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GCSE · Physics

P-RP Physics Required Practicals and Uncertainties

AQA 8464 · Calculator allowed · about 125 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Required practicals use a range of measuring equipment. For each quantity in parts (a) to (f), name one piece of equipment a student could use to measure it.

(a)The mass of a metal cube.(1)

(b)The potential difference across a component in a circuit.(1)

(c)The current flowing through a component in a circuit.(1)

(d)The angle between a ray of light and the normal.(1)

(e)The force applied to stretch a spring.(1)

(f)The time between a trolley passing two light gates.(1)

(Total for Question 1 is 6 marks)

State one safety precaution a student should take in each of the required practicals below, and the hazard it addresses.

(a)Heating a metal block with an electrical immersion heater in the specific heat capacity practical.(1)

(b)Directing a ray box or laser at a mirror or glass block in the light practical.(1)

(Total for Question 2 is 2 marks)

Reece investigates the reflection of light using a plane mirror, a ray box and a protractor, directing a single narrow ray of light at the mirror.

(a)State the law of reflection.(1)

(b)Describe how Reece draws the normal at the point of incidence and marks the paths of the incident and reflected rays, and explain why an accurate normal is essential for measuring the angles correctly.(3)

(c)The angle between the incident ray and the mirror surface itself (not the normal) is measured as 58 degrees. Calculate the angle of incidence, measured from the normal.(2)

(d)Using the law of reflection, state the angle of reflection for this ray.(1)

(Total for Question 3 is 7 marks)

Priya measures the density of a metal cube. The cube has a side length of 2.00 cm, measured using vernier calipers, and a mass of 21.6 g, measured using a top-pan balance. The equation linking density, mass and volume is: density = mass / volume

(a)State the equation linking the volume of a cube to its side length.(1)

(b)Calculate the volume of the cube, in cm^3.(2)

(c)Calculate the density of the metal.(2)

(d)Explain why using vernier calipers, rather than a millimetre ruler, to measure the side length improves the accuracy of the calculated density.(2)

(Total for Question 4 is 7 marks)

Kwame uses a ripple tank to investigate water waves. A motor drives a dipper at a set frequency, and a lamp shines through the water onto a screen so the wave crests can be seen and measured. The equation linking wave speed, frequency and wavelength is: wave speed = frequency * wavelength

(a)The dipper vibrates at a frequency of 5.0 Hz. State what is meant by the frequency of a wave.(1)

(b)Kwame measures the distance across 5 complete wavelengths, rather than just one. Explain why this gives a more precise value for the wavelength.(2)

(c)The distance across 5 complete wavelengths is 20.0 cm. Calculate the wavelength of the ripples, in metres.(2)

(d)Calculate the speed of the ripples.(3)

(e)The frequency of the dipper is increased while the depth of water in the tank stays the same. State and explain the effect this has on the wavelength of the ripples.(2)

(Total for Question 5 is 10 marks)

Zara investigates how the type of surface affects the rate of emission of infrared radiation, using a Leslie cube filled with boiling water. The cube has four vertical faces of equal area: matt black, matt white, shiny black and shiny silver. An infrared detector, connected to a data logger, is held at the same fixed distance from each face in turn, and the reading (in arbitrary detector units) is recorded after one minute.

Surface: matt black	matt white	shiny black	shiny silver
Detector reading (units): 85	65	45	20

(a)Identify the independent variable in this investigation.(1)

(b)Identify two variables that must be controlled for this to be a valid comparison between surfaces.(2)

(c)Using the data, identify which surface emits infrared radiation at the greatest rate, and explain this in terms of the surface's properties.(2)

(d)Explain why the detector must be kept at the same fixed distance from each face of the cube.(2)

(Total for Question 6 is 7 marks)

Freya investigates how the resistance of a nichrome wire depends on its length. A crocodile clip changes the length of wire connected in the circuit, and Freya adjusts a variable resistor so the current is kept at 0.50 A for each length. The equation linking resistance, potential difference and current is: resistance = potential difference / current

Length (cm): 20	40	60
Current (A): 0.50	0.50	0.50
Potential difference (V): 1.0	2.0	3.0
Resistance (ohms): 2.0	4.0	?

