PAG

Question 1

Free fall experiment

Answer 1

Method and Calculations

• Measure the height (h):
  
  • Measure the vertical distance from the bottom of the ball bearing to the trapdoor.
• Release the ball bearing:
  
  • Simultaneously start the timer and disconnect the electromagnet by flicking the switch.
  • The ball bearing falls, knocking the trapdoor down, breaking the circuit, and stopping the timer.
• Record and repeat:
  
  • Record the time (t) shown on the timer.
  • Repeat the experiment three times and calculate the average time.
• Calculate acceleration due to gravity (g):
  
  • Use the equation: h = 0.5 * g * t² (from page 50).
  • Rearrange to solve for g = 2h / t².
• Repeat for different heights:
  
  • Perform the experiment for several heights, calculate g for each, and average the results.

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Analysis (y = mx + c)

• Plot a graph:
  
  • Plot h (y-axis) against t² (x-axis).
  • The graph should be linear, with the equation h = 0.5g * t², corresponding to y = mx + c, where:
    
    • Gradient (m) = 0.5g.
    • y-intercept (c) = 0.
• Determine g:
  
  • Calculate g = 2 * gradient.

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Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Use a ruler with a high resolution to measure height (h) accurately.
  • Ensure the timer is precise and starts/stops exactly when the ball bearing is released/hits the trapdoor.
  • Repeat the experiment multiple times to reduce random errors.
• Safety:
  
  • Place a cushion or soft material below the trapdoor to prevent damage or injury from the falling ball bearing.
• Limitations:
  
  • Air resistance may affect the motion of the ball bearing, especially at higher heights.
  • Human reaction time may introduce errors when starting/stopping the timer manually.
  • The trapdoor mechanism may not break the circuit instantaneously.
• Improvements:
  
  • Use a light gate or electronic sensor to measure time more accurately.
  • Perform the experiment in a vacuum to eliminate air resistance.
  • Use a data logger to automatically record the time and reduce human error.

Question 2

Young’s Modulus (PAG)

Answer 2

Method and Calculations

• Set up the wire:
  
  • Use a thin and long test wire for more accurate measurements, reducing uncertainty.
  • Clamp the wire to the bench and hang weights off one end, starting with the smallest weight necessary to straighten the wire.
• Measure dimensions:
  
  • Find the wire’s cross-sectional area by measuring its diameter with a micrometer and using the formula for the area of a circle.
  • Measure the unstretched length from the fixed end of the wire to the marker.
• Record extensions:
  
  • Record the starting position of the marker.
  • Increase the weight in steps and record the marker reading each time to determine the extension.
• Calculate stress and strain:
  
  • Use the results to calculate stress and strain of the wire.
  • Plot a stress-strain curve.

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Analysis (y = mx + c)

• Plot a graph:
  
  • Plot stress (y-axis) against strain (x-axis).
  • The graph should show a linear region (Hooke’s Law) where stress ∝ strain, corresponding to y = mx + c, where:
    
    • Gradient (m) = Young’s modulus.
    • y-intercept (c) = 0.

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Accuracy, Safety, Limitations, and Improvements

• Systematic Errors:
  
  • Use a vernier scale for more precise readings of extension.
  • Ensure the wire returns to its original length after removing the load to avoid permanent deformation.
• Random Errors:
  
  • Reduce parallax error by reading the marker carefully.
  • Repeat the experiment for all loads and calculate an average extension.
  • Measure the wire’s diameter at several points and take an average to reduce uncertainty in cross-sectional area.
• Safety Considerations:
  
  • Wear safety goggles in case the wire snaps.
  • Place a cushion or soft surface below the mass hanger to catch it if it falls.
• Improvements:
  
  • Use a digital micrometer for more accurate diameter measurements.
  • Ensure the wire is perfectly vertical to avoid uneven stretching.
  • Use a data logger to automatically record extensions for greater precision.

Question 3

Resistivity (PAG)

Answer 3

Method and Calculations

• Measure the wire dimensions:
  
  • Measure the diameter of the wire in at least three places and calculate the mean diameter.
  • Halve the mean diameter to find the mean radius.
  • Use the radius to calculate the cross-sectional area (A = πr²).
• Set up the experiment:
  
  • Clamp the wire and attach the flying lead.
  • Close the switch and measure the current (I) and potential difference (V) across the test wire.
  • Calculate the resistance (R) using R = V/I.
• Repeat for different lengths:
  
  • Reposition the flying lead for different wire lengths and repeat the process.
  • Record the mean resistance for each length.

