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An object accelerates from rest with a constant acceleration of \(3.0\text{ m/s}^2\) for \(4.0\text{ s}\). It then travels at a constant speed for \(5.0\text{ s}\). What is the total distance travelled by the object?

A student wants to determine the density of a collection of identical small metal spheres. She places a measuring cylinder containing \(50\text{ cm}^3\) of water on a balance, and the balance reads \(250\text{ g}\). She then gently drops 20 spheres into the water. The water level rises to \(74\text{ cm}^3\), and the balance reading increases to \(430\text{ g}\). What is the density of the metal of the spheres?

An electric motor is used to lift a \(50\text{ kg}\) load vertically upwards through a height of \(12\text{ m}\) in a time of \(8.0\text{ s}\). The efficiency of the motor system is \(60\%\). What is the average electrical power input to the motor? (Take \(g = 10\text{ N/kg}\))

A bubble of gas is released from the bottom of a lake. The temperature of the water is constant. At the bottom of the lake, the total pressure is \(3.0 \times 10^5\text{ Pa}\). At the surface of the lake, the atmospheric pressure is \(1.0 \times 10^5\text{ Pa}\). The initial volume of the bubble at the bottom is \(2.0\text{ cm}^3\). What is the volume of the bubble when it reaches the surface?

A ray of light is incident on the boundary between a transparent liquid and air. The refractive index of the liquid is \(1.25\). What is the critical angle for this liquid-air boundary?

A metal wire of length \(L\) and circular cross-section of radius \(r\) has a resistance \(R\). A second wire is made of the same metal but has a length \(2L\) and a cross-sectional radius \(2r\). What is the resistance of the second wire in terms of \(R\)?

A radioactive sample has a count rate of 640 counts per minute (including a background count rate of 40 counts per minute). After 12 hours, the count rate of the sample decreases to 115 counts per minute (including the same background count rate of 40 counts per minute). What is the half-life of the radioactive isotope?

An artificial satellite orbits the Earth in a circular orbit of radius \(8000\text{ km}\). It completes one orbit in \(2.0\text{ hours}\). What is the average orbital speed of the satellite?

A student uses a micrometer screw gauge to measure the diameter of a steel ball. With the jaws closed, the reading is \(+0.04\text{ mm}\) (a positive zero error). When measuring the ball, the main scale reads \(4.5\text{ mm}\) and the thimble scale reads 32 divisions. Each division on the thimble represents \(0.01\text{ mm}\). What is the actual diameter of the steel ball?

A ball of mass \(0.15\text{ kg}\) is dropped onto a concrete floor. It strikes the floor vertically downwards at a speed of \(8.0\text{ m/s}\) and rebounds vertically upwards at a speed of \(6.0\text{ m/s}\). The ball is in contact with the floor for \(0.070\text{ s}\). What is the average force exerted by the floor on the ball during the collision?

An electrical heater of power \(150\text{ W}\) is used to heat a \(0.50\text{ kg}\) block of ice at \(0^\circ\text{C}\). The heater is switched on for \(5.0\text{ minutes}\). During this time, \(120\text{ g}\) of the ice melts to form water at \(0^\circ\text{C}\). How much thermal energy from the heater is lost to the surroundings during this process? (Specific latent heat of fusion of ice = \(3.3 \times 10^5\text{ J/kg}\))

A potential divider circuit consists of a light-dependent resistor (LDR) and a fixed resistor of resistance \(4.0\text{ k}\Omega\) connected in series across a \(6.0\text{ V}\) d.c. power supply. A voltmeter is connected in parallel with the fixed resistor. The resistance of the LDR is \(2.0\text{ k}\Omega\) in bright light and \(8.0\text{ k}\Omega\) in the dark. What are the voltmeter readings in bright light and in the dark?

Which statement about redshift and the expansion of the Universe is correct?

An ideal step-down transformer is connected to a \(240\text{ V}\) a.c. mains supply. The primary coil has 600 turns and the secondary coil has 30 turns. The transformer supplies power to a lamp rated \(12\text{ V}, 24\text{ W}\). What is the current in the primary coil?