(a)State the equation linking resistance, potential difference and current.(1)

(b)Complete the table by calculating the resistance of the 60 cm length of wire.(2)

(c)Explain why Freya keeps the current the same for each length of wire, rather than allowing it to vary.(2)

(d)Calculate the gradient of a graph of resistance (y-axis) against length (x-axis), using the data for 20 cm and 60 cm.(3)

(e)State what the gradient calculated in part (d) represents.(1)

(Total for Question 7 is 9 marks)

Tomasz measures the density of an irregularly shaped stone using a displacement (eureka) can, a measuring cylinder and a top-pan balance.

(a)Describe how Tomasz uses the displacement can and measuring cylinder to find the volume of the stone.(3)

(b)The mass of the stone is 40.5 g and the volume of water displaced is 15.0 cm^3. Calculate the density of the stone.(2)

(c)The measuring cylinder has a scale resolution of 1.0 cm^3. Calculate the percentage uncertainty in the volume of water displaced (15.0 cm³).(2)

(Total for Question 8 is 7 marks)

Jayden investigates the extension of a spring as increasing force is applied. The unstretched length of the spring is 10.0 cm. The equation linking force, spring constant and extension is: force = spring constant * extension

Force (N): 1.0	2.0	3.0	4.0	5.0
Length (cm): 12.0	14.0	16.0	18.0	21.0

(a)Calculate the extension of the spring when the force applied is 3.0 N.(1)

(b)Show that the spring obeys Hooke's law for forces between 1.0 N and 4.0 N, by calculating the spring constant using two different pairs of results.(4)

(c)Identify, with a reason, the force in the table at which the spring exceeds its limit of proportionality.(2)

(d)Calculate the elastic potential energy stored in the spring when it is extended by 8.0 cm, within the limit of proportionality. Use the equation: elastic potential energy = 0.5 * spring constant * (extension)² [Higher Tier only](3)

(Total for Question 9 is 10 marks)

Ben investigates the acceleration of a trolley on a ramp. Two light gates are set up along the ramp, connected to a data logger, and an interrupt card of known width is attached to the trolley. The equation linking acceleration, change in velocity and time is: acceleration = (final velocity - initial velocity) / time

(a)The interrupt card has a width of 5.0 cm. State the equation used to calculate the trolley's velocity as it passes through a light gate.(1)

(b)The trolley's velocity at the first light gate is 0.20 m/s and at the second light gate is 0.80 m/s. The time taken to travel between the gates is 0.40 s. Calculate the acceleration of the trolley.(3)

(c)State one variable that should be controlled when investigating the effect of the mass of the trolley on its acceleration.(1)

(d)The interrupt card's width (5.0 cm) is measured using a ruler with a resolution of 0.1 cm. Calculate the percentage uncertainty in this measurement.(2)

(e)Explain why using light gates gives a more precise measurement of the trolley's velocity than a student using a stopwatch and metre rule.(2)

(Total for Question 10 is 9 marks)

Olivia investigates the current through a filament lamp for a range of potential differences, using a circuit with a variable resistor, an ammeter in series, and a voltmeter connected in parallel across the lamp.

Potential difference (V): 0	1.0	2.0	3.0	4.0
Current (A): 0	0.20	0.32	0.40	0.46

(a)State the name of the circuit component Olivia uses to vary the potential difference across the lamp.(1)

(b)Calculate the resistance of the filament lamp when the potential difference is 1.0 V.(2)

(c)Calculate the resistance of the filament lamp when the potential difference is 4.0 V.(2)

(d)Using your answers to (b) and (c), describe how the resistance of the filament lamp changes as the potential difference across it increases.(2)

(e)Explain, in terms of energy and particles, why the resistance of the filament increases as the potential difference across it increases.(3)

(Total for Question 11 is 10 marks)

Aaliyah sets up a stationary (standing) wave on a stretched string, using a signal generator connected to a vibration transducer at one end, with the string passing over a pulley and a hanging weight at the other end to keep the tension constant. The frequency is adjusted until a clear stationary wave pattern with well-defined nodes and antinodes forms along the string.