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Analysis (y = mx + c)

• Plot a graph:
  
  • Plot average resistance (y-axis) against length (x-axis).
  • The graph should be linear, with the equation R = (ρ/A) * L, corresponding to y = mx + c, where:
    
    • Gradient (m) = ρ/A.
    • y-intercept (c) = 0.
• Determine resistivity:
  
  • Calculate ρ = gradient × A, where A is the cross-sectional area.

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Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Use a micrometer for precise diameter measurements.
  • Ensure the flying lead makes good contact to avoid inconsistent readings.
  • Repeat measurements to reduce random errors.
• Safety Considerations:
  
  • Avoid overheating by ensuring the circuit is set up correctly.
  • Handle the wire carefully to prevent injury.
• Limitations:
  
  • The wire may not have a perfectly circular cross-section, affecting area calculations.
  • Temperature changes may alter the wire’s resistance.
• Improvements:
  
  • Use a digital multimeter for more accurate readings.
  • Perform the experiment in a temperature-controlled environment.
  • Measure the diameter at more than three points for a better mean value.

Question 4

Potential divider (PAG)

Answer 4

Method and Calculations

• Set up the heat sensor:
  
  • Use a thermistor in a potential divider circuit (as shown in Figure 3).
  • Place the thermistor in a beaker of ice water, measure the initial temperature, and record the voltage across the thermistor.
• Record data:
  
  • Gradually heat the beaker, recording the temperature and voltage at regular intervals over a suitable range.
• Plot a graph:
  
  • Plot voltage (y-axis) against temperature (x-axis).

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Analysis (y = mx + c)

• Interpret the graph:
  
  • The graph should show that as temperature increases, the voltage decreases.
  • This is because the thermistor’s resistance decreases with increasing temperature, causing it to take a smaller share of the total potential difference.
  • The relationship is non-linear due to the thermistor’s exponential response to temperature.

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Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Use a digital thermometer for precise temperature measurements.
  • Ensure the thermistor is fully submerged in the water for consistent readings.
  • Stir the water to maintain a uniform temperature.
• Safety Considerations:
  
  • Handle the hot water carefully to avoid burns.
  • Use a heat-resistant beaker and place it on a stable surface.
• Limitations:
  
  • The thermistor’s response may not be perfectly consistent due to manufacturing variations.
  • The non-linear relationship makes it harder to predict voltage changes at extreme temperatures.
• Improvements:
  
  • Use a data logger to automatically record voltage and temperature for greater precision.
  • Calibrate the thermistor using known temperature points for better accuracy.
  • Repeat the experiment with a different thermistor to check for consistency.

Question 5

Diffraction grating (PAG)

Answer 5

Method and Calculations

• Set up the experiment:
  
  • Pass monochromatic light through a diffraction grating to create a pattern of bright lines (maxima) on a dark background.
  • Identify the zero-order line (central maximum) and the first-order lines on either side.
• Measure the angle:
  
  • Use the small angle approximation to calculate the angle (θ) of the first-order line relative to the zero-order line, given the fringe width (x) and the distance to the screen (D).
• Calculate the wavelength:
  
  • Use the formula: nλ = d sinθ, where:
    
    • n = order of the maximum (e.g., 1 for first-order),
    • λ = wavelength of the light,
    • d = slit separation,
    • θ = angle between the maximum and the incident light.

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Analysis (y = mx + c)

• Interpret the pattern:
  
  • The bright lines are due to constructive interference, while the dark areas result from destructive interference.
  • For white light, the pattern splits into a spectrum from red (outside) to violet (inside) for each order, with the zero-order maximum remaining white.

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Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Use a laser or high-quality monochromatic light source for clear, sharp fringes.
  • Measure the distance to the screen (D) and fringe width (x) carefully to minimize errors in calculating θ.
• Safety Considerations:
  
  • Avoid looking directly into the laser beam or bright light sources to protect your eyes.
  • Ensure the setup is stable to prevent the diffraction grating or screen from moving during the experiment.
• Limitations:
  
  • The small angle approximation may introduce errors for larger angles.
  • The diffraction grating may have imperfections, leading to less distinct fringes.
• Improvements:
  
  • Use a vernier scale or digital caliper to measure fringe widths more accurately.
  • Repeat the experiment with different slit separations (d) to verify consistency.
  • Use a spectrometer for more precise angle measurements.