A radioactive source has a half-life of \(4.0\text{ hours}\). A detector is placed near the source and measures a count rate of 340 counts per minute. The background count rate is constant at 20 counts per minute. What is the measured count rate after \(12\text{ hours}\)?

A ray of light travels through a liquid and strikes the boundary with air. The refractive index of the liquid is 1.40. What is the critical angle for light in this liquid, and what happens to the ray of light if its angle of incidence at the boundary is \(50^\circ\)?

A toy car of mass \(0.50\text{ kg}\) moving at a speed of \(4.0\text{ m/s}\) collides with a stationary toy car of mass \(1.5\text{ kg}\). After the collision, the two cars stick together and move forward. What is the total kinetic energy lost during the collision?

A motorcycle accelerates from rest at a constant rate of \(3.0\text{ m/s}^2\) for \(6.0\text{ s}\). It then travels at a constant speed for \(10\text{ s}\) before decelerating uniformly to rest in a further \(4.0\text{ s}\). What is the total distance travelled by the motorcycle?

A ray of light traveling in a glass block of refractive index \(1.52\) is incident on the boundary with an unknown liquid. The critical angle for total internal reflection at this boundary is \(58.0^\circ\). What is the refractive index of the liquid? (Given: \(\sin(58.0^\circ) = 0.848\))

An artificial satellite orbits the Earth in a circular orbit of radius \(8.0 \times 10^6\text{ m}\). The orbital speed of the satellite is \(7.0\text{ km/s}\). How long does it take for the satellite to complete one full orbit?

A uniform metal wire of length \(L\) and cross-sectional area \(A\) has a resistance of \(16.0\ \Omega\). Another wire made of the same metal has a length of \(2L\) and a diameter that is twice that of the first wire. What is the resistance of the second wire?

A cylinder with a movable piston contains a fixed mass of gas at a constant temperature. The volume of the gas is initially \(120\text{ cm}^3\) and its pressure is \(1.5 \times 10^5\text{ Pa}\). The piston is slowly pushed in, decreasing the volume of the gas to \(40\text{ cm}^3\). What is the new pressure of the gas?

An electric heater of power \(600\text{ W}\) is used to heat a \(2.0\text{ kg}\) block of metal. The temperature of the block rises from \(20^\circ\text{C}\) to \(50^\circ\text{C}\) in \(3.0\text{ minutes}\). Assuming there is no thermal energy loss to the surroundings, what is the specific heat capacity of the metal?

A radioactive source has a half-life of \(20\text{ minutes}\). The measured count rate near the source, which includes a constant background radiation of \(15\text{ counts/minute}\), is initially \(255\text{ counts/minute}\). What will the measured count rate be after \(1.0\text{ hour}\)?

A car travels along a straight road. It accelerates from rest at a constant rate of \(2.0\text{ m/s}^2\) for \(6.0\text{ s}\), then travels at a constant speed for \(10\text{ s}\), and finally decelerates to rest at a constant rate in \(4.0\text{ s}\). What is the total distance traveled by the car?

Liquid X has a density of \(0.80\text{ g/cm}^3\) and liquid Y has a density of \(1.20\text{ g/cm}^3\). A mixture is made by mixing \(150\text{ cm}^3\) of liquid X with \(250\text{ cm}^3\) of liquid Y. There is no change in total volume when the liquids are mixed. What is the density of the mixture?

An electric pump is used to lift water from a well. The pump raises \(40\text{ kg}\) of water through a vertical height of \(12\text{ m}\) in a time of \(8.0\text{ s}\). The electrical power input to the pump is \(800\text{ W}\). The acceleration of free fall \(g\) is \(10\text{ m/s}^2\). What is the efficiency of the pump?

A uniform block of mass \(15\text{ kg}\) has dimensions \(0.20\text{ m} \times 0.30\text{ m} \times 0.50\text{ m}\). It lies on a flat, horizontal table. What is the difference between the maximum pressure and the minimum pressure that the block can exert on the table? (Take \(g = 10\text{ m/s}^2\))

A bubble of gas has a volume of \(2.0\text{ cm}^3\) at the bottom of a lake where the depth is \(20\text{ m}\). The temperature of the water is constant. The atmospheric pressure at the surface of the lake is \(1.0 \times 10^5\text{ Pa}\). The density of water is \(1000\text{ kg/m}^3\) and \(g = 10\text{ m/s}^2\). What is the volume of the bubble of gas when it reaches the surface?