(a)State how Aaliyah knows the string is vibrating at one of its resonant (natural) frequencies.(1)

(b)Define the term node, as used to describe a stationary wave.(1)

(c)The string forms 3 complete loops between the transducer and the pulley, over a total length of 90 cm. Calculate the wavelength of the stationary wave.(2)

(d)The frequency of the signal generator is 50 Hz. Calculate the speed of the wave on the string.(3)

(e)Suggest why a stroboscope is sometimes used to help view the vibrating string safely and clearly.(1)

(Total for Question 12 is 8 marks)

Aisha determines the specific heat capacity of a 1.0 kg aluminium block, using an electrical immersion heater in one hole in the block and a thermometer in a separate hole. The equations needed are: energy transferred electrically = current * potential difference * time, and energy transferred thermally = mass * specific heat capacity * change in temperature

(a)The block is wrapped in an insulating jacket during the experiment. Explain how this improves the accuracy of the calculated specific heat capacity.(2)

(b)The heater is operated with a current of 4.0 A and a potential difference of 12 V for 250 s. Calculate the energy transferred electrically to the block.(2)

(c)The temperature of the block rises from 20 degC to 32 degC. Calculate the specific heat capacity of the aluminium.(3)

(d)The thermometer has a resolution of 1 degC, and is read at the start and end of heating. Calculate the percentage uncertainty in the temperature rise of 12 degC.(2)

(e)Suggest one change to the experiment that would reduce this percentage uncertainty, other than using a more precise thermometer.(1)

(Total for Question 13 is 10 marks)

Josh investigates the effect of insulation on the cooling rate of a beaker of hot water. Two identical beakers are each filled with the same volume of water at the same starting temperature; one is wrapped in a layer of insulating foam and the other is left unwrapped. Both are placed in the same room, and the temperature of the water in each is recorded every 30 seconds.

(a)Identify the independent variable and the dependent variable in this investigation.(2)

(b)State two variables, other than insulation, that must be kept the same for this to be a fair test.(2)

(c)After 300 s, the temperature of the insulated beaker has fallen from 80 degC to 68 degC, and the temperature of the uninsulated beaker has fallen from 80 degC to 50 degC. Calculate the mean rate of cooling, in degC per second, for each beaker.(4)

(d)State which beaker has the greater rate of cooling, and explain this in terms of energy transfer.(2)

(Total for Question 14 is 10 marks)

Amara directs a ray of light from air into a rectangular glass block, and traces the path of the ray using pins (or a ray box) and a protractor. The angle of incidence in air is 40 degrees, and the angle of refraction inside the glass is measured as 25 degrees. The equation linking the refractive index of a material to these angles is: refractive index = sin(angle of incidence) / sin(angle of refraction) [Higher Tier only]

(a)State what happens to the speed and the wavelength of the light as it passes from air into the glass block.(2)

(b)Calculate the refractive index of the glass. [Higher Tier only](3)

(c)The critical angle of the glass can be found using: sin(critical angle) = 1 / refractive index. Calculate the critical angle of this glass. [Higher Tier only](3)

(d)State what happens to a ray of light travelling inside the glass block that strikes the glass-air boundary at an angle greater than the critical angle.(1)

(e)Describe how Amara ensures the angle of refraction is measured accurately, referring to the use of the normal.(2)

(Total for Question 15 is 11 marks)

A student measures the mass and volume of a small alloy sample in order to calculate its density.

Mass = 24.0 g, measured with an uncertainty of plus or minus 0.1 g
Volume = 8.00 cm³, measured with an uncertainty of plus or minus 0.16 cm³

(a)Calculate the percentage uncertainty in the mass measurement.(1)

(b)Calculate the percentage uncertainty in the volume measurement.(1)

(c)When two measured quantities are multiplied or divided to find a derived quantity, the percentage uncertainties of each measurement are added together to find the total percentage uncertainty. Calculate the total percentage uncertainty in the calculated density.(2)

(d)Calculate the density of the sample, and use your answer to part (c) to express this with its absolute uncertainty, in the form (density plus or minus uncertainty) g/cm^3.(3)

(Total for Question 16 is 7 marks)

Aisha carries out the specific heat capacity practical described in Question 13, and calculates a value for the specific heat capacity of the aluminium block that is significantly higher than the accepted value found in a data book.

