \(L=100\,\text{cm}=1.0\,\text{m}\),

The frequency of the fundamental note is 85 Hz.

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(a) Difference between plane polarized light and ordinary light: in plane (linearly) polarized light the vibrations of the electric field take place in only one plane perpendicular to the direction of travel, whereas in ordinary (unpolarized) light the vibrations occur in all planes perpendicular to the direction of travel.

(b) Two uses of polaroids:

• In sunglasses and camera filters to cut down glare from reflected light.
• In liquid-crystal displays (LCDs); also in polarimeters to measure sugar concentration, in stress analysis of materials, and in 3-D glasses.

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Mass of copper deposited (Faraday's first law): \(m=zIt\).

Volume of this copper: \(V=\dfrac{m}{\rho}\).

The copper is spread over the cathode area \(A=60\,\text{cm}^2=60\times10^{-4}\,\text{m}^2=6.0\times10^{-3}\,\text{m}^2\), and \(V=A\times d\), so

So the plating thickness \(d\approx1.1\times10^{-4}\,\text{m}\) (about \(0.11\,\text{mm}\)).

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Given \(u=250\,\text{ms}^{-1}\), \(\theta=30^{\circ}\), \(g=10\,\text{ms}^{-2}\).

(a) Total time of flight.

(b) Speed at maximum height. At the highest point the vertical component of velocity is zero, so the speed there is just the (unchanged) horizontal component:

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(a) Thermionic emission: the emission (giving off) of electrons from the surface of a metal when it is heated to a high temperature. The heat gives the free surface electrons enough kinetic energy to overcome the work function (the surface attractive forces) and escape from the metal.

(b) Two applications of electrical conduction through gases:

• Fluorescent tubes and neon/discharge advertising signs.
• Sodium and mercury-vapour street lamps (the cathode-ray/television tube and lightning are also acceptable examples).

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(a) Conditions of equilibrium for coplanar parallel forces

A number of coplanar parallel forces are in equilibrium when:

1. The algebraic sum of the forces is zero, i.e. the sum of the forces acting in one direction equals the sum of the forces acting in the opposite direction (the resultant force is zero).
2. The algebraic sum of the moments of the forces about any point is zero, i.e. the sum of the clockwise moments about the point equals the sum of the anticlockwise moments about that same point (the principle of moments).

(b) Balancing a metre rule

The rule balances by itself at the \(48\,\text{cm}\) mark, so the whole weight of the rule acts at the \(48\,\text{cm}\) mark.

(i) Mass of the metre rule

With the \(60\,\text{g}\) body hung at the \(6\,\text{cm}\) mark, the new balance point (fulcrum) is at the \(30\,\text{cm}\) mark. The body sits on one side of the fulcrum and the weight of the rule acts on the other side. Taking moments about the \(30\,\text{cm}\) fulcrum:

The mass of the metre rule is 80 g.

(ii) New balance point with the body at the 13 cm mark

Let the new balance point be at the \(x\,\text{cm}\) mark. The body (\(60\,\text{g}\)) now acts at \(13\,\text{cm}\) and the rule's weight (\(80\,\text{g}\)) still acts at \(48\,\text{cm}\). Taking moments about the fulcrum at \(x\):

The new balance point is 33 cm from the zero end.

(c) Pulling a box up an inclined plane

Box mass \(=70\,\text{kg}\), so its weight \(W=mg=70\times10=700\,\text{N}\); length of plane \(L=5\,\text{m}\); height of platform \(h=2.5\,\text{m}\); frictional force \(F=1000\,\text{N}\); angle of incline \(\theta=30^{\circ}\).

(i) Diagram of the forces acting on the box while in motion

The four forces acting on the box are: its weight \(W\) acting vertically downwards; the normal (reaction) force \(N\) acting perpendicular to the surface of the plane; the effort \(E\) applied up along the plane; and the frictional force \(F\) acting down along the plane, opposing the upward motion.

(ii) Calculations

I. Minimum effort applied in pulling up the box

Since the box moves up at uniform (constant) speed, the effort must balance the component of the weight along the plane together with the friction acting down the plane:

The minimum effort is 1350 N.