Question 6

Plank constant (PAG)

Answer 6

Method and Calculations

• Set up the experiment:
  
  • Use monochromatic LEDs emitting a single wavelength of light.
  • Set the variable resistor to its maximum resistance to prevent current flow initially.
• Measure threshold voltage (V₀):
  
  • In a dark room, adjust the resistor until the LED just begins to light up.
  • Record the threshold voltage (V₀) and the wavelength (λ) of the emitted light.
• Repeat and average:
  
  • Repeat the experiment multiple times, averaging the results for V₀.
  • Perform the experiment for a range of LEDs with different wavelengths.
• Plot a graph:
  
  • Plot threshold voltage (V₀) against the inverse of the wavelength (1/λ).
  • The graph should be a straight line with the gradient = hc/e.
• Calculate Planck constant (h):
  
  • Use the gradient to calculate h = (gradient × e) / c.

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Analysis (y = mx + c)

• Interpret the graph:
  
  • The equation eV₀ = hc/λ corresponds to y = mx + c, where:
    
    • y = V₀,
    • x = 1/λ,
    • gradient (m) = hc/e,
    • y-intercept (c) = 0.
• Determine Planck constant (h):
  
  • Substitute the gradient into the equation h = (gradient × e) / c.

Accuracy, Safety, Limitations, and Improvements

• Systematic Errors:
  
  • Human error in identifying the exact voltage at which the LED begins to glow.
  • Use a black viewing tube in a darkened room for better accuracy.
  • A more accurate method: Plot a current vs. voltage graph and extrapolate to find the threshold voltage.
• Random Errors:
  
  • LEDs emit a narrow spectrum of light (∼60 nm width), not a single frequency.
  • The quoted wavelength is the central wavelength, but the lower end is emitted when the LED just glows, introducing error.
• Safety Considerations:
  
  • Do not stare directly at brightly lit LEDs, especially blue LEDs (close to UV).
  • Limit current to ≤ 50 mA (check LED ratings) to avoid damage.
  • Use a 330 Ω resistor to limit current.
  • Potentiometer hazard: Incorrect wiring can cause short circuits, leading to overheating and fire.
    
    • Turn off power immediately if burning is smelled.
  • Keep water away from electrical equipment.
• Improvements:
  
  • Use a spectrometer to measure the exact wavelength of light emitted by the LED.
  • Use a data logger to record voltage and current more accurately.
  • Repeat the experiment with a wider range of LEDs to improve the reliability of the graph.

Question 7

Internal resistance (PAG)

Answer 7

Method and Calculations

• Set up the circuit:
  
  • Set the variable resistor to its highest resistance.
  • Record the current (I) and potential difference (V) across the circuit.
• Repeat measurements:
  
  • Adjust the load resistance and repeat the measurements for multiple values.
  • Calculate the mean current and voltage for each resistance.
• Plot a graph:
  
  • Plot a V-I graph with mean data points and draw a line of best fit.
  • Ensure all variables, including temperature, are kept constant.
• Analyze results:
  
  • Determine the gradient (-r) and intercept (E) from the graph.
  • Use the equation V = E - Ir, where:
    
    • E = electromotive force (e.m.f.),
    • r = internal resistance.

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Analysis (y = mx + c)

• Interpret the graph:
  
  • The equation V = E - Ir corresponds to y = mx + c, where:
    
    • y = V,
    • x = I,
    • gradient (m) = -r,
    • y-intercept (c) = E.
• Determine internal resistance and e.m.f.:
  
  • The gradient gives the internal resistance (r).
  • The y-intercept gives the e.m.f. (E).

===

Accuracy, Safety, Limitations, and Improvements

• Systematic Errors:
  
  • Close the switch briefly to take readings, preventing changes in the internal resistance of the battery.
• Random Errors:
  
  • Use fairly new cells to avoid variations in e.m.f. and internal resistance.
  • Wait for readings to stabilise before recording.
  • Take multiple repeats (at least 3) and calculate a mean to reduce errors.
• Safety Considerations:
  
  • Electrical components can get hot with prolonged use.
  • Switch off the power supply if burning is smelled.
  • Keep liquids away from equipment to avoid damage.
• Improvements:
  
  • Use a data logger to record current and voltage automatically for greater precision.
  • Perform the experiment in a temperature-controlled environment to minimize thermal effects.
  • Use a digital multimeter for more accurate measurements of current and voltage.