A ray of light travels from glass into air. The refractive index of the glass is \(1.50\). The angle of incidence in the glass is \(45.0^\circ\). Which statement correctly describes what happens to the ray?

Two copper wires, P and Q, have different dimensions. Wire P has length \(L\) and diameter \(d\). Wire Q has length \(2L\) and diameter \(2d\). What is the ratio \(\frac{\text{resistance of P}}{\text{resistance of Q}}\)?

A student measures the count rate from a radioactive source near a Geiger-Müller (GM) tube. Before bringing the source near, the background count rate is measured as \(24\text{ counts/minute}\). With the source in place, the measured count rate is \(360\text{ counts/minute}\). After exactly \(6.0\text{ hours}\), the measured count rate decreases to \(66\text{ counts/minute}\). What is the half-life of the radioactive source?

A model rocket is launched vertically upwards. Its velocity increases at a constant rate of \(15\text{ m/s}^2\) for the first \(4.0\text{ s}\). The engine then shuts off, and the rocket is in free fall with an acceleration of \(10\text{ m/s}^2\) downwards until it reaches its maximum height. Air resistance is negligible. What is the total time from launch until the rocket reaches its maximum height?

An alloy is made by mixing \(200\text{ g}\) of metal X (density \(8.0\text{ g/cm}^3\)) with \(300\text{ g}\) of metal Y (density \(6.0\text{ g/cm}^3\)). No change in volume occurs during mixing. What is the density of the alloy?

A trolley of mass \(2.0\text{ kg}\) travels at \(6.0\text{ m/s}\) to the right. It collides with a second trolley of mass \(3.0\text{ kg}\) travelling at \(2.0\text{ m/s}\) to the left. After the collision, the two trolleys stick together and move with a common velocity. What is their common velocity?

An electric heater rated at \(50\text{ W}\) is used to heat \(200\text{ g}\) of a liquid in a well-insulated container. The liquid is already at its boiling point. It takes \(400\text{ s}\) of heating to completely vaporise all of the liquid. What is the specific latent heat of vaporisation of the liquid?

A ray of light in air strikes the flat surface of a transparent glass block at an angle of incidence of \(45^\circ\). The refractive index of the glass is \(1.5\). What is the angle of refraction inside the glass block?

A wire of length \(L\) and cross-sectional area \(A\) has a resistance of \(8.0\ \Omega\). A second wire made of the same metal has a length of \(2L\) and a cross-sectional area of \(4A\). What is the resistance of the second wire?

A radioactive sample has a measured count rate of \(360\text{ counts/minute}\) in a laboratory where the background radiation level is constant at \(40\text{ counts/minute}\). After \(12\text{ hours}\), the measured count rate of the sample (including background) has fallen to \(80\text{ counts/minute}\). What is the half-life of the radioactive isotope?

An artificial satellite orbits the Earth in a circular path of radius \(r\) with a constant speed \(v\). The time taken for one complete orbit is \(T\). If the orbital radius is increased to \(4r\) and the orbital speed decreases to \(0.5v\), what is the new orbital period in terms of \(T\)?

A cyclist starts from rest and accelerates.

(a) Define acceleration. [1]

(b) The cyclist accelerates uniformly at \(1.5\text{ m/s}^2\) for \(6.0\text{ s}\).

(i) Calculate the velocity of the cyclist at \(t = 6.0\text{ s}\). [2]

(ii) The cyclist then travels at this constant velocity for another \(12.0\text{ s}\). Finally, she decelerates uniformly to rest in a further \(4.0\text{ s}\). Describe the features of a velocity-time graph representing this entire \(22.0\text{ s}\) journey, specifying the key coordinates \((t, v)\) at each phase. [2]

(iii) Calculate the total distance traveled by the cyclist during the entire \(22.0\text{ s}\) journey. [3]

A small trolley A of mass \(2.5\text{ kg}\) travels at a velocity of \(4.0\text{ m/s}\) on a friction-free horizontal track. It collides with a stationary trolley B of mass \(1.5\text{ kg}\). After the collision, the two trolleys stick together and move with a common velocity \(v\).

