WAEC SSCE - Physics - 2019
Pregunta 1 Informe
Which of the following thermometers is used to measure the temperature of the human body?
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Pregunta 2 Informe
The diagram above illustrates an object moving in a circular path at a constant speed. Which of the arrows indicates the direction of linear velocity?
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Pregunta 3 Informe
Which property of a wave remains constant when the wave travels from one medium into another?
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Pregunta 4 Informe
A loaded spring is set in simple harmonic motion. The force that tends to restore the load to its equilibrium position is
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Pregunta 5 Informe
Which of the following materials does not serve as a safety device in electrical circuits?
Detalles de la respuesta
Connecting wires, earth wires, and fuses serve as safety devices in electrical circuits, while switches are not safety devices but rather control devices that allow the flow of current to be turned on or off. Therefore, the correct answer is switch.
Pregunta 6 Informe
Which of the following properties is not exhibited by sound waves?
Detalles de la respuesta
The property that is not exhibited by sound waves is polarization. Polarization is a property of transverse waves, which are waves that vibrate perpendicular to the direction of their motion. Sound waves, on the other hand, are longitudinal waves, which means that they vibrate parallel to the direction of their motion. Since sound waves are not transverse, they cannot exhibit polarization. Diffraction, interference, and reflection are all properties of sound waves. Diffraction is the bending of sound waves around obstacles or through openings. Interference occurs when two or more sound waves interact with each other, either constructively or destructively. Reflection is the bouncing back of sound waves when they hit a surface. In summary, sound waves are longitudinal waves and cannot exhibit polarization, but they can exhibit other properties such as diffraction, interference, and reflection.
Pregunta 8 Informe
If the efficiency of a transformer is 100%, which of the following equations would be correct?
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Pregunta 9 Informe
The diagram above represents an experimental set-up for verifying?
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Pregunta 10 Informe
A transverse pulse of frequency 9 Hz traves 4.5m in 0.6 s. Calculate the wavelength of the pulse.
Detalles de la respuesta
The formula for the speed of a wave is given by: v = λf where v is the speed of the wave, λ is the wavelength, and f is the frequency. We are given the frequency of the pulse as 9 Hz and the time it takes to travel a distance of 4.5 m as 0.6 s. We can use these values to calculate the speed of the pulse as follows: v = d/t = 4.5 m/0.6 s = 7.5 m/s Now, we can use the formula v = λf to calculate the wavelength of the pulse: λ = v/f = 7.5 m/s / 9 Hz = 0.83 m Therefore, the wavelength of the pulse is 0.83 m. Answer option (C) is correct.
Pregunta 11 Informe
Which of the following graphs of a charge Q against potential difference V across the capacitor is correct?
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Pregunta 12 Informe
A device consumes 100 W of power when connected to a 120 V source. Calculate its resistance.
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Pregunta 13 Informe
Which of the following liquids has the highest surface tension?
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Pregunta 14 Informe
Which of the following instruments can be used to compare the magnitudes of charges on two given bodies?
Detalles de la respuesta
The instrument that can be used to compare the magnitudes of charges on two given bodies is the Gold-leaf electroscope. When a charged object is brought close to the electroscope, the charge is transferred to the metal leaves causing them to repel each other. By comparing the extent of separation of the leaves with a known charge, the magnitude of the charge on the given bodies can be determined. Electrophorus and ebonite rods are used for charging objects, and proof planes are used to transfer charge from one body to another.
Pregunta 15 Informe
Which of the following quantities is a vector?
Detalles de la respuesta
Out of the given options, the quantity that is a vector is momentum. A vector quantity has both magnitude and direction. Momentum is the product of mass and velocity, and it has both magnitude and direction. On the other hand, volume, energy, and speed are scalar quantities that have only magnitude but no direction associated with them.
Pregunta 16 Informe
The diagram above illustrates a meter bridge circuit under balanced condition. Determine the value of x.
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Pregunta 17 Informe
The time rate of increase in velocity is called
Detalles de la respuesta
The time rate of increase in velocity is called acceleration. Acceleration is a measure of how quickly an object changes its velocity, and it is calculated as the change in velocity per unit of time. Velocity is a vector quantity that describes an object's speed and direction of motion. If an object's velocity changes over time, either in magnitude (speed) or direction, it is said to be accelerating. The acceleration of an object is the rate at which its velocity changes, and it is a measure of the force acting on an object. Force is a vector quantity that describes the interaction between two objects that results in a change in motion. Force is proportional to acceleration, so a greater force will result in a greater acceleration. Momentum is a vector quantity that describes an object's mass and velocity. Momentum is conserved in an isolated system, meaning that the total momentum of the system remains constant, although the momentum of individual objects within the system may change. Speed is a scalar quantity that describes the magnitude of an object's velocity, without considering its direction. Speed is a measure of how quickly an object is moving, but it does not take into account changes in direction. Therefore, the time rate of increase in velocity is called acceleration.
Pregunta 18 Informe
The wire of a platinum resistance thermometer has d resistance of 3.5\(\Omega\) at 0 °C and 10.52\(\Omega\) at 100°C. Calculate the temperature of the wire when its resistance is 7.5\(\Omega\).
Detalles de la respuesta
The resistance (R) of a wire is proportional to the temperature (T) in degrees Celsius. The equation of the resistance-temperature relationship is given by: R = R0 (1 + αT) Where R0 is the resistance at 0°C, α is the temperature coefficient of resistance and T is the temperature in degrees Celsius. To solve this problem, we can use the resistance-temperature relationship to find α, and then use it to find the temperature at the given resistance. First, we need to find the value of α. We can use the two resistance values given to set up two equations: R1 = R0 (1 + αT1) R2 = R0 (1 + αT2) where R1 and R2 are the resistances at temperatures T1 and T2, respectively. Substituting the given values: 3.5 = R0 (1 + α(0)) 10.52 = R0 (1 + α(100)) Solving for R0: 3.5 = R0 1 + α(100) = 10.52/R0 Rearranging the second equation: α = (10.52/R0 - 1)/100 Substituting R0 = 3.5: α = (10.52/3.5 - 1)/100 = 0.0032/°C Now we can use the resistance-temperature relationship to find the temperature at the given resistance: R = R0 (1 + αT) 7.5 = 3.5 (1 + 0.0032T) Solving for T: T = (7.5/3.5 - 1)/0.0032 = 57°C Therefore, the temperature of the wire when its resistance is 7.5Ω is 57°C. The correct option is 57 \(^o\)C.
Pregunta 19 Informe
Which of the following cases cannot produce total internal reflection? A light ray travelling from
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Pregunta 20 Informe
In an elastic collision, momentum is conserved as well as well as?