Evaluate the method used in this practical, explaining possible sources of error and suggesting improvements that would produce a more accurate result. In your answer, refer to both systematic and random errors.

(Total for Question 17 is 6 marks)

A student plots a graph of potential difference against current for a fixed length of wire at a constant temperature, obtaining a straight line through the origin.

(a)State what the gradient of this graph represents.(1)

(b)One point on the line is (current = 0.40 A, potential difference = 2.0 V). Calculate the resistance of the wire.(2)

(c)This wire has a length of 50 cm and a resistance of 5.0 ohms. Assuming resistance is directly proportional to length (at the same temperature), calculate the resistance of a 125 cm length of the same wire.(3)

(d)Suggest one reason why, in a real experiment, the resistance of a very long length of this wire might not be exactly proportional to its length.(2)

(Total for Question 18 is 8 marks)

Mark scheme · P-RP Physics Required Practicals and Uncertainties

Question 1

(a) B1 top-pan balance, oe
(a) Answer: Top-pan balance.
(b) B1 voltmeter, connected in parallel with the component
(b) Answer: Voltmeter (connected in parallel).
(c) B1 ammeter, connected in series with the component
(c) Answer: Ammeter (connected in series).
(d) B1 protractor, oe
(d) Answer: Protractor.
(e) B1 newtonmeter (forcemeter), oe; allow slotted masses of known weight
(e) Answer: Newtonmeter (forcemeter).
(f) B1 light gates connected to a data logger (or timer), oe
(f) Answer: Light gates connected to a data logger.

Question 2

(a) B1 do not touch the heater or block during or immediately after use, as they can cause burns/scalds, oe; allow using a heatproof mat
(a) Answer: Do not touch the heater or block during or shortly after use, as they get hot enough to cause burns.
(b) B1 do not look directly into the beam / do not shine it towards anyone's eyes, as it can damage the retina, oe
(b) Answer: Do not look directly into the light beam, or shine it at anyone's eyes, as it can damage the retina.

Question 3

(a) B1 angle of incidence = angle of reflection (both measured from the normal), oe
(a) Answer: Angle of incidence = angle of reflection.
(b) B1 draws a straight line perpendicular (at 90 degrees) to the mirror line, at the point where the ray strikes it, using a protractor or set square, oe
(b) B1 marks the path of the incident ray and the reflected ray with crosses/pencil dots at two points on each, removes the mirror, and joins the points with a ruler, oe
(b) B1 the angles of incidence and reflection must both be measured from the normal, not the mirror surface, so an inaccurately drawn normal would make both angle measurements wrong, oe
(b) Answer: Draw the normal at 90 degrees to the mirror at the point of incidence; mark the incident and reflected ray paths with dots, remove the mirror, and join the dots with a ruler. The normal must be accurate because both angles are measured from it, not the mirror surface.
(c) M1 90 - 58, oe
(c) A1 32 degrees cao
(c) Answer: 32 degrees
(d) B1 32 degrees, ft from (c)
(d) Answer: 32 degrees

Question 4

(a) B1 volume = (side length)³, oe
(a) Answer: Volume = side length^3.
(b) M1 2.00³, oe
(b) A1 8.00 cm³ cao
(b) Answer: 8.00 cm³
(c) M1 density = 21.6 / 8.00, oe
(c) A1 2.70 g/cm³ cao
(c) Answer: 2.70 g/cm³
(d) B1 vernier calipers have a smaller resolution than a millimetre ruler, so the length reading has a smaller absolute uncertainty, oe
(d) B1 since volume depends on length cubed, a small percentage uncertainty in length gives a much larger percentage uncertainty in the calculated volume (and so density), so improving the length measurement improves the density calculation, oe
(d) Answer: Vernier calipers have a smaller resolution than a ruler, so the length has a smaller percentage uncertainty; because volume is length cubed, this uncertainty is magnified in the volume (and density) calculation, so a more precise length measurement gives a more accurate density.