(a) State the principle of conservation of momentum. [2]

(b) Calculate the common velocity \(v\) of the trolleys after the collision. [3]

(c) Calculate the magnitude of the impulse exerted on trolley B during the collision. [3]

An electric heater rated at \(150\text{ W}\) is placed inside a solid block of lead of mass \(0.80\text{ kg}\).

(a) Define specific heat capacity. [2]

(b) The block of lead is initially at a temperature of \(20^\circ\text{C}\). The specific heat capacity of lead is \(130\text{ J/(kg }^\circ\text{C)}\).

(i) Calculate the energy required to heat the lead block to its melting point of \(327^\circ\text{C}\). [2]

(ii) Assuming there is no loss of thermal energy to the surroundings, calculate the time taken by the heater to raise the temperature of the lead block to \(327^\circ\text{C}\). [2]

(c) Once the block reaches \(327^\circ\text{C}\), it begins to melt. Explain, in terms of intermolecular forces and particle arrangement, why the temperature of the lead remains constant during melting even though the heater is still supplying thermal energy. [2]

A ray of monochromatic light is incident on the boundary between a glass prism and the air. The refractive index of the glass is \(1.52\).

(a) State what is meant by the critical angle. [2]

(b) Calculate the critical angle \(c\) for the boundary between the glass and air. [2]

(c) The light ray is traveling inside the glass prism and strikes the inner surface of the glass at an angle of incidence of \(42.0^\circ\).

(i) Determine whether the light ray will emerge into the air or undergo total internal reflection. Explain your answer with reference to the critical angle calculated in (b). [2]

(ii) State the name of one practical application of total internal reflection in telecommunications. [2]

A cell of electromotive force (e.m.f.) \(9.0\text{ V}\) and negligible internal resistance is connected in series with a fixed resistor of resistance \(12\\ \Omega\) and a thermistor.

(a) Define electromotive force (e.m.f.). [2]

(b) At a certain room temperature, the resistance of the thermistor is \(18\\ \Omega\).

(i) Calculate the total resistance of the series circuit. [1]

(ii) Calculate the current in the circuit. [2]

(iii) Calculate the electrical energy delivered to the \(12\\ \Omega\) fixed resistor in a time of \(5.0\text{ minutes}\). [3]

An experiment is conducted to demonstrate electromagnetic induction.

(a) State Faraday's law of electromagnetic induction. [2]

(b) A student drops a bar magnet vertically, north pole pointing downwards, through a long solenoid connected to a sensitive center-zero millivoltmeter.

(i) Describe and explain the movement of the meter's pointer as the north pole enters the top of the solenoid. [3]

(ii) Describe the movement of the pointer as the south pole of the magnet leaves the bottom of the solenoid. Explain why the maximum deflection in this stage is larger than the maximum deflection observed in (b)(i). [3]

An artificial satellite orbits the Earth in a circular path.

(a) State the name of the force that keeps the satellite in its circular orbit, and state the direction in which this force acts. [2]

(b) The satellite orbits at a height of \(600\text{ km}\) above the Earth's surface. The radius of the Earth is \(6400\text{ km}\).

(i) State the radius of the satellite's circular orbit. [1]

(ii) The satellite travels with a constant orbital speed of \(7.5\text{ km/s}\). Calculate the time taken, in minutes, for the satellite to complete one full orbit. [3]

(c) Explain why the satellite is constantly accelerating even though it is traveling at a constant speed. [2]

A sample containing a radioactive isotope decays by emitting beta-minus (\(\beta^-\)) particles.

(a) State two differences between an alpha particle and a beta-minus particle. [2]

(b) The activity of the sample is monitored. The constant background radiation in the laboratory is measured to be \(24\text{ counts/minute}\). The initial raw count rate of the sample, including background, is \(412\text{ counts/minute}\). After \(15.0\text{ hours}\), the raw count rate of the sample is \(72.5\text{ counts/minute}\).

