Physics 0625 | Paper 3 Mock 01 | Theory (Core)

(a) Acceleration during the first 10 s [2]

From the velocity-time graph, the bus accelerates from 0 to 15 m/s in the first 10 s:

\( a = \frac{\Delta v}{\Delta t} = \frac{15 - 0}{10} \) [1]

\( a = 1.5 \text{ m/s}^2 \) [1]

The straight line from the origin shows uniform (constant) acceleration.

(b) Total distance travelled [2]

The total distance is found from the area under the velocity-time graph. The graph forms a trapezium (or can be split into three regions):

• Region 1 (0 to 10 s): triangle, area = \( \tfrac{1}{2} \times 10 \times 15 = 75 \text{ m} \)
• Region 2 (10 to 30 s): rectangle, area = \( 20 \times 15 = 300 \text{ m} \)
• Region 3 (30 to 40 s): triangle, area = \( \tfrac{1}{2} \times 10 \times 15 = 75 \text{ m} \)

Total distance = 75 + 300 + 75 = 450 m [2]

(c) Deceleration as the bus stops [2]

From the graph, the bus decelerates from 15 m/s to 0 between t = 30 s and t = 40 s:

\( \text{deceleration} = \frac{15 - 0}{40 - 30} = \frac{15}{10} \) [1]

\( = 1.5 \text{ m/s}^2 \) [1]

The deceleration happens to equal the initial acceleration, giving the graph a symmetric shape. Deceleration is simply acceleration in the direction opposing the motion.

(a) Name the process [1]

Refraction [1]

Refraction is the bending of light as it passes from one medium to another, caused by a change in speed.

(b) Why the submerged part appears in a different position [3]

Light from the submerged part of the pencil travels from water into air. [1] As it crosses the boundary, the light speeds up (air is less optically dense than water) and the rays bend away from the normal. [1] When the refracted rays reach the observer's eye, the brain traces them back in straight lines. These projected lines meet at a point that is above and closer to the surface than the real position of the pencil, so the submerged portion appears raised. [1]

(c) Calculate the apparent depth [2]

Using the formula: \(\text{apparent depth} = \dfrac{\text{real depth}}{n}\)

\(\text{apparent depth} = \dfrac{12}{1.33}\) [1]

\(\text{apparent depth} = \mathbf{9.0 \text{ cm}}\) [1]

The bottom of the pencil appears to be at 9.0 cm below the surface rather than 12 cm, a shift of 3.0 cm upward.

(a) Completing the six missing table entries

The six entries that were missing are shown in bold above. [1] for alpha = helium nucleus; [1] for gamma = electromagnetic wave; [1] for beta charge = -1 and beta stopped by aluminium.

(b) Why alpha curves toward the negative plate and beta toward the positive plate

• Alpha particles carry a positive charge (+2). In the electric field between the plates, they experience a force toward the negatively charged plate (opposite charges attract). [1]
• This force deflects the alpha path upward toward the negative plate. [1]
• Beta particles carry a negative charge (-1), so they are attracted toward the positive plate, curving their path downward. [1]

Gamma radiation has no charge (it is an electromagnetic wave), so it passes straight through the electric field without deflection.

(c) One practical use for each type of radiation

• Alpha: used in smoke alarms. The alpha particles ionise air in the detector; smoke disrupts this, triggering the alarm. [1]
• Beta: used in thickness monitoring in industry (e.g. paper or metal sheet manufacture). A beta source and detector are placed either side of the material; changes in detected count rate indicate thickness variation. [1]
• Gamma: used for sterilising medical equipment or as a medical tracer for imaging inside the body. Its high penetrating power makes it suitable for both applications. [1]

(a) Double insulation means the appliance has two separate layers of insulation. [1] The live internal components are surrounded by their own insulation, and the entire outer casing is also made of an insulating material such as plastic. [1]

The double-insulation symbol (a square inside a square, as shown on the rating plate) indicates this construction. Even if the inner insulation fails, the outer insulating case still prevents any conducting path to the user.

(b) Since the outer case is made of an insulating material, it can never become live, even if an internal wire comes loose. [1] There is therefore no conducting path from the live parts through the case to the user, so no earth connection is needed. [1]

An earth wire is only necessary when a metal case could become live. With a plastic case providing a second insulating barrier, the risk of the case conducting electricity is eliminated.

(c) The colour of the neutral wire is blue. [1]

The three wire colours in the UK standard are: live = brown, neutral = blue, earth = green and yellow stripes.