Detalles de la respuesta
In an elastic collision, both momentum and kinetic energy are conserved. Momentum is defined as the product of an object's mass and velocity, and it is a measure of an object's motion. In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision. This means that the momentum of the objects involved in the collision is conserved. Kinetic energy is defined as the energy an object possesses due to its motion. In an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. This means that the kinetic energy of the objects involved in the collision is conserved. In contrast, potential energy is a measure of an object's potential to do work, and it is related to an object's position or configuration. In an elastic collision, potential energy is not conserved because the objects change position or configuration during the collision. Therefore, in an elastic collision, momentum and kinetic energy are conserved, while potential energy is not conserved.
Pregunta 21 Informe
The vacuum in a thermoflask reduces heat loss resulting from
Detalles de la respuesta
The vacuum in a thermoflask reduces heat loss resulting from conduction and convection by creating a space with no air molecules between the inner and outer layers of the flask, which minimizes heat transfer through these processes. Additionally, the reflective surfaces of the inner layer further minimize heat loss by reflecting any radiation back into the flask.
Pregunta 22 Informe
A small amount of air is introduced into the vacuum above the mercury in a mercury barometer tube. The mercury level goes down because the air molecules
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Pregunta 23 Informe
The graph above illustrates the variation of temperature \(\theta\) with time (t) for a solid that is being heated. Which processes take place at segments P and Q respectively?
Detalles de la respuesta
The graph shows the change in temperature of a solid as it is heated over time. At segment P, the temperature remains constant despite the application of heat. This is because the energy is being used to break the bonds between the molecules in the solid, rather than increasing their kinetic energy and temperature. This process is called melting, which is the transition from solid to liquid phase. At segment Q, the temperature again remains constant, but this time at a higher level than at segment P. This is because the energy is being used to break the bonds between the molecules in the liquid, rather than increasing their kinetic energy and temperature. This process is called boiling, which is the transition from liquid to gas phase. Therefore, the correct answer is "Melting and boiling".
Pregunta 24 Informe
The mass of a load is doubled while the force acting on it is halved. The resulting acceleration of the load is
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Pregunta 25 Informe
The nucleon and proton numbers of a neutral atom of an element are 238 and 92 respectively. Determine the number of neutrons in the atom.
Detalles de la respuesta
The nucleon number of an atom is the total number of protons and neutrons in its nucleus, while the proton number is the number of protons. Therefore, to determine the number of neutrons in an atom, we can subtract the proton number from the nucleon number. In this case, the nucleon number is 238 and the proton number is 92. Number of neutrons = Nucleon number - Proton number Number of neutrons = 238 - 92 Number of neutrons = 146 Therefore, the answer is: 146 neutrons.
Pregunta 26 Informe
A body of mass 2 kg is released from a point 100 m above the ground. Calculate its kinetic energy 80m from the point of release.
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Pregunta 27 Informe
An a.c. the generator can be converted to a d.c. generator by replacing the
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Pregunta 28 Informe
The induced current in a coil always flows in a direction so as to oppose the change that causes it. This statement is known as
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Lenz's law states that the induced current in a coil always flows in a direction so as to oppose the change that causes it. For example, if there is a change in magnetic flux passing through a coil, it will induce an electromotive force (EMF) and a current will start flowing in the coil. This induced current will create a magnetic field that opposes the original change in magnetic flux. Lenz's law is a consequence of the law of conservation of energy and is a fundamental law in electromagnetism.
Pregunta 29 Informe
Calculate the quantity of heat needed to change the temperature of 60g of ice at 0 °C to 80 °C. [specific latent heat of fusion of ice= 3.36 x 10\(^5\) Jkg\(^{-1}\) specific heat capacity of water 4.2 x 10\(^3\) J kg\(^{-1}\) K\(^{-1}\)]
Detalles de la respuesta
The heat needed to change the temperature of 60g of ice at 0°C to 80°C can be calculated using the equation for heat transfer: Q = m * c * ΔT Where Q is the heat transferred, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature. First, the heat needed to melt the ice can be calculated using the specific latent heat of fusion: Qfusion = m * Lf Where Lf is the specific latent heat of fusion. Qfusion = 60g * 3.36 x 10^5 J/kg = 2.016 x 10^5 J Next, the heat needed to raise the temperature of the water from 0°C to 80°C can be calculated using the specific heat capacity of water: Qheat = m * c * ΔT Qheat = 60g * 4.2 x 10^3 J/kg/K * 80°C = 2.016 x 10^5 J The total heat needed to change the temperature of the ice to 80°C is the sum of the heat needed to melt the ice and the heat needed to raise the temperature of the water: Q = Qfusion + Qheat = 2.016 x 10^5 J + 2.016 x 10^5 J = 4.032 x 10^5 J = 40.32 kJ Therefore, the quantity of heat needed to change the temperature of 60g of ice at 0°C to 80°C is 40.32 kJ.
Pregunta 30 Informe
Which of the following statements about a moving object is correct?
Detalles de la respuesta
The correct statement about a moving object is "At a steady velocity, the resultant force acting on it must be equal to zero." This means that when an object is moving at a constant speed in a straight line (i.e., at a steady velocity), the net force acting on it is zero. This does not mean that there are no forces acting on the object, but rather that the forces are balanced such that they cancel each other out. If the object were to accelerate or decelerate, there would be a net force acting on it. Similarly, air resistance can be a force acting on the object but it does not need to be zero for the object to move at a steady velocity, as long as it is balanced by other forces.
Pregunta 31 Informe
Which of the following graphs gives the correct relationship between energy and mass when mass is converted to energy.
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Pregunta 32 Informe
An instrument used to measure relative humidity is the?
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An instrument used to measure relative humidity is the hygrometer. Hygrometers measure the amount of water vapor present in the air, which is an indicator of the air's relative humidity. Hygrometers can be mechanical or electronic, and they may measure relative humidity directly or calculate it from measurements of temperature and dew point.
Pregunta 33 Informe
In which of the following media is the speed of sound the least?
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Pregunta 34 Informe
A ray of light traveling from a rectangular glass block of refractive index 1.5 into air strikes the block at an angle of incidence of 30. Calculate its angle of refraction.
Detalles de la respuesta
The angle of refraction of a ray of light traveling from one medium to another can be calculated using Snell's law. Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction of the two media. Mathematically, this can be expressed as: sin θincidence / sin θrefraction = n1 / n2 Where θincidence is the angle of incidence, θrefraction is the angle of refraction, n1 is the index of refraction of the first medium, and n2 is the index of refraction of the second medium. Given the angle of incidence of 30° and the indices of refraction of 1.5 for the rectangular glass block and 1.0 for air, we can calculate the angle of refraction as follows: sin θincidence / sin θrefraction = n1 / n2 sin 30° / sin θrefraction = 1.5 / 1.0 sin θrefraction = sin 30° / 1.5 θrefraction = sin-1(sin 30° / 1.5) = 19.47° Therefore, the angle of refraction of the ray of light traveling from the rectangular glass block into air is approximately 19.47°.