(i) Calculate the corrected initial count rate and the corrected count rate after \(15.0\text{ hours}\). [1]

(ii) Calculate the half-life of the radioactive isotope. [3]

(c) State one risk of exposure to beta radiation and describe a suitable safety precaution when handling this source. [2]

A toy truck of mass \(1.2\text{ kg}\) travelling at a speed of \(2.5\text{ m/s}\) collides with a stationary toy car of mass \(0.80\text{ kg}\). After the collision, the truck and the car couple together and move with a common velocity. (a) Define momentum. [1] (b) State the condition necessary for the total momentum of a system of interacting objects to remain constant. [1] (c) Calculate the common speed of the coupled truck and car immediately after the collision. [3] (d) Calculate the magnitude of the impulse exerted by the truck on the car during the collision. State the unit. [3]

An electric heater is used to heat a block of metal. The heater is rated at \(60\text{ W}\). The metal block has a mass of \(1.5\text{ kg}\). The heater is switched on for \(5.0\text{ minutes}\) and the temperature of the block rises from \(20\text{ }^\circ\text{C}\) to \(32\text{ }^\circ\text{C}\). (a) Calculate the total thermal energy supplied by the heater in this time. [2] (b) Calculate the specific heat capacity of the metal from these results. State the unit. [4] (c) In practice, some thermal energy is lost to the surroundings during heating. (i) State the effect of this thermal energy loss on the calculated value of the specific heat capacity. [1] (ii) Suggest one improvement to the apparatus or procedure to reduce this heat loss. [1]

A student investigates the focal length of a converging lens. Fig 1.1 shows the experimental setup. An illuminated object (a cross-wire) is placed at the zero end of a metre rule. A lens is placed on the rule at some distance \(u_1\) from the object. A screen is moved along the rule until a sharp, inverted image of the object is formed on the screen. The distance from the lens to the screen is the image distance, \(v_1\). (a) For the first trial, the lens is positioned at the \(35.0\text{ cm}\) mark, and the screen is at the \(68.0\text{ cm}\) mark. (i) Calculate the image distance \(v_1\). (ii) Calculate the focal length \(f_1\) of the lens using the equation: \(f_1 = \frac{u_1 v_1}{u_1 + v_1}\) where the object distance \(u_1 = 22.0\text{ cm}\). Give your answer to a suitable number of significant figures and include the unit. (b) The student repeats the procedure for a second trial, obtaining \(u_2 = 30.0\text{ cm}\) and \(v_2 = 24.5\text{ cm}\). Calculate the focal length \(f_2\) for this trial. (c) Calculate the average focal length \(f_{\text{avg}}\) of the lens using your values of \(f_1\) and \(f_2\). (d) Suggest two reasons why it is difficult to obtain an exact, precise position of the screen for the sharpest image. (e) State one precaution that the student should take to ensure that the measurements of \(u\) and \(v\) are accurate. (f) The student wants to check if the focal length is constant. State whether the two values \(f_1\) and \(f_2\) are within the limits of experimental accuracy, and justify your answer.

A student is investigating how the resistance of a wire depends on its length. The student connects a circuit containing a power supply, a switch, an ammeter, a voltmeter, and a length of resistance wire \(XY\) of total length \(100.0\text{ cm}\) fixed to a metre rule. (a) Draw a circuit diagram to show how this apparatus is connected to measure the current in the wire \(XY\) and the potential difference across a length \(L\) of the wire. (b) The student measures the current \(I_1\) in the wire and the potential difference \(V_1\) across a length \(L_1 = 20.0\text{ cm}\) of the wire. The pointer of the voltmeter has major markings at 0 V, 1 V, 2 V, and 3 V, with 10 small subdivisions between each. The pointer is at the 6th subdivision after the 1 V mark. The ammeter scale has major markings at 0 A, 0.5 A, and 1.0 A, with 10 small subdivisions between 0 and 0.5 A. The pointer is at the 8th subdivision after 0 A. (i) State the voltmeter reading \(V_1\). (ii) State the ammeter reading \(I_1\). (c) Calculate the resistance \(R_1\) of the \(20.0\text{ cm}\) length of wire using \(R_1 = \frac{V_1}{I_1}\). Include the unit. (d) The student repeats the measurements for a length \(L_2 = 60.0\text{ cm}\) and obtains \(V_2 = 2.4\text{ V}\) and \(I_2 = 0.20\text{ A}\). Calculate the resistance \(R_2\) for \(L_2 = 60.0\text{ cm}\). (e) Suggest why the current in the second measurement is lower than the current in the first measurement. (f) A student suggests that the resistance of the wire is directly proportional to its length. State whether the results support this suggestion. Justify your answer with a calculation.