Question 8

Oscilloscope (PAG)

Answer 8

Cathode Ray Oscilloscope (CRO):

• Displays voltage over time from a signal generator, known as a trace.
• The type of trace depends on the source:
  
  • AC supply: Produces a trace that alternates between positive and negative patterns.
  • Sound waves: Converted into electrical signals by a microphone can also be displayed.

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Oscilloscope Screen:

• Divided into divisions:
  
  • Vertical axis: Represents volts.
  • Horizontal axis: Represents time.
• Volts per division and seconds per division are controlled by the gain and timebase dials, respectively.

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Wave Properties:

• Oscilloscope traces can be used to calculate:
  
  • Frequency: 1 ÷ period
  • Period: Measured using the timebase.

Question 9

Polarising filters for light (PAG)

Answer 9

Polarisation:

• Observed by shining unpolarised light through two polarising filters aligned vertically and rotating the second filter.
• Rotating the second filter reduces light intensity as its transmission axis deviates from vertical.

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Key Observations:

• At 45 degrees between transmission axes:
  
  • Intensity through the second filter is half that of the first.
• At right angles (90 degrees):
  
  • No light passes through.
• After 180-degree rotation:
  
  • Transmission axes realign, allowing all light through.

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Applications:

• Polaroid sunglasses: Use polarising filters to block partially polarised light, reducing glare.

Question 10

Polarising filters for Microwave (PAG)

Answer 10

Metal Grilles and Microwaves:

• Metal grilles act like polarising filters for microwaves.
• Microwaves:
  
  • Have longer wavelengths than visible light.
  • Are a type of electromagnetic wave.

===

Polarisation Direction:

• Refers to the direction of the electric field, not the magnetic field.

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How Metal Grilles Work:

• Absorb electric fields aligned with their orientation using free electrons.
• Horizontal electric fields pass through vertically positioned grilles, and vice versa.
  
  • Unlike polarising filters, which block light when axes are perpendicular.

Question 11

Speed of sound (PAG)

Answer 11

Method and Calculations

• Set up the experiment:
  
  • Place a hollow tube in water to create a closed-end pipe.
  • Note the frequency (f) of a tuning fork and hold it above the tube.
• Produce resonance:
  
  • Tap the tuning fork gently to produce sound waves that travel down the tube and reflect at the air/water surface.
  • Adjust the tube’s height until the sound resonates the loudest, indicating the lowest resonant frequency of the closed tube.
• Measure and calculate:
  
  • The tube’s length at resonance is a quarter of the sound wave’s wavelength (λ/4).
  • Use the frequency and wavelength to calculate the speed of sound in air using the equation:
    
    • v = fλ.

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Analysis

• Resonance condition:
  
  • For a closed pipe, the lowest resonant frequency occurs when the tube length is λ/4.
  • The relationship between the tube length (L) and wavelength (λ) is: L = λ/4.
• Calculate speed of sound:
  
  • Rearrange the equation to find λ = 4L.
  • Substitute λ and the known frequency (f) into v = fλ to calculate the speed of sound.

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Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Ensure the tuning fork is struck gently to avoid overtones that could distort the resonance.
  • Measure the tube length carefully using a ruler with high precision.
  • Repeat the experiment to confirm the resonant length and calculate an average value.
• Safety Considerations:
  
  • Handle the tuning fork carefully to avoid injury or damage.
  • Ensure the tube is stable to prevent spills or accidents.
• Limitations:
  
  • The air/water surface may not be perfectly flat, affecting the reflection of sound waves.
  • Background noise can make it difficult to detect the loudest resonance.
• Improvements:
  
  • Use a microphone and oscilloscope to detect resonance more accurately.
  • Perform the experiment in a quiet environment to minimize interference.
  • Repeat with tuning forks of different frequencies to verify consistency.