Question 5

(a) B1 the number of complete waves (oscillations) passing a point per second, measured in hertz (Hz), oe
(a) Answer: The number of complete waves passing a fixed point each second.
(b) B1 a single wavelength is a small distance, so the fixed resolution of the ruler causes a relatively large percentage uncertainty, oe
(b) B1 measuring across several wavelengths increases the total distance measured for the same absolute uncertainty, reducing the percentage uncertainty; dividing by the number of wavelengths then gives a more precise mean wavelength, oe
(b) Answer: A single wavelength is a small distance, so a ruler's fixed resolution gives it a large percentage uncertainty. Measuring across several wavelengths and dividing reduces this percentage uncertainty, giving a more precise value.
(c) M1 20.0 / 5, oe
(c) A1 4.0 cm = 0.040 m cao
(c) Answer: 0.040 m
(d) M1 uses the wavelength in metres (0.040 m) from part (c), ft
(d) M1 wave speed = 5.0 * 0.040, oe
(d) A1 0.20 m/s cao
(d) Answer: 0.20 m/s
(e) B1 the wavelength decreases, oe
(e) B1 wave speed depends on water depth, which is unchanged, so speed stays constant; since wave speed = frequency * wavelength, increasing frequency (with constant speed) means wavelength must decrease, oe
(e) Answer: The wavelength decreases. Wave speed depends on the water depth, which has not changed, so speed stays constant; since speed = frequency x wavelength, a higher frequency means a smaller wavelength.

Question 6

(a) B1 the type/finish of the surface (which face of the Leslie cube the detector faces), oe
(a) Answer: The type of surface (which face of the cube is used).
(b) B1 any one of: volume/mass of water in the cube; starting temperature of the water; time before each reading is taken, oe
(b) B1 a second, different variable from the list above, oe; also allow the distance between the detector and each face, or the surface area of each face
(b) Answer: For example: the volume and starting temperature of the water in the cube, and the time before each reading is taken.
(c) B1 matt black (highest reading, 85 units)
(c) B1 matt, dull surfaces are better emitters (and absorbers) of infrared radiation than shiny surfaces, oe
(c) Answer: Matt black, with the highest reading (85 units); dull, matt surfaces are better emitters of infrared radiation than shiny, polished surfaces.
(d) B1 the intensity of infrared radiation detected decreases with distance from the source, oe
(d) B1 if the distance varied between readings, this would be an uncontrolled variable, so differences in the reading could not be attributed only to the surface type, oe
(d) Answer: Detected intensity falls with distance from the source. If distance varied, it would be an uncontrolled variable, making it impossible to say any difference was caused only by the surface type.

Question 7

(a) B1 resistance = potential difference / current, oe
(a) Answer: Resistance = potential difference / current.
(b) M1 3.0 / 0.50, oe
(b) A1 6.0 ohms cao
(b) Answer: 6.0 ohms
(c) B1 keeping the current the same for every length means any change in temperature (and so resistance) due to self-heating is the same each time, oe
(c) B1 this avoids the current itself being an uncontrolled variable that could otherwise affect the comparison between lengths, oe
(c) Answer: Keeping the current constant means the wire heats up by a similar amount each time, so any change in resistance can be attributed to the length of wire rather than to different amounts of self-heating at different currents.
(d) M1 gradient = (6.0 - 2.0) / (60 - 20), oe
(d) M1 = 4.0 / 40, oe
(d) A1 0.10 ohms/cm cao
(d) Answer: 0.10 ohms/cm
(e) B1 the resistance per unit length (per cm) of the wire, ft
(e) Answer: The resistance added per cm of extra wire length.

Question 8

(a) B1 fill the displacement can with water until it overflows from the spout, and let it stop dripping, with an empty measuring cylinder placed under the spout, oe
(a) B1 lower the stone gently into the can, e.g. on a piece of thread, so the displaced water flows into the measuring cylinder, oe
(a) B1 read the volume of water collected in the measuring cylinder at eye level, at the bottom of the meniscus; this volume equals the volume of the stone, oe
(a) Answer: Fill the can until it just overflows, place an empty measuring cylinder under the spout, then lower the stone in on a thread; the volume of water collected in the cylinder equals the stone's volume.
(b) M1 40.5 / 15.0, oe
(b) A1 2.70 g/cm³ cao
(b) Answer: 2.70 g/cm³
(c) M1 absolute uncertainty = plus or minus 0.5 cm³ (half the smallest scale division), then (0.5 / 15.0) x 100, oe
(c) A1 3.3% cao (awrt 3.3)
(c) Answer: 3.3%

