PAG

Question 1

Free fall experiment

Answer 1

• Measure the height (h) from the bottom of the ball bearing to the trapdoor.
• Simultaneously start the timer and disconnect the electromagnet by flicking the switch, releasing the ball bearing.
• The ball bearing falls, knocking the trapdoor down, breaking the circuit, and stopping the timer. Record the time (t) shown on the timer.
• Repeat the experiment three times and average the time taken to fall.
• Use the equation h = 0.5 * g * t² (from page 50) to calculate the acceleration due to gravity (g), where t is the time measured by the timer and h is the height fallen.
• Repeat the experiment for several different heights, calculating a value of g for each height, and average these values to find the final value of g.
• Make sure there’s a cushion

Question 2

Young’s Modulus (PAG)

Answer 2

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

Question 3

Resistivity (PAG)

Answer 3

• Calculate the cross-sectional area of the wire by measuring its diameter in at least three places and finding the mean diameter.
• Halve the mean diameter to find the mean radius and use it to calculate the cross-sectional area assuming a circular cross-section.
• Set up the experiment by clamping the wire and attaching the flying lead.
• Close the switch and measure the current and potential difference across the test wire to calculate its resistance.
• Repeat the measurement at least once to find the mean resistance and reposition the flying lead for different wire lengths.
• Plot a graph of average resistance against length and use the gradient of the graph to calculate the resistivity of the wire metal by multiplying it by the cross-sectional area.

Question 4

Potential divider (PAG)

Answer 4

• A light-dependent resistor (LDR) has high resistance in the dark and lower resistance in the light, while an NTC thermistor has high resistance at low temperatures and lower resistance at high temperatures.
• By using these components in a potential divider, the output voltage can vary with light or heat, making them useful as light or heat sensors.
• Figure 3 shows a circuit for a heat sensor using a thermistor.
• To create a heat sensor:
  
  • Place the thermistor in a beaker of ice water, measure the initial temperature, and record the voltage across the thermistor.
  • Gradually heat the beaker, recording the temperature and voltage at regular intervals over a suitable range.
• Plot a graph of voltage against temperature, observing that:
  
  • As the temperature increases, the voltage decreases due to the thermistor’s decreasing resistance, allowing it to take a smaller share of the total potential difference.

Question 5

Diffraction grating (PAG)

Answer 5

• Monochromatic light passing through a diffraction grating creates a pattern of bright lines (maxima) on a dark background due to constructive and destructive interference.
• The central line of maximum brightness is the zero-order line, while the lines on each side are called first-order lines.
• The angle of the first-order line relative to the zero-order line can be calculated using the small angle approximation, given the fringe width (x) and the distance to the screen (D).
• Knowing the slit separation (d), the order of the maximum (n), and the angle (θ) between the maximum and the incident light allows for the calculation of the wavelength of the incident light.
• White light passing through a diffraction grating splits into its component wavelengths, creating a spectrum from red (outside) to violet (inside) for each order in the pattern.
• The zero-order maximum remains white since all wavelengths produce a maximum when θ = 0.

Question 6

Plank constant (PAG)

Answer 6

• Use the threshold voltage of LEDs to determine the Planck constant, employing monochromatic LEDs emitting a single wavelength of light.
• 𝑒𝑉 =
  ℎ𝑐/𝜆 (Energy of electron = Energy of photon)
• Start by setting the variable resistor to its maximum resistance to prevent current flow. in a dark room
• Adjust the resistor until the LED just begins to light up, recording the threshold voltage (V₀) and the wavelength of the emitted light.
• Repeat the experiment multiple times, averaging the results for V₀, and perform the experiment for a range of LEDs.
• Plot a graph of threshold voltages against the inverse of the wavelength (1/λ) to obtain a straight line of best fit, with the gradient representing hc/e
• Substitute the gradient into the equation to calculate the Planck constant (h).

Question 7

Internal resistance (PAG)

Answer 7

• Set the variable resistor to its highest resistance.
• Record current (I) and potential difference (V) across the circuit.
• Repeat measurements for multiple load resistances, calculating mean values for each.
• Plot a V-I graph with mean data points and draw a line of best fit.
• Keep all variables constant, including temperature.
• Analyze results by determining the gradient (-r) and intercept (E) from the graph.
  (V = E -Ir)

Question 8

Oscilloscope (PAG)

Answer 8

• A cathode ray oscilloscope (CRO) displays voltage over time from a signal generator, known as a trace.
• The type of trace depends on the source connected; for example, an AC supply produces a trace that alternates between positive and negative patterns.
• Sound waves converted into electrical signals by a microphone can also be observed on an oscilloscope.
• The screen is divided into squares called divisions, with the vertical axis representing volts and the horizontal axis representing time.
• The volts per division and seconds per division are controlled by the gain and timebase dials, respectively.
• Oscilloscope traces can be used to calculate wave properties such as frequency by using frequency = 1/period over the time base.