Question 12

Semi circle light rays (PAG)

Answer 12

Method and Calculations

• Set up the experiment:
  
  • Place the glass block on paper and shine light from the ray box into the curved surface of the block.
• Find the critical angle:
  
  • Rotate either the ray box or the glass block until the refracted ray from the glass block makes an angle of 90° (grazes the surface).
  • Use a protractor to measure the angle of incidence (c) of the ray of light within the block; this is the critical angle.
• Calculate refractive index:
  
  • Use the formula: n = (sin c)^–1 to calculate the refractive index (n) of the glass block.

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Analysis

• Critical angle and refraction:
  
  • At the critical angle (c), the refracted ray travels along the boundary between the glass and air (angle of refraction = 90°).
  • The relationship between the refractive index (n) and the critical angle (c) is given by:
    
    • n = 1 / sin c.
• Interpretation:
  
  • A higher refractive index corresponds to a smaller critical angle, indicating greater bending of light.

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Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Ensure the ray box produces a narrow, well-defined beam of light for precise measurements.
  • Use a protractor with high precision to measure the angle of incidence.
  • Repeat the experiment to confirm the critical angle and calculate an average value.
• Safety Considerations:
  
  • Handle the glass block carefully to avoid breakage or injury.
  • Avoid shining the light directly into eyes.
• Limitations:
  
  • The curved surface of the glass block may introduce errors in measuring the angle of incidence.
  • The ray box may produce a beam that is not perfectly collimated, affecting accuracy.
• Improvements:
  
  • Use a semicircular glass block to simplify the alignment of the incident and refracted rays.
  • Perform the experiment in a darkened room to improve visibility of the light beam.
  • Use a digital angle finder for more precise angle measurements.

Question 13

Center of mass (PAG)

Answer 13

1. If you hang an object from a single point, the centre of mass will always lie directly below that point
2. So hang an object from two different points and draw a line straight down the object (the plumb line)
3. The point at which these lines intersect is the centre of mass

Question 14

Number of Photons equation

Answer 14

Energy of wave supplier ÷ energy of one photon

Question 15

Specific Heat Capacity (PAG)

Answer 15

Measuring Specific Heat Capacity

• Measure initial conditions:
  
  • Measure the mass (m) and initial temperature (T₁) of the substance.
• Heat the substance:
  
  • Use a heater to heat the substance, monitoring the change in temperature (ΔT).
  • Measure the current (I) and voltage (V) across the heater, and record the time (t) it is on.
• Calculate energy supplied:
  
  • Use the formula: E = V × I × t.
• Calculate specific heat capacity (c):
  
  • Use the formula: E = m × c × ΔT.
  • Rearrange to find: c = E / (m × ΔT).

Estimating Specific Heat Capacity Using Mixing Method

• Mix hot and cold substances:
  
  • Mix a hot substance (mass m₁, specific heat capacity c₁, initial temperature T₁) with a cold substance (mass m₂, specific heat capacity c₂, initial temperature T₂).
  • Measure the final temperature (T₀) once thermal equilibrium is reached.
• Calculate specific heat capacity:
  
  • Use the formula: m₁c₁(T₁ - T₀) = m₂c₂(T₀ - T₂).
  • Rearrange to find the unknown specific heat capacity (c₁ or c₂).

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Analysis

• Energy transfer:
  
  • In the heating method, the energy supplied by the heater is equal to the energy absorbed by the substance.
  • In the mixing method, the energy lost by the hot substance is equal to the energy gained by the cold substance (assuming no heat loss to the surroundings).
• Assumptions:
  
  • No heat is lost to the surroundings in the mixing method.
  • The heater is 100% efficient in the heating method.

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Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Use a thermometer with high precision to measure temperature changes.
  • Ensure the heater is fully submerged and the substance is well-insulated to minimize heat loss.
  • Repeat measurements to reduce random errors.
• Safety Considerations:
  
  • Handle hot substances carefully to avoid burns.
  • Ensure electrical equipment (e.g., heater) is properly insulated to prevent electric shocks.
• Limitations:
  
  • Heat loss to the surroundings can affect results in both methods.
  • The mixing method assumes no heat loss, which is not always realistic.
• Improvements:
  
  • Use a calorimeter to minimize heat loss in the mixing method.
  • Perform the experiment in a temperature-controlled environment.
  • Use a data logger to monitor temperature changes continuously.

