# Unofficial Physics Olympiad Answers - 2023 BPhO Senior Physics Challenge

TLDRThis video offers an in-depth walkthrough of the presenter's solutions to the 2023 British Physics Olympiad Senior Physics Challenge paper. The presenter discusses various questions, including multiple-choice and problem-solving scenarios, covering topics like car tire rotations, fluid pressure, sound wave phase differences, and the dynamics of moving objects. The explanations are designed to help viewers understand the physics concepts and problem-solving strategies, with an emphasis on the importance of practicing Olympiad-style questions to prepare for exams.

###### Takeaways

- π The video provides solutions to the 2023 British Physics Olympiad Senior Physics Challenge paper.
- π The presenter estimated the diameter of a car tire to calculate rotations made during a 40,000 km journey, highlighting the importance of approximation in physics.
- π The video explains that pressure at a depth in a fluid is independent of the vessel's shape and is proportional to the depth due to fluid density and gravitational field strength.
- π The presenter worked out the phase difference of a sound wave received compared to where it was sent by calculating the wavelength and using it to determine the phase shift.
- π The video explores the velocities of two balls thrown vertically in opposite directions, concluding that the final impact speed is the same due to symmetry.
- π The presenter analyzed the motion of a spinning rod on a horizontal surface, calculating the speed and frequency of rotation and the velocity at different points on the rod.
- π§΅ The video discusses the center of mass of a hanging cable and how it changes when the cable is straightened by an applied force, increasing gravitational potential energy.
- π The presenter tackled a problem involving a rod moving down a slope and a wedge, using Newton's Second Law to determine uniform acceleration and the relationship between speeds.
- π The video explains the behavior of balloons when inflated multiple times, noting the ease of inflation due to the material's hysteresis properties.
- π The presenter calculated the internal resistance of a cell using changes in terminal voltage and current, applying Ohm's Law in a series circuit context.

###### Q & A

### What is the approximate diameter of a car tire mentioned in the script?

-The script estimates the diameter of a car tire to be about 0.6 meters, with a possible range between 0.5 and 0.7 meters.

### How many rotations does the car tire make when driven for 40,000 km?

-The car tire makes approximately 2.1 * 10^7 rotations when driven for 40,000 km, based on the estimated circumference of the tire.

### What is the principle behind the pressure at a depth in a fluid, as discussed in the script?

-The pressure at a depth in a fluid is proportional to the height or depth of the fluid above it, and it does not depend on the shape of the vessel containing the fluid.

### How is the wavelength of a sound wave calculated in the script?

-The wavelength of a sound wave is calculated using the wave speed equation, which results in a wavelength of exactly 2 meters in the script's example.

### What is the phase difference of the sound wave received compared to where it's sent, as per the script?

-The script concludes that the sound wave received is 180Β° out of phase compared to where it's sent due to the extra distance of half a wavelength.

### How does the final velocity of a ball thrown upwards compare to the initial velocity when it hits the sea, according to the script?

-The final velocity of the ball when it hits the sea is the same as the initial velocity with which it was thrown upwards, due to the conservation of energy.

### What is the relationship between the speed of the tip of a rotating rod and its frequency of rotation, as explained in the script?

-The frequency of rotation is the tip speed divided by the product of Pi and the diameter of the rod (V / (Pi * D)).

### How does the script determine the center of mass of a freely hanging cable?

-The center of mass of the cable is determined to be along the line where half the cable's mass is above and half is below, effectively at the halfway point of the cable's length.

### What happens to the center of mass of the cable when a force is applied to straighten it out, according to the script?

-When a force is applied to straighten the cable, the center of mass moves upwards by a small distance due to the increase in gravitational potential energy.

### What is the significance of the motion of a rod and a wedge when the rod slides down a smooth slope, as per the script?

-The rod and the wedge will both undergo uniform acceleration due to the constant force of gravity and friction acting on them, resulting in uniform motion.

### How is the speed of the wedge related to the speed of the rod sliding down the slope, according to the script?

-The speed of the wedge (V) is related to the speed of the rod (U) by the equation tan(Theta) = U / V, where Theta is the angle of the slope.

### What is the expression for the speed of the rod (U) when M1 equals M2 and Theta is 30Β°, as derived in the script?

-The expression for the speed of the rod (U) is derived to be U^2 = GH / 2, leading to U = sqrt(GH / 2), where G is the acceleration due to gravity and H is the height the rod falls through.

### How does the script explain the observation of a piece of mud on the top of a Caterpillar track moving relative to an observer?

-The script explains that the speed of the mud on the top of the track is twice the translational speed of the vehicle due to the tangential velocity of the wheel rim plus the translational speed of the vehicle itself.

### What is the significance of the internal resistance and EMF in the context of the script's discussion on a DC Supply?

-The internal resistance and EMF are crucial in determining the terminal voltage and the behavior of the circuit when different resistors are connected. The internal resistance can be calculated using the change in terminal voltage and the current through the circuit.

### Why does the script mention that the first time a balloon is inflated, it's difficult, but subsequent inflations are easier?

-The script refers to the material properties of the balloon, where the first inflation stretches the material, making subsequent inflations easier due to the material's increased elasticity and reduced resistance to expansion.

### How does the script calculate the work done in blowing up a balloon to a certain radius?

-The script calculates the work done by considering the change in volume (which is proportional to the cube of the radius change) and the average pressure during the inflation process, using the formula work done = pressure * change in volume.

### What is the significance of the maximum pressure point on the pressure-radius graph in the script?

-The maximum pressure point on the graph signifies the point where the rate of change of pressure with respect to the radius is zero, indicating the elastic limit of the balloon material.