Question 9

Polarising filters for light (PAG)

Answer 9

• Polarisation is observed by shining unpolarised light through two polarising filters aligned vertically and rotating the second.
• Rotating the second filter reduces the light intensity as its transmission axis deviates from vertical.
• At a 45-degree angle between transmission axes, the intensity passing through the second filter is half that of the first; at right angles, no light passes through.
• Further rotation causes intensity to increase until the axes realign after a 180-degree rotation, allowing all light through.
• Polaroid sunglasses use polarising filters to block partially polarised light, reducing glare.

Question 10

Polarising filters for Microwave (PAG)

Answer 10

• Metal grilles work like polarising filters for microwaves.
• Microwaves have longer wavelengths than visible light and are a type of electromagnetic wave.
• Polarisation direction is about the direction of the electric field, not the magnetic field.
• Metal grilles absorb electric fields aligned with their orientation using free electrons.
• Horizontal electric fields pass through vertically positioned grilles, and vice versa, unlike polarising filters.

Question 11

Speed of sound (PAG)

Answer 11

• Place a hollow tube in water to create a closed-end pipe.
• Note the frequency of a tuning fork and hold it above the tube.
• 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.
• The tube’s length at this frequency is a quarter of the sound wave’s wavelength.
• Use the frequency and wavelength to calculate the speed of sound in air using the equation v = fλ.

Question 12

Semi circle light rays (PAG)

Answer 12

-Place the glass block on paper and shine light from the ray box into the
curved surface of the block.
-Rotate either the ray-box or the block until the refracted ray from the glass
block makes an angle of 90°.
-Use a protractor to measure the angle of incidence of the ray of light within
the block; this is the critical angle c.
-The refractive index n is calculated using n = (sin c)
–1

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

Lightgates, Data Loggers, Video Techniques

Answer 15

Light Gates:
- Accurate method to measure time for a trolley moving through a set distance.
- A card on the trolley interrupts light beams at two gates:
- One at the start (release point).
- One at the end (bottom of the ramp).
- Time (t) between gates is used to calculate:
- Initial speed (u) and final speed (v).
- Acceleration (a) using v = u + at.

Data Loggers:
- Electronic devices that record and store data for analysis.
- Can be triggered by sensors (e.g., light gates) or record at regular intervals.
- More accurate than manual methods, eliminating human reflex errors.

Video Techniques:
- Useful for analysing motion like freefall, projectiles, and terminal velocity.
- Requires:
- Known frames per second (fps) to determine time.
- A ruler or scale in the shot to measure distance.

Question 16

Specific Heat Capacity (PAG)

Answer 16

• Measuring Specific Heat Capacity:
  
  • Measure the mass and initial temperature of the substance.
  • Heat the substance with a heater, monitoring the change in temperature.
  • Measure current (I) and voltage (V) across the heater, and time how long it’s on (t).
  • Calculate the energy supplied: E = V × I × t.
  • Use E = m × c × ΔT to calculate the specific heat capacity (c).
• Estimating Specific Heat Capacity Using Mixing Method:
  
  • Mix a hot substance with a cold substance and measure the temperature once thermal equilibrium is reached.
  • Assume no heat is lost to the surroundings.
  • Use the formula: m₁c₁(T₁ - T₀) = m₂c₂(T₂ - T₀) to find the specific heat capacity of the unknown substance, where c₂ is known.

Question 17

Specific Latent Heat (PAG)

Answer 17

• Measuring specific latent heat of fusion:
  
  • Use a heating coil in one funnel of ice.
  • Connect the coil to an ammeter and voltmeter.
  • Turn the heater on for three minutes and measure the current and voltage.
  • Calculate the energy transferred using W = VIt.
  • Use a second unheated funnel to measure the mass of ice melted at room temperature.
  • Find the mass of ice melted due to the heater by subtracting the unheated mass from the heated mass.
  • Calculate the specific latent heat of fusion using E = mL, where L is the latent heat.
• Measuring specific latent heat of vaporisation:
  
  • Place a heating coil in a beaker of water, and insulate the outside of the beaker.
  • Connect the coil to an ammeter and voltmeter.
  • Start heating the water and monitor the mass of water as it boils, using a mass balance.
  • Measure the voltage and current across the heating coil.
  • Once the mass decreases by about 15 g, stop the timer.
  • Calculate the energy transferred by the heater using W = VIt.
  • Find the specific latent heat of vaporisation using L = E/m, where E is the energy transferred and m is the mass lost.

Question 18

Boyle’s Law (PAG)

Answer 18

• 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 19

Absolute Zero (PAG)

Answer 19

• 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 20

Circular Motion (PAG)

Answer 20

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 21

SHM (PAG)

Answer 21

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 22

Capacitors in Series and Parallel (PAG)

Answer 22

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 23

Investigating Charging and Discharging Capacitors (PAG)

Answer 23

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 24

Magnetic Flux Density (PAG)

Answer 24

• 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 25

Magnetic Flux (PAG)

Answer 25

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 26

Transformers (PAG)

Answer 26

• 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 27

Terminal Velocity in Fluids

Answer 27

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.