Pregunta 35 Informe
Which of the following statements about a neutral atom is correct? The
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A neutral atom is an atom that has an equal number of protons and electrons. The protons are located in the nucleus of the atom, along with the neutrons, and the electrons occupy the space surrounding the nucleus. The number of protons in the nucleus of an atom determines the chemical element to which it belongs. A neutral atom has no overall charge, meaning that the positive charge of the protons is balanced by the negative charge of the electrons. Hence, the correct statement about a neutral atom is that the number of protons is equal to that of electrons.
Pregunta 36 Informe
The anomalous expansion of water occurs in the range
Detalles de la respuesta
The anomalous expansion of water refers to a phenomenon in which water expands instead of contracting as it cools below a certain temperature. This is a unique property of water, as most substances contract when they cool. The temperature range in which the anomalous expansion of water occurs is from 4°C to 0°C. As water cools below 4°C, it starts to contract, but as it approaches 0°C, it expands again. This means that at 0°C, water is actually less dense than it is at 4°C. Therefore, the answer is: 0°C to 4°C. This is the temperature range in which the anomalous expansion of water occurs.
Pregunta 37 Informe
A freshly demagnetized bar magnet is placed in the East-West direction to ensure that
Detalles de la respuesta
Placing a freshly demagnetized bar magnet in the East-West direction helps ensure that the molecular magnets within the magnet remain randomly arranged. This is because, in this position, the magnet is perpendicular to the Earth's magnetic field, which would otherwise affect the alignment of the molecular magnets. By keeping the molecular magnets in a random arrangement, the magnet can be effectively demagnetized and can be magnetized again in a desired direction.
Pregunta 38 Informe
A rectangular piece of iron measuring 4 cm by 3 cm at 20\(^o\)C is heated until its temperature increases by 100 C. Calculate the new area of the metal. [Linear expansivity of iron is 1.2x 10\(^{-5}\) K\(^{-1}\)]
Detalles de la respuesta
The change in the area of a rectangular piece of iron due to an increase in temperature can be calculated using the formula for linear expansion: ΔL = α * L * ΔT Where ΔL is the change in length, α is the linear expansivity, L is the original length, and ΔT is the change in temperature. The new length of the iron can be calculated by adding the change in length to the original length: L' = L + ΔL The new area of the iron can be calculated by using the new length and width: A' = L' * W First, the change in length of the iron can be calculated for both the length and the width: ΔL = α * L * ΔT = 1.2 x 10^-5 K^-1 * 4 cm * 100°C = 4.8 x 10^-3 cm L' = L + ΔL = 4 cm + 4.8 x 10^-3 cm = 4.0048 cm ΔL = α * L * ΔT = 1.2 x 10^-5 K^-1 * 3 cm * 100°C = 3.6 x 10^-3 cm W' = W + ΔL = 3 cm + 3.6 x 10^-3 cm = 3.0036 cm The new area of the iron can be calculated using the new length and width: A' = L' * W' = 4.0048 cm * 3.0036 cm = 12.0288 cm^2 Therefore, the new area of the metal after a temperature increase of 100°C is 12.0288 cm^2.
Pregunta 39 Informe
An 800 kg car moving at 80 km hr\(^{-1}\) collides with a 1200 kg car moving at 40 km hr\(^{-1}\) in the same direction. If the cars stick together, calculate their common velocity.
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Pregunta 40 Informe
Which of the following waves is not mechanical?
Detalles de la respuesta
The main idea of this question is to identify a type of wave that is not mechanical. Mechanical waves require a medium to travel through, such as a solid, liquid or gas. Sound waves and water waves are examples of mechanical waves. On the other hand, radio waves are a type of electromagnetic wave and do not require a medium to travel through. Therefore, the answer to the question is "Radio waves."
Pregunta 41 Informe
The area under a velocity-time graph represents
Detalles de la respuesta
The area under a velocity-time graph represents the distance traveled by an object. Velocity is the rate of change of displacement with respect to time, which means it indicates how far an object has traveled in a specific amount of time. The area under the velocity-time graph shows the product of velocity and time, which is distance. To calculate the distance traveled, we need to find the area enclosed by the velocity-time graph, which may consist of different shapes depending on the motion of the object. For example, if the object is moving at a constant velocity, the area would be a rectangle. If the object is accelerating, the area would be a triangle or a trapezoid. Therefore, the correct answer is "distance".
Pregunta 42 Informe
Which of the following devices is used for storing electric charges?
Detalles de la respuesta
A capacitor is a device that is used for storing electric charges. It consists of two conductive plates separated by an insulating material called a dielectric. When a voltage is applied to the capacitor, electric charges are stored on the plates. The amount of charge that can be stored on a capacitor is proportional to the voltage applied and the capacitance of the capacitor, which is a measure of its ability to store electric charges. A transformer is a device that is used to change the voltage of an alternating current (AC) electrical supply. It works by using electromagnetic induction to transfer energy from one coil of wire to another. An ammeter is a device that is used to measure the current in an electrical circuit. It works by detecting the flow of electric charges through a conductor and measuring the resulting electric potential difference. A potentiometer is a device that is used to measure the potential difference (voltage) between two points in an electrical circuit. It works by comparing the voltage being measured to a reference voltage, and it can also be used to adjust the voltage in a circuit. Therefore, a capacitor is the device used for storing electric charges.
Pregunta 43 Informe
Which of the following statements is the correct reason for using soft iron in making the armature or an electric bell?
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Pregunta 44 Informe
An electron of mass 9.1 x 10\(^{-31}\) kg moves with a speed of 2.0 x 10\(^6\) ms\(^{-1}\) round the nucleus of an atom in a Circular path of radius 6.1 x 10(^{11}\) m. Determine the angular speed of the electron.
Detalles de la respuesta
The angular speed of the electron can be determined using the formula: ω = v / r where ω is the angular speed, v is the velocity of the electron, and r is the radius of the circular path. Substituting the given values, we get: ω = (2.0 x 10^6 m/s) / (6.1 x 10^11 m) ω = 3.28 x 10^(-5) rad/s Therefore, the angular speed of the electron is 3.28 x 10^(-5) rad/s. Hence, the correct option is: 3.28 x 10^16 rad s^(-1)
Pregunta 45 Informe
When ultraviolet light is incident on certain metallic p articles are emitted. These particles are called
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Pregunta 46 Informe
An electron of mass 9.1 x 10\(^{-31}\) kg moves with a speed of 2.0 x 10\(^6\) ms\(^{-1}\) round the nucleus of an atom in a Circular path of radius
6.1 x 10\(^{11}\) m. Calculate the centripetal force acting on the electron.