A student is investigating the rate of cooling of hot water in two beakers under different conditions. Beaker \(A\) is uninsulated. Beaker \(B\) is insulated with a single layer of bubble wrap. Both beakers are filled with hot water. The temperature \(\theta\) of the water in each beaker is recorded every \(30\text{ s\) for \(180\text{ s}\). (a) The thermometer for beaker \(A\) at the start of the experiment (\(t = 0\)) has major markings at 70 \(^\circ\text{C}\), 80 \(^\circ\text{C}\), 90 \(^\circ\text{C}\) with 10 small divisions between 80 \(^\circ\text{C}\) and 90 \(^\circ\text{C}\). The liquid column ends exactly 4 divisions above 80 \(^\circ\text{C}\). (i) Record the initial temperature \(\theta_0\) of the water in beaker \(A\). (ii) State one precaution the student must take when reading the thermometer to ensure the temperature is recorded accurately. (b) Table 3.1 shows the recorded temperature readings: Time \(t\) / \(\text{s}\) | Temperature of \(A\), \(\theta_A\) / \(^\circ\text{C}\) | Temperature of \(B\), \(\theta_B\) / \(^\circ\text{C}\) [0, 84.0, 84.0], [30, 79.5, 81.5], [60, 76.0, 79.5], [90, 73.0, 77.5], [120, 70.5, 76.0], [150, 68.5, 74.5], [180, 67.0, 73.5]. (i) Calculate the average rate of cooling \(R_A\) of the water in beaker \(A\) during the first \(90\text{ s}\). Use the equation: \(R_A = \frac{\theta_0 - \theta_{90}}{t}\) where \(t = 90\text{ s}\). Include the unit. (ii) Calculate the average rate of cooling \(R_B\) of the water in beaker \(B\) during the first \(90\text{ s}\). (c) Compare the rates of cooling and state whether the bubble wrap insulation is effective. Justify your answer by reference to the calculated rates of cooling. (d) A student suggests that using a lid on beaker \(B\) would make the experiment a more fair comparison of the insulation properties of the wrap itself. Suggest why using lids on both beakers is a good idea to focus on the insulation on the sides. (e) Another student wants to repeat the experiment to see if the thickness of the insulation affects the cooling rate. Describe how the apparatus can be modified and state what variables should be kept constant.

A student is investigating the balancing of a metre rule to determine its mass \(M\). The student places a pivot under the metre rule at a distance \(d\) from the zero end. A known load \(P = 1.0\text{ N}\) is suspended from the rule at a distance \(x = 10.0\text{ cm}\) from the zero end. The position of the pivot \(d\) is adjusted until the metre rule balances horizontally. For \(x = 10.0\text{ cm}\), the rule balances when the pivot is at the \(d = 34.0\text{ cm}\) mark. (a) (i) Explain what is meant by the 'centre of gravity' of the metre rule, and state its likely position on a uniform metre rule. (ii) Describe the forces acting on the rule and their respective positions when balanced. (b) Write down: (i) the distance \(a\) from the pivot to the load \(P\). (ii) the distance \(b\) from the pivot to the centre of gravity of the rule. (c) Calculate the weight \(W\) of the metre rule using the principle of moments: \(P \times a = W \times b\). (d) Calculate the mass \(M\) of the metre rule in grams, using \(g = 10\text{ N/kg}\). (e) Suggest one practical reason why it is difficult to find the exact balance point \(d\) of the metre rule. (f) Describe a method to find the centre of gravity of an irregularly-shaped piece of cardboard.