Question 9

(a) B1 6.0 cm cao (from 16.0 - 10.0)
(a) Answer: 6.0 cm
(b) M1 extension at 1.0 N = 2.0 cm = 0.020 m; spring constant = 1.0 / 0.020 = 50 N/m, oe
(b) M1 extension at 4.0 N = 8.0 cm = 0.080 m; spring constant = 4.0 / 0.080 = 50 N/m, oe
(b) A1 both values of the spring constant are equal (50 N/m)
(b) A1 valid conclusion: since force / extension (the spring constant) is constant over this range, force is directly proportional to extension, so the spring obeys Hooke's law, oe
(b) Answer: At 1.0 N, k = 1.0 / 0.020 = 50 N/m; at 4.0 N, k = 4.0 / 0.080 = 50 N/m. Since k is the same both times, the spring obeys Hooke's law over this range.
(c) B1 between 4.0 N and 5.0 N (at 5.0 N)
(c) B1 because the extension at 5.0 N (11.0 cm) is greater than the 10.0 cm that proportionality (using k = 50 N/m) would predict, showing extension is no longer directly proportional to force, oe
(c) Answer: Between 4.0 N and 5.0 N; if proportional, 5.0 N should give an extension of 10.0 cm, but the actual extension is 11.0 cm, so proportionality no longer holds.
(d) M1 converts extension to metres: 8.0 cm = 0.080 m, oe
(d) M1 0.5 * 50 * 0.080², oe
(d) A1 0.16 J cao
(d) Answer: 0.16 J

Question 10

(a) B1 velocity = distance / time (width of card / time the card blocks the light gate), oe
(a) Answer: Velocity = distance / time.
(b) M1 (0.80 - 0.20) / 0.40, oe
(b) M1 = 0.60 / 0.40, oe
(b) A1 1.5 m/s² cao
(b) Answer: 1.5 m/s²
(c) B1 the angle/height of the ramp (or the force accelerating the trolley), oe
(c) Answer: The angle (height) of the ramp.
(d) M1 absolute uncertainty = plus or minus 0.05 cm (half the smallest scale division), then (0.05 / 5.0) x 100, oe
(d) A1 1.0% cao
(d) Answer: 1.0%
(e) B1 light gates time electronically with a very small resolution, removing human reaction-time error, oe
(e) B1 human reaction time (typically 0.2-0.3 s) is significant compared with the short time intervals involved, so a stopwatch gives a much larger percentage uncertainty than a light gate, oe
(e) Answer: Light gates record time electronically, removing human reaction-time error; a stopwatch's reaction-time error is large compared with the short time intervals involved, giving it a much bigger percentage uncertainty.

Question 11

(a) B1 variable resistor (rheostat), oe
(a) Answer: Variable resistor.
(b) M1 1.0 / 0.20, oe
(b) A1 5.0 ohms cao
(b) Answer: 5.0 ohms
(c) M1 4.0 / 0.46, oe
(c) A1 8.7 ohms (2 s.f.), awrt 8.7
(c) Answer: 8.7 ohms
(d) B1 resistance increases as potential difference (and current) increases, ft
(d) B1 correctly quotes both values, e.g. from 5.0 ohms at 1.0 V to 8.7 ohms at 4.0 V, ft
(d) Answer: Resistance increases as potential difference increases, from 5.0 ohms at 1.0 V to 8.7 ohms at 4.0 V.
(e) B1 as potential difference (and current) increases, more energy is transferred electrically to the filament, so its temperature increases, oe
(e) B1 at a higher temperature the (positive) ions in the filament vibrate with greater amplitude, oe
(e) B1 this causes more frequent/greater collisions between the charge carriers (electrons) and the vibrating ions, which increases the resistance, oe
(e) Answer: More energy is transferred to the filament, raising its temperature. At a higher temperature the ions vibrate more, so charge carriers collide with them more often, increasing resistance.