Detalles de la respuesta
The centripetal force acting on an electron moving in a circular path around the nucleus of an atom is given by the equation: F = (mv\(^2\))/r Where F is the centripetal force, m is the mass of the electron, v is the velocity of the electron, and r is the radius of the circular path. Substituting the given values into the equation, we have: F = (9.1 x 10\(^{-31}\) kg) x (2.0 x 10\(^6\) ms\(^{-1}\))\(^2\) / (6.1 x 10\(^{11}\) m) F = 6.0 x 10\(^{-8}\) N Therefore, the correct answer is: 6.0 x 10\(^{-8}\) N.
Pregunta 47 Informe
Two bodies of masses 3.0 kg and 2.0 kg are separated by a distance of 50 cm. Calculate the force of attraction between them. [G = 6.67 x 10\(^{-11}\) Nm\(^2\) kg\(^2\)]
Detalles de la respuesta
We can use the formula for gravitational force between two masses: F = (G x m1 x m2)/r^2 where F = force of attraction G = gravitational constant m1 and m2 = masses of the bodies r = distance between the centers of the two bodies Plugging in the given values, we get: F = (6.67 x 10^-11 Nm^2/kg^2) x (3.0 kg) x (2.0 kg) / (0.50 m)^2 F = 1.6 x 10^-9 N Therefore, the force of attraction between the two bodies is 1.6 x 10^-9 N. Answer: 1.6 x 10^-9 N
Pregunta 48 Informe
In the diagram above, the time taken to trace a wave between P and Q is
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Pregunta 49 Informe
Which of the following characteristics of waves can a ripple tank be used to demonstrate?
I. Reflection
II. Refraction
III. Diffraction
Detalles de la respuesta
A ripple tank is a scientific apparatus that can be used to demonstrate the behavior of waves. It produces waves on the surface of water that can be observed and studied. I. Reflection: When waves encounter a boundary or obstacle, they can bounce back or reflect. A ripple tank can be used to demonstrate reflection by placing a barrier in the path of the waves and observing how they bounce back. II. Refraction: Waves can also change direction or bend when they pass through a medium with a different density or refractive index. A ripple tank can demonstrate refraction by placing a block in the path of the waves and observing how they change direction as they pass through it. III. Diffraction: When waves encounter an obstacle with a small opening or gap, they can bend and spread out, creating a diffraction pattern. A ripple tank can demonstrate diffraction by creating waves with a single source and observing how they spread out as they pass through a gap or opening. Therefore, the correct answer is "I, II and III".
Pregunta 50 Informe
(a) (i) Define force and state its S.I unit.
(ii) List the two types of solid friction.
(b) A car travelling at a constant speed of \(30\ \mathrm{ms}^{-1}\) for \(20\ \mathrm{s}\) was suddenly decelerated when the driver sighted a pot-hole. It took the driver \(6\ \mathrm{s}\) to get to the pot-hole with a reduced speed of \(18\ \mathrm{ms}^{-1}\). He maintained the steady speed for another \(10\ \mathrm{s}\) to cross the pot-hole. The brakes were then applied and the car came to rest \(5\ \mathrm{s}\) later.
(i) Draw the velocity-time graph for the journey.
(ii) Calculate the deceleration during the last \(5\ \mathrm{s}\) of the journey.
(iii) Calculate the total distance covered.
(a) (i) Force is a push or pull which changes, or tends to change, the state of rest or uniform motion of a body in a straight line.
The S.I. unit of force is the newton (N).
(ii) The two types of solid friction are:
- Static friction;
- Dynamic (sliding or kinetic) friction.
(b) (i) Velocity-time graph
The successive points plotted are t time tand tvelocity tas follows: \[(0,30),\ (20,30),\ (26,18),\ (36,18),\ (41,0).\]
(ii) Deceleration during the last 5 s
For the final stage,
\[ a=\frac{v-u}{t}=\frac{0-18}{5}=-3.6\ \text{m s}^{-2}. \]
Therefore, the deceleration is \(3.6\ \text{m s}^{-2}\).
(iii) Total distance covered
The total distance is the area under the velocity-time graph.
| Part of journey | Area under graph | Distance (m) |
|---|---|---|
| \(0\) to \(20\) s | \(30\times20\) | \(600\) |
| \(20\) to \(26\) s | \(\frac{1}{2}(30+18)\times6\) | \(144\) |
| \(26\) to \(36\) s | \(18\times10\) | \(180\) |
| \(36\) to \(41\) s | \(\frac{1}{2}\times18\times5\) | \(45\) |
\[ \text{Total distance}=600+144+180+45=\boxed{969\ \text{m}}. \]
Detalles de la respuesta
(a) (i) Force is a push or pull which changes, or tends to change, the state of rest or uniform motion of a body in a straight line.
The S.I. unit of force is the newton (N).
(ii) The two types of solid friction are:
- Static friction;
- Dynamic (sliding or kinetic) friction.
(b) (i) Velocity-time graph
The successive points plotted are t time tand tvelocity tas follows: \[(0,30),\ (20,30),\ (26,18),\ (36,18),\ (41,0).\]
(ii) Deceleration during the last 5 s
For the final stage,
\[ a=\frac{v-u}{t}=\frac{0-18}{5}=-3.6\ \text{m s}^{-2}. \]
Therefore, the deceleration is \(3.6\ \text{m s}^{-2}\).
(iii) Total distance covered
The total distance is the area under the velocity-time graph.
| Part of journey | Area under graph | Distance (m) |
|---|---|---|
| \(0\) to \(20\) s | \(30\times20\) | \(600\) |
| \(20\) to \(26\) s | \(\frac{1}{2}(30+18)\times6\) | \(144\) |
| \(26\) to \(36\) s | \(18\times10\) | \(180\) |
| \(36\) to \(41\) s | \(\frac{1}{2}\times18\times5\) | \(45\) |
\[ \text{Total distance}=600+144+180+45=\boxed{969\ \text{m}}. \]
Pregunta 51 Informe
%IMG%
The diagram above illustrates a structure of a typical photocell.
(i) Identify each of the parts labelled A and B.
(ii) State one function each of A and B.
(iii) Einstein’s photoelectric equation can be written as \(E = hf - W_o\). State what each of the terms \(E\), \(hf\) and \(W_o\) represent.
(b) A photon is incident on a metal whose work function is \(1.32\ \text{eV}\). An electron is emitted from the surface with a maximum kinetic energy of \(1.97\ \text{eV}\). Calculate the frequency of the photon. \([1\ \text{eV} = 1.6 \times 10^{-19}\ \text{J}]\)
(c)(i) Define half-life of a radioactive element.
(ii) Sketch a graph of the relation \(N = N_0e^{-\lambda t}\) and indicate the half-life.