(d) A circuit breaker (or residual current device, RCD). [1]

A circuit breaker operates like a fuse in that it disconnects the circuit when the current is too high, but unlike a fuse it can be reset (switched back on) after the fault is fixed, rather than needing to be replaced. An RCD specifically detects a difference between the current in the live and neutral wires, which indicates current leaking to earth (possibly through a person), and disconnects extremely quickly.

(a) When the wavelength is much smaller than the gap width d:

• The waves pass through the gap and continue mostly as plane (straight) wavefronts, with a shadow zone behind each section of wall where no waves reach. [1]
• Only slight curving of the wavefronts occurs at the very edges of the gap. [1]

Diffraction is negligible when the gap is much wider than the wavelength. The waves travel through almost as if the walls were not there, and the regions directly behind the harbour walls receive little wave energy.

(b) When the wavelength is approximately equal to d:

• The waves spread out much more after passing through the gap. [1]
• The wavefronts become semicircular, reaching areas behind the harbour walls that were previously in the shadow zone. [1]

Maximum diffraction occurs when the gap width is comparable to (or smaller than) the wavelength. The gap effectively acts as a new point source, radiating circular wavefronts into the harbour.

(c) The wave effect is called diffraction. [1]

Diffraction is the spreading of waves as they pass through a gap or around an obstacle. It is a property of all waves.

(d)

• Waves diffract through the harbour entrance and spread into the enclosed area. [1]
• Even though the entrance is narrow, diffraction causes the waves to spread out and reach boats moored deep inside the harbour. [1]

In fact, a narrower entrance (closer to the wavelength of the sea waves) produces stronger diffraction, so the waves spread more effectively into the harbour interior. This is why boats far from the entrance can still bob up and down on the diffracted waves.

(a) Completed speed column using \(v = f \times \lambda\):

[1 for correct formula applied, 1 for all five values correct]

Every calculation gives 24 cm/s, confirming the wave speed is constant.

(b) As frequency increases, the wavelength decreases. They are inversely proportional (when speed is constant). [1]

Doubling the frequency from 4.0 to 8.0 Hz halves the wavelength from 6.0 to 3.0 cm, consistent with \(\lambda = v/f\).

(c) The wave equation is: wave speed = frequency \(\times\) wavelength, or \(v = f\lambda\). [1]

(d)

• The wave speed in a ripple tank depends on the depth of the water, not on the frequency. [1]
• Since the depth does not change when the motor frequency is adjusted, the speed remains constant at 24 cm/s. [1]

The source determines how many waves are produced per second (frequency), but the medium determines how fast each wave travels. Changing one does not affect the other.

(e) Measure the distance across several wavelengths on the screen and divide by the number of wavelengths. [1]

This technique averages out any measurement error, giving a more precise value than trying to measure a single wavelength, which may be only a few centimetres across.

(a) When the short wire is connected across the lamp, the lamp goes out (stops working). [1]

The short wire has a very low resistance compared to the lamp. In a parallel arrangement, current takes the path of least resistance. Since nearly all the current flows through the short wire rather than through the lamp filament, the lamp receives essentially no current and produces no light. [1]

(b) The current from the battery increases greatly. [1]

The short wire effectively reduces the total resistance of the circuit to a very small value (just the wire's own tiny resistance plus the internal resistance of the battery). By \( I = \frac{V}{R} \), a much smaller R at the same voltage produces a much larger current.

(c) In a household mains circuit, the large current caused by a short circuit can make the wires overheat. This can melt the insulation surrounding the wires and potentially start a fire. [1]

Mains circuits carry much higher voltages (230 V or 240 V), so the currents during a short circuit can be extremely large and dangerous.

(d) A fuse or circuit breaker would protect the circuit from damage during a short circuit. [1]

A fuse contains a thin wire that melts and breaks the circuit when the current exceeds a safe value. A circuit breaker is an automatic switch that trips open when excessive current is detected, and can be reset after the fault is fixed.

(a) Period of the pendulum

The period is the time for one complete oscillation. The student timed 20 oscillations in 32 s:

\( T = \frac{\text{total time}}{\text{number of oscillations}} = \frac{32}{20} \) [1]

\( T = 1.6 \text{ s} \) [1]

(b) Frequency of the pendulum

Frequency is the number of oscillations per second, and is the reciprocal of the period:

\( f = \frac{1}{T} = \frac{1}{1.6} \) [1]

\( f = 0.625 \text{ Hz} \) [1]

This means the pendulum completes 0.625 full swings every second.

(c) Why 20 oscillations were timed rather than one

Timing a single oscillation (1.6 s) would introduce a large percentage error because human reaction time (typically 0.2-0.3 s) is a significant fraction of 1.6 s. By timing 20 oscillations (32 s total), the reaction time error becomes a much smaller fraction of the measured time, greatly reducing the percentage error [1]. For example, a 0.2 s reaction time error on a 32 s measurement gives only about 0.6% error, compared to about 13% on a 1.6 s measurement.