### How does the script describe the counterintuitive behavior of balloons connected by a tube?

-The script demonstrates that when two balloons of different sizes and pressures are connected, the smaller balloon can actually decrease in size while the larger one increases, until they reach equal pressure and size, contrary to the expectation that they would simply equalize.

###### Outlines

##### π Introduction to British Physics Olympiad Solutions

The speaker introduces the video, which is dedicated to discussing their unofficial solutions to the 2023 British Physics Olympiad Senior Physics Challenge paper. They mention the presence of a link to download their solutions and encourage viewers to follow along as they delve into the problems, starting with multiple-choice questions.

##### π Analyzing Tire Rotations and Fluid Pressure

The first summary discusses the calculation of a car tire's rotations based on its diameter and the distance traveled. The speaker uses an estimated tire diameter and the circumference formula to determine the number of rotations. They also address a question about fluid pressure in a vessel of varying shape, explaining that pressure depends only on depth, not shape, due to constant fluid density and gravitational field strength.

##### π Exploring Sound Wave Phases and Ballistic Motion

This section covers the analysis of a sound wave's phase difference and the comparison of final velocities of two balls thrown in opposite directions from a cliff. The speaker calculates the wavelength of the sound wave and determines the phase difference based on the distance traveled. They also discuss the principles of ballistic motion, explaining that the final velocities of the balls will be the same due to the symmetry of their trajectories.

##### π Investigating the Dynamics of a Rotating Rod

The speaker examines the motion of a uniformly spinning rod on a horizontal surface, focusing on its rotational and translational speeds. They calculate the average speed at the ends of the rod and use it to determine the frequency of rotation. Additionally, they explore the velocity's magnitude at a rod's end after a quarter rotation, employing Pythagoras' theorem to find the resultant velocity.

##### π§ The Mechanics of a Cable's Center of Mass

This part delves into the concept of a cable's center of mass and how it changes when a force is applied to straighten the cable. The speaker explains that the center of mass moves upward due to the increase in gravitational potential energy, even though parts of the cable move downward. They provide a clear visualization of this concept and its implications on the cable's dynamics.

##### π Applying Newton's Laws to a Rod and Wedge System

The speaker applies Newton's Second Law to analyze the motion of a rod and wedge system. They describe the uniform acceleration of both the rod and the wedge, given the constant forces involved. Using geometric relationships and energy conservation principles, they derive equations for the speeds of the rod and wedge and calculate specific values given certain conditions.

##### π οΈ The Physics of a Caterpillar Track Vehicle

This section explores the relative motion of a piece of mud on the top of a caterpillar track vehicle. The speaker compares the motion of the track to that of a car wheel, explaining the superposition of tangential and translational velocities. They calculate the speed at which an observer would need to fly over the rod to see only its rotational motion.

##### π Understanding Internal Resistance and EMF in Circuits

The speaker discusses the relationship between internal resistance, EMF, and terminal voltage in electrical circuits. They provide equations and explain how to calculate the internal resistance of a cell using changes in terminal voltage and external resistance. They also explore the effects of changing the load resistor on the terminal voltage.

##### π The Behavior of Balloons Under Pressure

This part examines the behavior of balloons when inflated, focusing on the pressure-volume relationship and the concept of hysteresis. The speaker describes the difficulty of inflating a balloon the first time and how subsequent inflations become easier. They also discuss the experimental setup of connecting two balloons of different sizes and pressures and observe the redistribution of air and equalization of pressure.

##### π Conclusion and Reflection on the Olympiad Experience

In conclusion, the speaker reflects on the challenges of the British Physics Olympiad questions, emphasizing the importance of the physics and math skills developed through such competitions. They encourage viewers to engage with Olympiad problems to better prepare for exams and invite feedback on their solutions.

###### Mindmap

###### Keywords

##### π‘British Physics Olympiad

##### π‘Multiple Choice Questions

##### π‘Circumference

##### π‘Pressure

##### π‘Wavelength

##### π‘Phase

##### π‘Kinematic Equations

##### π‘Center of Mass

##### π‘Gravitational Potential Energy

##### π‘Uniform Acceleration

##### π‘Energy Conservation

###### Highlights

Unofficial solutions to the 2023 British Physics Olympiad Senior physics challenge paper are discussed.

Estimation of a car tire's diameter and the calculation of its rotations over a distance.

Explanation of fluid pressure at different depths in a vessel, regardless of its shape.

Analysis of sound wave phase differences based on wavelength and distance traveled.

The comparison of final velocities of two balls thrown vertically in opposite directions.

Visualization of the rotational and translational motion of a rod on a horizontal surface.

Calculation of the frequency of a rod's rotation and the velocity of its ends.

Determination of the center of mass for a freely hanging cable and its change upon force application.

Energy transfer and conservation in a system involving a rod and a wedge.

Derivation of expressions for the speeds of the rod and wedge using energy equations.

Investigation of the motion type and acceleration of a rod on a smooth slope.

Calculation of the velocity at which an observer must fly to see only the rod's rotational motion.

Explanation of the counterintuitive behavior of balloons when connected and inflated.

Analysis of the pressure-volume relationship and work done in inflating a balloon.

Differentiation of a pressure-volume equation to find the radius at maximum pressure.

Practical demonstration of connecting two balloons with different pressures and radii.

Discussion on the ease of inflating a balloon after initial stretching and its relation to hysteresis loops.

Final thoughts on the value of practicing Olympiad questions for exam preparation.

###### Transcripts

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