(a)(i) Parts of the photocell (standard evacuated photocell): A is the photocathode (emitter) - a curved metal plate coated with a photosensitive material. B is the anode (collector) - a small metal rod or ring placed in front of the cathode.
(a)(ii) Functions: A (photocathode) emits electrons when light of sufficient frequency falls on it. B (anode) collects the emitted photoelectrons, so completing the circuit and allowing a photocurrent to flow.
(a)(iii) Terms in Einstein's equation \(E = hf - W_0\): \(E\) is the maximum kinetic energy of the emitted photoelectron; \(hf\) is the energy of the incident photon (h = Planck's constant, f = frequency); \(W_0\) is the work function, the minimum energy needed to release an electron from the metal surface.
(b) Frequency of the photon: Photon energy \(= KE_{max} + W_0 = 1.97 + 1.32 = 3.29\,\text{eV}\).
\[ E = 3.29\times1.6\times10^{-19} = 5.264\times10^{-19}\,\text{J}. \]
\[ f = \frac{E}{h} = \frac{5.264\times10^{-19}}{6.6\times10^{-34}} \approx 7.98\times10^{14}\,\text{Hz}. \]
(c)(i) Half-life: The half-life of a radioactive element is the time taken for half the atoms (nuclei) originally present in a sample to decay.
(c)(ii) Graph of \(N = N_0 e^{-\lambda t}\): Plot \(N\) (number of undecayed nuclei) on the vertical axis against time \(t\). The curve starts at \(N_0\) and falls exponentially towards zero. The half-life \(t_{1/2}\) is read on the time axis at the point where \(N = N_0/2\).
Detalles de la respuesta
(a)(i) Parts of the photocell (standard evacuated photocell): A is the photocathode (emitter) - a curved metal plate coated with a photosensitive material. B is the anode (collector) - a small metal rod or ring placed in front of the cathode.
(a)(ii) Functions: A (photocathode) emits electrons when light of sufficient frequency falls on it. B (anode) collects the emitted photoelectrons, so completing the circuit and allowing a photocurrent to flow.
(a)(iii) Terms in Einstein's equation \(E = hf - W_0\): \(E\) is the maximum kinetic energy of the emitted photoelectron; \(hf\) is the energy of the incident photon (h = Planck's constant, f = frequency); \(W_0\) is the work function, the minimum energy needed to release an electron from the metal surface.
(b) Frequency of the photon: Photon energy \(= KE_{max} + W_0 = 1.97 + 1.32 = 3.29\,\text{eV}\).
\[ E = 3.29\times1.6\times10^{-19} = 5.264\times10^{-19}\,\text{J}. \]
\[ f = \frac{E}{h} = \frac{5.264\times10^{-19}}{6.6\times10^{-34}} \approx 7.98\times10^{14}\,\text{Hz}. \]
(c)(i) Half-life: The half-life of a radioactive element is the time taken for half the atoms (nuclei) originally present in a sample to decay.
(c)(ii) Graph of \(N = N_0 e^{-\lambda t}\): Plot \(N\) (number of undecayed nuclei) on the vertical axis against time \(t\). The curve starts at \(N_0\) and falls exponentially towards zero. The half-life \(t_{1/2}\) is read on the time axis at the point where \(N = N_0/2\).
Pregunta 52 Informe
(a) Define diffusion
(b) State two factors that affect the rate of diffusion
(a) Diffusion: Diffusion is the net movement of molecules of a substance from a region of higher concentration to a region of lower concentration, as a result of the random motion of the molecules, until the molecules are evenly distributed.
(b) Two factors that affect the rate of diffusion:
- Temperature - a higher temperature gives the molecules greater average kinetic energy, so they move faster and diffuse more rapidly.
- Relative molecular mass (density) of the substance - lighter (less dense) molecules move faster and therefore diffuse more quickly than heavier ones.
(The concentration gradient and the medium of diffusion, gas versus liquid, are also acceptable factors.)
Detalles de la respuesta
(a) Diffusion: Diffusion is the net movement of molecules of a substance from a region of higher concentration to a region of lower concentration, as a result of the random motion of the molecules, until the molecules are evenly distributed.
(b) Two factors that affect the rate of diffusion:
- Temperature - a higher temperature gives the molecules greater average kinetic energy, so they move faster and diffuse more rapidly.
- Relative molecular mass (density) of the substance - lighter (less dense) molecules move faster and therefore diffuse more quickly than heavier ones.
(The concentration gradient and the medium of diffusion, gas versus liquid, are also acceptable factors.)
Pregunta 53 Informe
A stone of mass 20g is released from a catapult whose rubber is stretched through 5cm. If the force constant of the rubber is 200Nm\(^{-1}\), calculate the speed with which the stone leaves the catapult.
The stretched rubber stores elastic potential energy, which is converted into the kinetic energy of the stone when it is released.
Data: mass \(m = 20\ \text{g} = 0.02\ \text{kg}\); extension \(x = 5\ \text{cm} = 0.05\ \text{m}\); force constant \(k = 200\ \text{Nm}^{-1}\).
Elastic potential energy stored in the rubber:
\[ E = \tfrac{1}{2}kx^{2} = \tfrac{1}{2}\times200\times(0.05)^{2} = \tfrac{1}{2}\times200\times0.0025 = 0.25\ \text{J} \]By conservation of energy, this equals the kinetic energy of the stone as it leaves the catapult:
\[ \tfrac{1}{2}mv^{2} = 0.25 \] \[ v^{2} = \frac{2\times0.25}{0.02} = \frac{0.5}{0.02} = 25 \] \[ v = \sqrt{25} = 5\ \text{ms}^{-1} \]The stone leaves the catapult with a speed of \(5\ \text{ms}^{-1}\).
Detalles de la respuesta
The stretched rubber stores elastic potential energy, which is converted into the kinetic energy of the stone when it is released.
Data: mass \(m = 20\ \text{g} = 0.02\ \text{kg}\); extension \(x = 5\ \text{cm} = 0.05\ \text{m}\); force constant \(k = 200\ \text{Nm}^{-1}\).
Elastic potential energy stored in the rubber:
\[ E = \tfrac{1}{2}kx^{2} = \tfrac{1}{2}\times200\times(0.05)^{2} = \tfrac{1}{2}\times200\times0.0025 = 0.25\ \text{J} \]By conservation of energy, this equals the kinetic energy of the stone as it leaves the catapult:
\[ \tfrac{1}{2}mv^{2} = 0.25 \] \[ v^{2} = \frac{2\times0.25}{0.02} = \frac{0.5}{0.02} = 25 \] \[ v = \sqrt{25} = 5\ \text{ms}^{-1} \]The stone leaves the catapult with a speed of \(5\ \text{ms}^{-1}\).
Pregunta 54 Informe
(a) (i) Explain latent heat.