Question 16

Specific Latent Heat (PAG)

Answer 16

Method and Calculations

Measuring Specific Latent Heat of Fusion

• Set up the experiment:
  
  • Use a heating coil in one funnel of ice.
  • Connect the coil to an ammeter and voltmeter.
• Heat the ice:
  
  • Turn the heater on for three minutes and measure the current (I) and voltage (V).
  • Calculate the energy transferred using W = VIt.
• Measure melted ice:
  
  • Use a second unheated funnel to measure the mass of ice melted at room temperature.
  • Subtract the unheated mass from the heated mass to find the mass of ice melted due to the heater (m).
• Calculate latent heat of fusion:
  
  • Use the formula: E = mL, where L is the specific latent heat of fusion.
  • Rearrange to find: L = E/m.

Measuring Specific Latent Heat of Vaporisation

• Set up the experiment:
  
  • Place a heating coil in a beaker of water, and insulate the outside of the beaker.
  • Connect the coil to an ammeter and voltmeter.
• Heat the water:
  
  • Start heating the water and monitor the mass of water as it boils, using a mass balance.
  • Measure the voltage (V) and current (I) across the heating coil.
  • Once the mass decreases by about 15 g, stop the timer.
• Calculate energy transferred:
  
  • Use the formula: W = VIt.
• Calculate latent heat of vaporisation:
  
  • Use the formula: L = E/m, where E is the energy transferred and m is the mass lost.

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Analysis

• Energy transfer:
  
  • In both experiments, the energy supplied by the heater is used to change the state of the substance (ice to water or water to steam) without changing its temperature.
• Key equations:
  
  • For fusion: E = mL_f.
  • For vaporisation: E = mL_v.

===

Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Use a high-precision mass balance to measure the mass of ice or water.
  • Ensure the heating coil is fully submerged and the system is well-insulated to minimize heat loss.
  • Repeat measurements to reduce random errors.
• Safety Considerations:
  
  • Handle hot water and steam carefully to avoid burns.
  • Ensure electrical equipment (e.g., heater) is properly insulated to prevent electric shocks.
• Limitations:
  
  • Heat loss to the surroundings can affect results.
  • The mass of ice melted at room temperature may vary due to environmental factors.
• Improvements:
  
  • Use a calorimeter to minimize heat loss.
  • Perform the experiment in a temperature-controlled environment.
  • Use a data logger to monitor temperature and mass changes continuously.

Question 17

Boyle’s Law (PAG)

Answer 17

• Apparatus: Set up the system with a sealed tube containing air and oil, a Bourdon gauge for pressure measurement, and a tyre pump to vary pressure.
• Method:
  
  • Increase pressure by pumping air into the system.
  • Measure pressure with the Bourdon gauge and record volume by multiplying the length of the air-containing part of the tube by the tube’s radius squared.
  • Gradually increase pressure at set intervals and wait for temperature to stabilize before recording readings.
  • Multiply pressure and volume at each point; they should give the same value if Boyle’s Law is valid.
  • Repeat the experiment and calculate the mean for each reading.
• Graph: Plot pressure (p) against volume (v), and you should get a straight line confirming the inverse proportionality between pressure and volume.

Question 18

Absolute Zero (PAG)

Answer 18

• Setup:
  
  • Submerge a stoppered flask filled with air into a beaker of water.
  • Connect the stopper to a Bourdon gauge with tubing (ensure the tubing’s volume is much smaller than the flask’s volume).
• Method:
  
  • Record the temperature of the water and the pressure on the Bourdon gauge.
  • Insert an electric heater, heat the water for a few minutes, then remove it.
  • Stir the water to ensure a uniform temperature and allow time for heat transfer to the air inside the flask.
  • Record the pressure and temperature.
  • Repeat several times, heating the water incrementally until it starts to boil.
  • Repeat the entire experiment twice more with fresh cool water.
• Analysis:
  
  • Verify the Pressure Law: Multiplying pressure and temperature together should yield a constant.
  • Plot a graph of pressure (p) against temperature (T).
  • Draw a line of best fit and extrapolate it to the x-axis to estimate the value of absolute zero.