(a)

• As the ratio of gap width to wavelength increases, the amount of diffraction decreases. [1]
• The most diffraction occurs when the ratio is close to 1 or less (gap width equal to or smaller than the wavelength). [1]

The table shows this trend clearly: at a ratio of 0.5, the wavefronts are almost fully circular (maximum spreading), while at a ratio of 8.0, there is very little spreading. Diffraction is strongest when the gap is comparable to the wavelength.

(b) The most effective diffraction (fully circular wavefronts) occurs at a gap/wavelength ratio of 0.5 (or 1.0). [1]

At ratio 0.5 the gap is smaller than the wavelength, forcing the waves to spread in all directions as if the gap were a point source.

(c) She could increase the depth of the water in the tank. [1]

Water waves travel faster in deeper water. Since the motor keeps the frequency constant, \(v = f\lambda\) means a higher speed produces a longer wavelength.

(d)

\(v = f \times \lambda = 5.0 \times 2.0 = 10\text{ cm/s}\) [1]

(e)

• The wavelength of visible light is extremely small (about \(5 \times 10^{-7}\) m) compared to the width of a window (perhaps 1 m). [1]
• The gap/wavelength ratio is therefore extremely large (around 2 000 000), so there is negligible diffraction and light passes through as a straight beam with sharp shadow edges. [1]

This is exactly the same physics as the 16.0 cm gap in the experiment: when the gap is many times larger than the wavelength, the waves pass through with almost no spreading.

(f) Measure the angle of spread of the diffracted wavefronts (e.g. using a protractor or by photographing the pattern and measuring digitally). [1]

Quantifying the angle allows a numerical comparison between different gap/wavelength ratios, rather than relying on qualitative descriptions.

(g) Mop up any water spills immediately to prevent slipping, or keep electrical connections away from the water. [1]

(h) The sloped edges (beaches) absorb the waves and prevent reflections from the tank walls. [1]

Without beaches, reflected waves would overlap with the incident waves and create a confused interference pattern, making it impossible to observe the diffraction clearly.

(a) Initial speed of trolley B [1]

Trolley B is stationary before the collision, so its initial speed is 0 m/s. [1]

(b) Type of collision [1]

When A stops completely and B moves off at A's original speed, both momentum and kinetic energy are conserved. This is an elastic collision. [1]

In an elastic collision between two objects of equal mass where one is initially stationary, the moving object stops and the stationary one moves off with the same speed. This is a classic result of simultaneous conservation of momentum and kinetic energy.

(c) Distance-time graph for trolley A [2]

Before the collision: Trolley A moves at constant speed, so its distance-time graph is a straight line with a positive (constant) gradient. [1]

After the collision: Trolley A is stationary, so its distance remains constant. The graph is a horizontal line. [1]

(d) Kinetic energy of A before the collision [2]

\( KE = \frac{1}{2}mv^2 = \frac{1}{2} \times 0.50 \times 2.0^2 \) [1]

\( KE = \frac{1}{2} \times 0.50 \times 4.0 = 1.0 \text{ J} \) [1]

(e) Kinetic energy of B after the collision [1]

Since this is an elastic collision, kinetic energy is conserved. Trolley B moves at 2.0 m/s with the same mass as A, so its kinetic energy is 1.0 J. [1]

You can verify: \( KE_B = \frac{1}{2} \times 0.50 \times 2.0^2 = 1.0 \text{ J} \), confirming no kinetic energy was lost.

(a) Complete the table with one use and one danger for each type [6]

Each type of electromagnetic radiation has properties that make it useful for specific applications but also potentially hazardous. Gamma rays carry the most energy per photon, making them effective at destroying bacteria (sterilisation) or cancer cells (radiotherapy), but that same energy can ionise healthy cells and damage DNA. Microwaves penetrate into food and are absorbed by water molecules, making them ideal for cooking, but they can similarly heat body tissues internally. Infrared radiation is emitted by all warm objects and can be detected for thermal imaging, but concentrated infrared causes burns.

(b) Speed of all electromagnetic waves in a vacuum [1]

3 × 10⁸ m/s [1]

This is one of the fundamental constants of physics. All electromagnetic waves, regardless of type, travel at this same speed in a vacuum.

(c) Which end of the spectrum has the highest energy [1]

The gamma-ray end (shortest wavelength, highest frequency). [1]

Energy is proportional to frequency (\(E = hf\)). Since gamma rays have the highest frequency, they carry the most energy per photon. This is why they are the most penetrating and most dangerous type of electromagnetic radiation.