(ii) State two factors that affect the rate of evaporation of a liquid
(b) Explain each of the following observations:
(i) On a dry day, water in a clay pot is cooler than water in a closed plastic container;
(ii) Food gets cooked faster in a pressure cooker than in an ordinary cooking pot.
(c) State two effects of heat on a substance.
(d) A 40 V electric heater is used to supply a current of 12 A for 1400 s to a body of mass 1.5 kg at the melting point of the body. The body melts and its temperature rises through \(60^o\)C in an extra 72 s. Determine the:
(i) latent heat of fusion of the body;
(ii) specific heat capacity of the body.
(a)(i) Latent heat: Latent heat is the quantity of heat energy absorbed or given out by a substance during a change of state (for example melting or boiling) at constant temperature. The heat is used to change the arrangement/spacing of the molecules rather than to raise the temperature.
(a)(ii) Two factors affecting the rate of evaporation: (1) Temperature of the liquid; (2) Surface area of the liquid exposed. (Draught/wind speed and humidity of the surrounding air are also acceptable.)
(b)(i) Clay pot cooler than closed plastic container: A clay pot is porous, so water seeps to the outside and evaporates. Evaporation takes latent heat of vaporisation from the remaining water, cooling it. In the sealed plastic container no evaporation (or escape of vapour) can occur, so no cooling takes place and the water stays warmer.
(b)(ii) Faster cooking in a pressure cooker: In a sealed pressure cooker the steam produced raises the pressure above the water. Increased pressure raises the boiling point of the water above 100 °C, so the food is cooked at a higher temperature, which speeds up cooking.
(c) Two effects of heat on a substance: (1) It causes expansion (increase in size); (2) It causes a rise in temperature or a change of state. (Change in electrical resistance or chemical change are also acceptable.)
(d) Power of heater \(P = VI = 40\times12 = 480\,\text{W}\).
(i) Latent heat of fusion: Heat supplied to melt the body \(= P t_1 = 480\times1400 = 672000\,\text{J}\). This equals \(mL\):
\[ L = \frac{Pt_1}{m} = \frac{672000}{1.5} = 4.48\times10^{5}\,\text{J kg}^{-1}. \]
(ii) Specific heat capacity: Heat supplied in the extra 72 s \(= 480\times72 = 34560\,\text{J} = mc\,\Delta\theta\):
\[ c = \frac{34560}{1.5\times60} = 384\,\text{J kg}^{-1}\,\text{K}^{-1}. \]
Detalles de la respuesta
(a)(i) Latent heat: Latent heat is the quantity of heat energy absorbed or given out by a substance during a change of state (for example melting or boiling) at constant temperature. The heat is used to change the arrangement/spacing of the molecules rather than to raise the temperature.
(a)(ii) Two factors affecting the rate of evaporation: (1) Temperature of the liquid; (2) Surface area of the liquid exposed. (Draught/wind speed and humidity of the surrounding air are also acceptable.)
(b)(i) Clay pot cooler than closed plastic container: A clay pot is porous, so water seeps to the outside and evaporates. Evaporation takes latent heat of vaporisation from the remaining water, cooling it. In the sealed plastic container no evaporation (or escape of vapour) can occur, so no cooling takes place and the water stays warmer.
(b)(ii) Faster cooking in a pressure cooker: In a sealed pressure cooker the steam produced raises the pressure above the water. Increased pressure raises the boiling point of the water above 100 °C, so the food is cooked at a higher temperature, which speeds up cooking.
(c) Two effects of heat on a substance: (1) It causes expansion (increase in size); (2) It causes a rise in temperature or a change of state. (Change in electrical resistance or chemical change are also acceptable.)
(d) Power of heater \(P = VI = 40\times12 = 480\,\text{W}\).
(i) Latent heat of fusion: Heat supplied to melt the body \(= P t_1 = 480\times1400 = 672000\,\text{J}\). This equals \(mL\):
\[ L = \frac{Pt_1}{m} = \frac{672000}{1.5} = 4.48\times10^{5}\,\text{J kg}^{-1}. \]
(ii) Specific heat capacity: Heat supplied in the extra 72 s \(= 480\times72 = 34560\,\text{J} = mc\,\Delta\theta\):
\[ c = \frac{34560}{1.5\times60} = 384\,\text{J kg}^{-1}\,\text{K}^{-1}. \]
Pregunta 55 Informe
(a) (i) State Newton’s Law of Universal Gravitation.
(ii) Define gravitational field.
(b) (i) Derive the equation relating the universal gravitational constant, G, and the acceleration of free fall, g, at the surface of the earth from Newton’s law of universal gravitation.
(ii) State two assumptions for which the relationship in 8(b)(i) holds.
(c) Calculate the force of attraction between a star of mass 2.00 x 1030 kg and the earth assuming the star is located 1.50 x 108 km from the earth. [Mass of the earth = 5.98 x 1024kg; G = 6.67 x 10-11N m\(^{2}\) kg-2; g = 10 m s\(^{-2}\)
(d) (i) Define escape velocity.
(ii) State two differences between the acceleration of free fall (g) and the universal gravitational constant (G).
(a)(i) Newton's Law of Universal Gravitation: Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
\[ F = \frac{G m_1 m_2}{r^{2}} \]
(a)(ii) Gravitational field: A gravitational field is a region of space in which a body of mass experiences a force of attraction. Its strength at a point is the force per unit mass acting on a small mass placed at that point.
(b)(i) Relationship between G and g: Consider a body of mass \(m\) resting on the earth's surface. The earth (mass \(M\), radius \(R\)) attracts it with a force which, by Newton's law, is
\[ F = \frac{G M m}{R^{2}}. \]
This same force is the weight of the body, \(F = mg\). Equating the two:
\[ mg = \frac{G M m}{R^{2}} \quad\Rightarrow\quad g = \frac{G M}{R^{2}}. \]
(b)(ii) Assumptions: (1) The earth is a perfect sphere of uniform density, so its whole mass may be taken to act at its centre. (2) The body is small compared with the earth, and effects such as the earth's rotation and air resistance are neglected.
(c) Force between the star and the earth:
\[ r = 1.50\times10^{8}\,\text{km} = 1.50\times10^{11}\,\text{m} \]
\[ F = \frac{G M_{star} M_{earth}}{r^{2}} = \frac{(6.67\times10^{-11})(2.00\times10^{30})(5.98\times10^{24})}{(1.50\times10^{11})^{2}} \]
\[ F = \frac{7.98\times10^{44}}{2.25\times10^{22}} \approx 3.55\times10^{22}\,\text{N}. \]
(d)(i) Escape velocity: The minimum velocity with which a body must be projected from the surface of the earth (or a planet) so that it completely overcomes the gravitational pull and escapes without ever returning. \(v_e = \sqrt{2gR}\).