Question 12

(a) B1 a stable, clear stationary wave pattern forms, with well-defined nodes and antinodes (rather than a small, blurred vibration), oe
(a) Answer: A stable, large-amplitude stationary wave pattern forms, with clear nodes and antinodes.
(b) B1 a point on the wave with (approximately) zero amplitude, which does not oscillate, oe
(b) Answer: A point on a stationary wave that does not oscillate (zero amplitude).
(c) M1 wavelength = 2 * 90 / 3, oe
(c) A1 60 cm = 0.60 m cao
(c) Answer: 0.60 m
(d) M1 uses wavelength in metres (0.60 m) from part (c), ft
(d) M1 speed = 50 * 0.60, oe
(d) A1 30 m/s cao
(d) Answer: 30 m/s
(e) B1 it flashes at (or near) the vibration frequency, making the fast-moving string appear to move slowly or appear stationary, so its shape can be seen clearly and safely, oe
(e) Answer: The strobe flashes near the vibration frequency, making the fast-moving string appear to move slowly, so it can be observed clearly and safely.

Question 13

(a) B1 the insulation reduces the thermal energy transferred from the block to the surroundings, oe
(a) B1 without it, some electrical energy would heat the surroundings rather than the block, making the temperature rise smaller than it should be for that energy input, so the calculated specific heat capacity would be a systematic overestimate, oe
(a) Answer: Insulation reduces heat loss to the surroundings; without it, some energy heats the surroundings instead of the block, making the calculated specific heat capacity too high (a systematic error).
(b) M1 4.0 * 12 * 250, oe
(b) A1 12000 J (1.2 x 10⁴ J) cao
(b) Answer: 12000 J
(c) M1 rearranges to specific heat capacity = energy / (mass * change in temperature), oe
(c) dM1 12000 / (1.0 * 12), oe
(c) A1 1000 J/(kg degC) cao
(c) Answer: 1000 J/(kg degC)
(d) M1 absolute uncertainty = plus or minus 1 degC (0.5 degC from each of the two readings), then (1 / 12) x 100, oe
(d) A1 8.3% cao (awrt 8.3)
(d) Answer: 8.3%
(e) B1 use a larger temperature rise, e.g. by heating for longer or using a smaller mass block, so the same absolute uncertainty becomes a smaller percentage of a bigger temperature change, oe
(e) Answer: Increase the temperature rise (e.g. heat for longer), so the fixed absolute uncertainty is a smaller percentage of a larger change.

Question 14

(a) B1 independent variable: whether the beaker is insulated or not, oe
(a) B1 dependent variable: temperature of the water (over time), oe
(a) Answer: Independent variable: whether the beaker has insulation. Dependent variable: the water temperature over time.
(b) B1 volume of water in each beaker, oe
(b) B1 starting temperature of the water, oe; allow the room/surrounding temperature, absence of draughts, or whether a lid is used
(b) Answer: For example, the volume of water in each beaker and the starting temperature of the water.
(c) M1 insulated: change in temperature = 80 - 68 = 12 degC, oe
(c) A1 insulated rate = 12 / 300 = 0.04 degC/s cao
(c) M1 uninsulated: change in temperature = 80 - 50 = 30 degC, oe
(c) A1 uninsulated rate = 30 / 300 = 0.10 degC/s cao
(c) Answer: Insulated: 0.04 degC/s. Uninsulated: 0.10 degC/s.
(d) B1 the uninsulated beaker, ft from part (c)
(d) B1 it loses thermal energy to the surroundings at a faster rate, because the insulation on the other beaker reduces the rate of energy transfer (by conduction/convection) to the surroundings, oe
(d) Answer: The uninsulated beaker cools faster; insulation reduces the rate at which thermal energy is transferred to the surroundings.