Question 19

Circular Motion (PAG)

Answer 19

1. Setup: Attach a bung to a string threaded through a plastic tube and weigh the washers used to anchor the free end. Measure the radius r (distance from the bung to the reference mark).
2. Spin the Bung: Rotate the bung in a horizontal circle while maintaining the reference mark level with the tube’s top. Adjust the speed to prevent the mark from moving.
3. Measure Time Period: Record the time, T, for one circle or multiple circles for greater accuracy.
4. Calculate Angular Speed: Use the formula ⍵ = 2π/T to determine the angular speed of the bung.
5. Find Centripetal Force: Calculate using F = m⍵²r, where m is the mass of the bung.
6. Observation: Repeat for different values of r. As r increases, the time period (T) lengthens, but the centripetal force remains constant, equal to the weight of the washers (W = mg).

Question 20

SHM (PAG)

Answer 20

Using Sensors and a Data Logger:
- A position sensor connected to a data logger records the displacement-time graph for a mass-spring system oscillating in SHM.
- From the graph, you can measure the amplitude (A), time period (T), and calculate the frequency (f) using F=t_-1
- As oscillations progress, amplitude decreases due to energy loss, but time period and frequency remain constant.

Without Sensors and a Data Logger:
- A pendulum setup with a ruler, protractor, and stopwatch can investigate SHM manually.
- Measure the length of the string, mass weight, and initial displacement angle (<10°) for accurate results.
- Record time periods (T) for oscillations and calculate frequency (f). Changing the string length affects T, but mass and angle have no effect.

Question 21

Capacitors in Series and Parallel (PAG)

Answer 21

Capacitors in Series

• Set up the first circuit with three identical capacitors connected in series.
• Set the variable resistor to a high resistance value and record it, leaving enough room to decrease the resistance during the experiment.
• Close the switch to start the process of charging the capacitors. Record the initial current in the circuit.
• Use the data logger connected to the voltmeter to record the potential difference across the capacitors over time.
• Adjust the variable resistor to maintain a constant current as much as possible, although it may be difficult as the capacitors approach full charge.
• Monitor the current: Once the capacitors are fully charged (current drops to zero), open the switch

Capacitors in Parallel

• Set up the second circuit
  using another three identical capacitors connected in parallel. Repeat steps 1-5 for this second configuration, ensuring the variable resistor starts at the same resistance value as in the first experiment.
• Plot a graph of current vs. time for each circuit. Use the constant current value you maintained and the time when the current drops to zero, indicating the capacitors are fully charged.
• Plot a graph of charge vs. potential difference for each circuit. Use the equation ΔQ = IΔt to calculate the charge stored by the capacitors at each time reading recorded by the data logger.
• The resulting graphs for charge vs. potential difference should be straight lines through the origin. The gradient of these graphs represents the total capacitance of the capacitors in the circuit.
• Compare the experimental results with theoretical calculations of capacitance for capacitors in series and parallel, ensuring the gradient of your charge vs. potential difference graph matches the expected capacitance.

Question 22

Investigating Charging and Discharging Capacitors (PAG)

Answer 22

Investigating Charging a Capacitor

• Set up the test circuit as shown in Figure 1, including a fixed resistor to slow down the charging process.
• Close the switch to begin charging the capacitor while the data logger records both the potential difference (from the voltmeter) and the current (from the ammeter) over time.
• Observe the current: When the current drops to zero, the capacitor is fully charged.
• Plot graphs of current, potential difference, and charge against time (using the equation ΔQ = IΔt).
• At the start of charging, the current is high because the potential difference across the capacitor is zero, meaning there is no opposing voltage.
• As the capacitor charges, the potential difference across the capacitor increases, causing the current to decrease. The charge (Q) on the capacitor is directly proportional to the potential difference (V) across it.Investigating Discharging a Capacitor
• Open the switch and disconnect the power supply to start discharging the capacitor, as shown in Figure 3.
• Close the switch to allow the capacitor to begin discharging, while the data logger records potential difference and current over time.
• Observe the current: When the current and potential difference reach zero, the capacitor is fully discharged.
• Plot graphs of current, potential difference, and charge against time (similar to the charging investigation).
• Initially, the current is high during discharging, but as charge leaves the plates, the potential difference decreases, and the electrostatic repulsion reduces the current flow.