(d)(ii) Two differences between g and G:
- g (acceleration of free fall) varies from place to place on the earth and from planet to planet, whereas G (universal gravitational constant) has the same value everywhere in the universe.
- g is a vector with unit m s-2, while G is a scalar constant with unit N m2 kg-2.
Detalles de la respuesta
(a)(i) Newton's Law of Universal Gravitation: Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
\[ F = \frac{G m_1 m_2}{r^{2}} \]
(a)(ii) Gravitational field: A gravitational field is a region of space in which a body of mass experiences a force of attraction. Its strength at a point is the force per unit mass acting on a small mass placed at that point.
(b)(i) Relationship between G and g: Consider a body of mass \(m\) resting on the earth's surface. The earth (mass \(M\), radius \(R\)) attracts it with a force which, by Newton's law, is
\[ F = \frac{G M m}{R^{2}}. \]
This same force is the weight of the body, \(F = mg\). Equating the two:
\[ mg = \frac{G M m}{R^{2}} \quad\Rightarrow\quad g = \frac{G M}{R^{2}}. \]
(b)(ii) Assumptions: (1) The earth is a perfect sphere of uniform density, so its whole mass may be taken to act at its centre. (2) The body is small compared with the earth, and effects such as the earth's rotation and air resistance are neglected.
(c) Force between the star and the earth:
\[ r = 1.50\times10^{8}\,\text{km} = 1.50\times10^{11}\,\text{m} \]
\[ F = \frac{G M_{star} M_{earth}}{r^{2}} = \frac{(6.67\times10^{-11})(2.00\times10^{30})(5.98\times10^{24})}{(1.50\times10^{11})^{2}} \]
\[ F = \frac{7.98\times10^{44}}{2.25\times10^{22}} \approx 3.55\times10^{22}\,\text{N}. \]
(d)(i) Escape velocity: The minimum velocity with which a body must be projected from the surface of the earth (or a planet) so that it completely overcomes the gravitational pull and escapes without ever returning. \(v_e = \sqrt{2gR}\).
(d)(ii) Two differences between g and G:
- g (acceleration of free fall) varies from place to place on the earth and from planet to planet, whereas G (universal gravitational constant) has the same value everywhere in the universe.
- g is a vector with unit m s-2, while G is a scalar constant with unit N m2 kg-2.
Pregunta 56 Informe
(a) (i) Define atomic spectra.
(ii) Differentiate between emission spectra and absorption spectra.
(b)
The diagram above illustrates an electron transition from energy level \(n = 3\) to \(n = 1\). Calculate the:
(i) energy of the photon
(ii) frequency of the photon
(ii) wavelength of the photon \([h = 6.6 \times 10^{-34}\text{ J s},\ c = 3.0 \times 10^8\text{ ms}^{-1};\ 1\text{ ev} = 1.6 \times 10^{-19}\text{ J}]\)
c)(i)Differentiate between soft x-rays and hard x-rays
(ii) Draw the circuit symbol for a p-n junction diode.
(iiii) Give the reason for doping a semiconductor material
(a)(i) Atomic spectra are the characteristic discrete lines of definite wavelengths or frequencies emitted or absorbed by atoms when electrons move between quantised energy levels.
(a)(ii) An emission spectrum consists of bright lines on a dark background. It is produced when excited electrons fall from higher to lower energy levels, emitting photons. An absorption spectrum consists of dark lines on a bright continuous background. It is produced when atoms absorb photons of particular energies, causing electrons to move from lower to higher energy levels.
(b) Transition from \(n=3\) to \(n=1\)
From the energy-level diagram, \(E_3=-1.51\text{ eV}\) and \(E_1=-13.6\text{ eV}\).
(i) Energy of the photon
\[\Delta E=E_3-E_1=-1.51-(-13.6)=12.09\text{ eV}.\]
\[\Delta E=12.09\times1.6\times10^{-19}=1.934\times10^{-18}\text{ J}.\]
Energy of the photon = \(1.93\times10^{-18}\text{ J}\) \((=12.09\text{ eV})\).
(ii) Frequency of the photon
Using \(E=hf\),
\[f=\frac{E}{h}=\frac{1.934\times10^{-18}}{6.6\times10^{-34}}=2.93\times10^{15}\text{ Hz}.\]
Frequency = \(2.93\times10^{15}\text{ Hz}\).
(iii) Wavelength of the photon
\[\lambda=\frac{c}{f}=\frac{3.0\times10^8}{2.93\times10^{15}}=1.02\times10^{-7}\text{ m}.\]
Wavelength = \(1.02\times10^{-7}\text{ m}\) (about \(102\text{ nm}\)).
(c)(i) Soft X-rays have relatively longer wavelengths, lower frequencies and energies, and low penetrating power. Hard X-rays have shorter wavelengths, higher frequencies and energies, and greater penetrating power.
(c)(ii) Circuit symbol for a p-n junction diode
(c)(iii) A semiconductor is doped to increase the number of charge carriers, thereby increasing its electrical conductivity (or reducing its resistivity).
Detalles de la respuesta
(a)(i) Atomic spectra are the characteristic discrete lines of definite wavelengths or frequencies emitted or absorbed by atoms when electrons move between quantised energy levels.
(a)(ii) An emission spectrum consists of bright lines on a dark background. It is produced when excited electrons fall from higher to lower energy levels, emitting photons. An absorption spectrum consists of dark lines on a bright continuous background. It is produced when atoms absorb photons of particular energies, causing electrons to move from lower to higher energy levels.
(b) Transition from \(n=3\) to \(n=1\)
From the energy-level diagram, \(E_3=-1.51\text{ eV}\) and \(E_1=-13.6\text{ eV}\).
(i) Energy of the photon
\[\Delta E=E_3-E_1=-1.51-(-13.6)=12.09\text{ eV}.\]
\[\Delta E=12.09\times1.6\times10^{-19}=1.934\times10^{-18}\text{ J}.\]
Energy of the photon = \(1.93\times10^{-18}\text{ J}\) \((=12.09\text{ eV})\).
(ii) Frequency of the photon
Using \(E=hf\),
\[f=\frac{E}{h}=\frac{1.934\times10^{-18}}{6.6\times10^{-34}}=2.93\times10^{15}\text{ Hz}.\]
Frequency = \(2.93\times10^{15}\text{ Hz}\).
(iii) Wavelength of the photon
\[\lambda=\frac{c}{f}=\frac{3.0\times10^8}{2.93\times10^{15}}=1.02\times10^{-7}\text{ m}.\]
Wavelength = \(1.02\times10^{-7}\text{ m}\) (about \(102\text{ nm}\)).
(c)(i) Soft X-rays have relatively longer wavelengths, lower frequencies and energies, and low penetrating power. Hard X-rays have shorter wavelengths, higher frequencies and energies, and greater penetrating power.