Question 15

(a) B1 the speed of the light decreases, oe
(a) B1 the wavelength of the light decreases (the frequency stays the same), oe
(a) Answer: The speed decreases, and the wavelength decreases (the frequency stays the same).
(b) M1 sin(40) / sin(25), oe
(b) M1 = 0.643 / 0.423 (or equivalent decimals), oe
(b) A1 1.5 (2 s.f.) or 1.52 (3 s.f.), awrt 1.5
(b) Answer: 1.5 (1.52 to 3 s.f.)
(c) M1 uses the refractive index from part (b), ft
(c) dM1 sin(critical angle) = 1 / 1.52, oe
(c) A1 41 degrees (2 s.f.), awrt 41, ft
(c) Answer: 41 degrees
(d) B1 total internal reflection occurs (all the light is reflected back into the glass; none is refracted out), oe
(d) Answer: Total internal reflection occurs.
(e) B1 draws the outline of the glass block, marks the point of entry and draws a normal line perpendicular to the block's surface at that point, oe
(e) B1 traces the path of the ray (e.g. using pins, or marking crosses along the emerging ray), removes the block, and joins the marks to draw the refracted ray; the angle between this ray and the normal is then measured with a protractor, oe
(e) Answer: Draw the block's outline and a normal perpendicular to its surface at the point of entry; trace the ray's path with marks, remove the block, join the marks, and measure the angle to the normal with a protractor.

Question 16

(a) B1 0.4% cao (from (0.1/24.0) x 100 = 0.417%, awrt 0.4)
(a) Answer: 0.4%
(b) B1 2.0% cao (from (0.16/8.00) x 100)
(b) Answer: 2.0%
(c) M1 adds the answers to (a) and (b), ft
(c) A1 2.4% cao (awrt 2.4), ft
(c) Answer: 2.4%
(d) M1 density = 24.0 / 8.00, oe
(d) dM1 absolute uncertainty = 2.4% of the density (ft from part c), oe
(d) A1 3.00 plus or minus 0.07 g/cm³ cao (allow appropriate rounding), ft
(d) Answer: 3.00 plus or minus 0.07 g/cm³

Question 17

Level 1 (1-2): Makes simple, undeveloped statement(s) about possible error(s) or improvement(s), with little or no linking to the effect on the result, and little use of correct scientific terms.
Level 2 (3-4): Gives some relevant sources of error and/or improvements, with limited explanation of how they affect the calculated specific heat capacity. May address only systematic error or only random error, not both.
Level 3 (5-6): Gives a detailed and coherent evaluation, correctly identifying and explaining at least one systematic error and one random error, linking each to a valid improvement and to the direction of its effect on the result (e.g. why the calculated value is too high), using correct scientific terminology throughout.
Indicative content:
- Heat energy is transferred to the surroundings/air rather than staying in the block; this is a systematic error
- This causes the measured temperature rise to be smaller than it should be for the energy actually supplied, so the calculated specific heat capacity (energy divided by mass times temperature rise) comes out too high
- Wrapping the block in an insulating jacket, and placing insulation between the block and the bench, would reduce this heat loss
- Placing the heater and thermometer in separate holes drilled close together improves thermal contact with the block and reduces temperature gradients within it
- Reading the ammeter, voltmeter and thermometer introduces random error; repeating the experiment and calculating a mean value for the temperature rise would reduce the effect of random error
- Using a joulemeter to measure energy transferred directly removes the need to separately time the heating and read the current and voltage, reducing random timing errors
- Starting and stopping the switch at the exact recorded times reduces timing-related random error
- Using a larger temperature rise (e.g. heating for longer, or using a smaller mass of metal) reduces the percentage impact of a fixed reading uncertainty on the temperature measurement

Question 18

(a) B1 the resistance of the wire, oe
(a) Answer: The resistance of the wire.
(b) M1 2.0 / 0.40, oe
(b) A1 5.0 ohms cao
(b) Answer: 5.0 ohms
(c) M1 scale factor = 125 / 50 (= 2.5), oe
(c) M1 5.0 * 2.5, ft from part (b)
(c) A1 12.5 ohms cao, ft
(c) Answer: 12.5 ohms
(d) B1 a longer wire carrying the same current dissipates more total energy, so it may heat up more, increasing its resistance above the value predicted by simple proportionality, oe
(d) B1 or: the wire's cross-sectional area/diameter may not be perfectly uniform along its whole length, oe (credit either valid reason once, both if two distinct reasons given)
(d) Answer: A longer wire may heat up more for the same current, increasing its resistance above the proportional prediction; or its cross-sectional area may not be perfectly uniform along its full length.

Physics Required Practicals and Uncertainties - Worksheets, Questions and Revision