Question 23

Magnetic Flux Density (PAG)

Answer 23

• Set up the experiment as shown in Figure 4, positioning a square hoop of metal wire so that the top of the hoop (length L) is perpendicular to the magnetic field.
• When a current flows, the length of the wire in the magnetic field will experience a downward force (due to Fleming’s Left-Hand Rule), causing a reading on the digital balance.
• Connect the d.c. power supply to a variable resistor to alter the current.
• Zero the digital balance when there is no current through the wire.
• Turn on the d.c. power supply, ensuring the mass reading is positive. If the mass is negative, swap the crocodile clips.
• Record the mass and current for different values of current using the variable resistor.
• Repeat the process for a large range of currents and take three readings for each current to improve accuracy.
• Convert the mass readings to force using F = mg.
• Plot a graph of force (F) against current (I), drawing a line of best fit.
• The graph should pass through the origin, showing that force is proportional to current.
• The gradient of the line will be equal to B / L, where B is the magnetic flux density and L is the length of the wire in the field.
• Divide the gradient by the length L to calculate the magnetic flux density B.

Question 24

Magnetic Flux (PAG)

Answer 24

1. Set up the magnets:
   
   • Place two bar magnets a small distance apart with opposite poles facing each other.
   • Ensure they are far enough apart not to snap together but close enough to create a uniform magnetic field.
2. Prepare the search coil:
   
   • Use a search coil (a small coil of wire with a known number of turns, N, and a known area, A).
   • Connect the coil to a data recorder set to measure the induced e.m.f. with a very small time interval between readings.
3. Position the coil:
   
   • Place the search coil in the middle of the magnetic field so that the coil’s area is parallel to the surface of the magnets.
   • Start the data recorder.
4. Induce e.m.f.:
   
   • While keeping the coil in the same orientation, immediately move the coil out of the magnetic field.
   • As the coil moves out, the e.m.f. will be induced due to the changing magnetic flux linkage, going from maximum (NΦ) to zero.
5. Plot and calculate:
   
   • Use the data from the recorder to plot a graph of induced e.m.f. against time.
   • Using Faraday’s Law, estimate the area under the graph to calculate the change in flux linkage.
   • The final flux linkage is zero, so the change in flux linkage equals the flux linkage in the uniform magnetic field.
   • Flux linkage = NΦ. To find Φ in area A, divide the total flux linkage change by the number of turns on the coil (N).
6. Repeat:
   
   • Repeat the experiment multiple times and calculate the mean value of Φ to improve precision.

Question 25

Transformers (PAG)

Answer 25

• Relationship Between Turns and Voltage:
  
  • Set up two cores with wire wrapped around them to form primary and secondary coils.
  • Start with a turns ratio of 1:2 (e.g., 5 turns in the primary coil and 10 in the secondary coil).
  • Turn on the a.c. supply at a low voltage for safety.
  • Measure the voltage across each coil while keeping the primary voltage constant.
  • Repeat for other ratios, such as 1:1 and 2:1.
  • Calculate n₁/n₂ and V₁/V₂; the ratios should be equal, confirming V₁/V₂ = n₁/n₂.
• Relationship Between Current and Voltage:
  
  • Add a variable resistor and ammeters to the transformer setup.
  • Record the current and voltage across each coil with a fixed number of turns.
  • Adjust the variable resistor to change the input current, recording the corresponding values for both coils.
  • For each current, confirm P = V₁I₁ = V₂I₂ (power remains constant, neglecting losses).

Question 26

Terminal Velocity in Fluids

Answer 26

Experiment Setup:

1. Wrap elastic bands or mark intervals on a tube of viscous liquid using a ruler.
2. Release a ball bearing from rest above the liquid.
3. Use a stopwatch to record the time it reaches each mark.
4. Calculate average speed between intervals using speed = distance / time.
5. Repeat multiple times for a range of readings.

Terminal Velocity:

• When the ball bearing reaches terminal velocity, the distance between intervals becomes constant.
• Plot a velocity-time graph:
  
  • Maximum velocity (terminal velocity) is where the graph plateaus (zero gradient).

Evaluating the Experiment:

Systematic Errors:

• Use a more viscous or denser fluid to slow the ball bearing.
• Use a taller tube to allow longer travel at terminal velocity.
• Use larger intervals to reduce percentage uncertainty in distance and time.

Random Errors:

• Repeat the experiment at least four times.
• Use ticker tape instead of a stopwatch for more precise time measurements.