(c)(ii) Circuit symbol for a p-n junction diode
(c)(iii) A semiconductor is doped to increase the number of charge carriers, thereby increasing its electrical conductivity (or reducing its resistivity).
Pregunta 57 Informe
(a) State the principle of operation of fibre optics.
(b) State two applications of fibre optics in medicine.
(a) Principle of operation of fibre optics: An optical fibre works on the principle of total internal reflection. It consists of a transparent core of high refractive index surrounded by a cladding of lower refractive index. Light entering one end strikes the core-cladding boundary at an angle greater than the critical angle, so it is totally internally reflected. The light is repeatedly reflected along the fibre and is thereby guided from one end to the other with very little loss, even when the fibre is bent.
(b) Two applications of fibre optics in medicine:
- Endoscopy - fibre-optic endoscopes are used to view and examine internal organs and cavities (for example the stomach, intestines and interior of the lungs) without major surgery.
- Keyhole (minimally invasive) surgery and laser delivery - fibres are used to transmit laser light to internal tissues for cutting, cauterising or treating them, and to illuminate the operating site during such procedures.
Detalles de la respuesta
(a) Principle of operation of fibre optics: An optical fibre works on the principle of total internal reflection. It consists of a transparent core of high refractive index surrounded by a cladding of lower refractive index. Light entering one end strikes the core-cladding boundary at an angle greater than the critical angle, so it is totally internally reflected. The light is repeatedly reflected along the fibre and is thereby guided from one end to the other with very little loss, even when the fibre is bent.
(b) Two applications of fibre optics in medicine:
- Endoscopy - fibre-optic endoscopes are used to view and examine internal organs and cavities (for example the stomach, intestines and interior of the lungs) without major surgery.
- Keyhole (minimally invasive) surgery and laser delivery - fibres are used to transmit laser light to internal tissues for cutting, cauterising or treating them, and to illuminate the operating site during such procedures.
Pregunta 58 Informe
%IMG%
(a) The diagram above illustrates a projectile motion. Identify each of the physical quantities labeled P, β, H and R.
(b) Write an equation to show the relationship between P, g and Rmax’ where g is the acceleration due to gravity and Rmax is maximum R.
(a) Identifying the labelled quantities (standard projectile diagram):
- P is the velocity of projection (the initial speed with which the body is launched).
- β is the angle of projection (the angle the initial velocity makes with the horizontal).
- H is the maximum height reached by the projectile.
- R is the horizontal range (the horizontal distance travelled before the projectile returns to the launch level).
(b) Relationship between P, g and Rmax:
The range of a projectile launched at speed \(P\) and angle \(\beta\) is
\[ R = \frac{P^{2}\sin 2\beta}{g}. \]
The range is greatest when \(\sin 2\beta = 1\), i.e. when \(\beta = 45^{\circ}\). Then
\[ R_{max} = \frac{P^{2}}{g}. \]
Equivalently, \(P = \sqrt{g\,R_{max}}\).
Detalles de la respuesta
(a) Identifying the labelled quantities (standard projectile diagram):
- P is the velocity of projection (the initial speed with which the body is launched).
- β is the angle of projection (the angle the initial velocity makes with the horizontal).
- H is the maximum height reached by the projectile.
- R is the horizontal range (the horizontal distance travelled before the projectile returns to the launch level).
(b) Relationship between P, g and Rmax:
The range of a projectile launched at speed \(P\) and angle \(\beta\) is
\[ R = \frac{P^{2}\sin 2\beta}{g}. \]
The range is greatest when \(\sin 2\beta = 1\), i.e. when \(\beta = 45^{\circ}\). Then
\[ R_{max} = \frac{P^{2}}{g}. \]
Equivalently, \(P = \sqrt{g\,R_{max}}\).
Pregunta 59 Informe
State three observable phenomena in which waves behave like a particle.
Observable phenomena in which electromagnetic waves behave like particles
- photoelectric effect;
- Compton effect (Compton scattering);
- pair production;
- blackbody radiation.
Detalles de la respuesta
Observable phenomena in which electromagnetic waves behave like particles
- photoelectric effect;
- Compton effect (Compton scattering);
- pair production;
- blackbody radiation.
Pregunta 60 Informe
List three magnetic elements that determine the earth’s magnetic field at a point.
The three magnetic elements that fully determine the earth's magnetic field at a point are:
- The angle of declination - the angle between the geographic (true) meridian and the magnetic meridian at the point.
- The angle of dip (inclination) - the angle that the total earth's magnetic field makes with the horizontal at the point.
- The horizontal component of the earth's magnetic field intensity \((B_H)\) - the strength of the horizontal part of the field at the point.
Together these three quantities specify both the direction and the magnitude of the earth's field at any location.
Detalles de la respuesta
The three magnetic elements that fully determine the earth's magnetic field at a point are:
- The angle of declination - the angle between the geographic (true) meridian and the magnetic meridian at the point.
- The angle of dip (inclination) - the angle that the total earth's magnetic field makes with the horizontal at the point.
- The horizontal component of the earth's magnetic field intensity \((B_H)\) - the strength of the horizontal part of the field at the point.
Together these three quantities specify both the direction and the magnitude of the earth's field at any location.
Pregunta 61 Informe
Explain each of the following terms as used in Electronics.
(a) free electrons;
(b) holes.
(a) Free electrons: These are the outermost (valence) electrons of the atoms of a conductor or semiconductor that are so loosely bound that they become detached from their parent atoms and are able to move about randomly throughout the material. Because they are mobile and carry negative charge, they act as the charge carriers responsible for the flow of electric current when a potential difference is applied.
(b) Holes: A hole is the vacancy (empty space) left behind in the covalent bond structure of a semiconductor when an electron leaves its position. It behaves as a mobile carrier of positive charge, equal in magnitude to the charge on an electron. When a neighbouring electron moves in to fill the vacancy, the hole appears to move in the opposite direction, so holes constitute a flow of positive charge and contribute to conduction (dominant in p-type material).
Detalles de la respuesta
(a) Free electrons: These are the outermost (valence) electrons of the atoms of a conductor or semiconductor that are so loosely bound that they become detached from their parent atoms and are able to move about randomly throughout the material. Because they are mobile and carry negative charge, they act as the charge carriers responsible for the flow of electric current when a potential difference is applied.
(b) Holes: A hole is the vacancy (empty space) left behind in the covalent bond structure of a semiconductor when an electron leaves its position. It behaves as a mobile carrier of positive charge, equal in magnitude to the charge on an electron. When a neighbouring electron moves in to fill the vacancy, the hole appears to move in the opposite direction, so holes constitute a flow of positive charge and contribute to conduction (dominant in p-type material).