II. Velocity ratio of the plane

(This agrees with \(\dfrac{\text{length}}{\text{height}}=\dfrac{5}{2.5}=2\).) The velocity ratio is 2.

III. Force ratio (mechanical advantage) of the plane

The force ratio of the plane is 0.52.

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Length \(L=5.0\,\text{m}\), diameter \(=2.0\,\text{mm}\Rightarrow r=1.0\,\text{mm}=1.0\times10^{-3}\,\text{m}\), extension \(e=0.25\,\text{mm}=0.25\times10^{-3}\,\text{m}\), force \(F=50\,\text{N}\).

(a) Stress \(=\dfrac{F}{A}\), where \(A=\pi r^2\).

(b) Strain \(=\dfrac{\text{extension}}{\text{original length}}\).

(Strain has no unit as it is a ratio of two lengths.)

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(a) Tensile stress: the stretching force acting per unit cross-sectional area of a material, \(\text{stress}=\dfrac{F}{A}\). Unit: \(\text{Nm}^{-2}\) (pascal).

(b) Tensile strain: the extension produced per unit original length of the material, \(\text{strain}=\dfrac{e}{L}\). It has no unit.

(c) Yield point: the point on the stress-strain (or load-extension) graph beyond which the material no longer returns to its original length when the load is removed; it begins to undergo permanent (plastic) deformation.

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(a) How a step-down transformer works

A transformer consists of two coils, a primary (input) coil and a secondary (output) coil, wound on a common laminated soft-iron core. In a step-down transformer the primary coil has more turns than the secondary coil (\(N_p > N_s\)).

When an alternating voltage is applied to the primary coil, the alternating current flowing in it sets up a continuously changing magnetic flux in the soft-iron core. The core carries this changing flux round to the secondary coil, so the secondary is linked by the same changing flux. By electromagnetic induction, the changing flux induces an alternating e.m.f. in the secondary coil. Because the secondary has fewer turns than the primary, the e.m.f. induced in it is smaller than the applied primary voltage, i.e. the voltage is stepped down (while the output current is correspondingly stepped up).

The simple diagram below shows the arrangement:

(b)(i) Three ways energy is lost in a transformer

1. Eddy-current loss in the iron core.
2. Hysteresis loss in the iron core.
3. Copper (resistance/heating) loss in the windings.

(b)(ii) How each loss is minimized

(c) Calculations

Efficiency \(=95\%=0.95\); lamp (secondary side) rated \(P_{out}=60\,\text{W},\; V_s=220\,\text{V}\); supply \(V_p=4400\,\text{V}\).

(i) Ratio of primary turns to secondary turns.

For a transformer the turns ratio equals the voltage ratio:

Therefore \(\;N_p:N_s = \mathbf{20:1}.\)

(ii) Current taken from the main circuit.

Using efficiency \(=\dfrac{\text{output power}}{\text{input power}}=\dfrac{V_s I_s}{V_p I_p}\):

The current taken from the mains is \(I_p \approx \mathbf{0.014\,A}\;(1.44\times10^{-2}\,\text{A},\ \text{about }14.4\,\text{mA}).\)

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(a) Electrolysis: the chemical decomposition of an electrolyte (in molten or aqueous solution) brought about by passing an electric current through it.

(b) Electrolyte: a compound which, when molten or dissolved in water, conducts electricity and is chemically decomposed by it (because it contains free-moving ions).

(c) Electrode: a conductor (rod or plate) through which the electric current enters or leaves the electrolyte. The one connected to the positive terminal is the anode; the one connected to the negative terminal is the cathode.

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Horizontal projection: initial horizontal speed \(u=4\,\text{ms}^{-1}\), horizontal range \(x=25\,\text{m}\), \(g=10\,\text{ms}^{-2}\).

Horizontal motion (constant velocity) gives the time of flight:

Vertical motion (falling from rest, initial vertical velocity zero) gives the height of the tower:

So the tower is about \(195\,\text{m}\) high.