My Solutions to the British Physics Olympiad, BPhO Senior Challenge 2019 Multiple Choice

ZPhysics
19 Dec 202011:15
EducationalLearning
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TLDRIn this informative video, the host guides viewers through solving problems from the 2019 British Physics Olympiad Senior Challenge, ideal for A-Level preparation. The script begins with an easy mass estimation of a car, followed by a detailed explanation of Planck's constant in different units. It continues with a dimensional analysis problem involving a boulder in a river and concludes with an everyday physics scenario of a falling plate. The host encourages viewers to pause and attempt the questions independently before checking the solutions, aiming to enhance their problem-solving skills.

Takeaways
  • 📚 The video is a tutorial for solving problems from the 2019 British Physics Olympiad Senior Challenge.
  • 🧠 The problems are suggested as good practice for A Level multiple choice questions, but they may be more difficult.
  • ⏸️ The audience is advised to pause the video to attempt the questions independently before checking the solutions.
  • 🚗 The first problem involves calculating the mass of a car, which is approximately 1000 kg or 10^3 kilograms.
  • ⚖️ Planck's constant is discussed in the context of unit conversion, emphasizing its measurement in joule-seconds and its equivalent in base units.
  • 🔍 The second problem explains how the numerical value of Planck's constant would change if measured in centimeter-gram-second (CGS) units instead of SI units.
  • 🔢 The third problem uses dimensional analysis to find a relationship between the mass of a boulder, its density, the speed of the river, and gravitational field strength.
  • 🎯 The correct answer for the third problem is determined by ensuring the units on both sides of the equation are dimensionally consistent.
  • 🍬 In the fourth problem, the number of molecules in a teaspoon of sugar is estimated to be around Avogadro's number, 6 × 10^23.
  • 🍽️ The fifth problem explores why a plate of food might land upside down after being knocked off a table, with the correct answer being the turning force applied by gravity as the plate slides off the edge.
  • 👍 The video concludes with an invitation for feedback on whether viewers would like to see more Physics Olympiad videos and a reminder that the solutions provided are not official.
Q & A

  • What is the approximate mass of a car mentioned in the video?

    -The approximate mass of a car mentioned in the video is 1,000 kilograms.

  • What is Planck's constant and in what units is it measured in the SI system?

    -Planck's constant, denoted by 'h', is a fundamental constant in quantum mechanics. In the SI system, it is measured in joule-seconds.

  • How does the numerical value of Planck's constant change if measured in centimeter-gram-second (CGS) units?

    -If Planck's constant is measured in CGS units instead of SI units, its numerical value increases by a factor of 10^7.

  • What is the relationship between a joule-second and kilogram-meter-squared-second squared?

    -A joule-second is equivalent to a kilogram-meter-squared-second squared because a joule is a derived unit of energy in the SI system, defined as a kilogram-meter squared per second squared.

  • What is the purpose of the British Physics Olympiad Senior Challenge problems discussed in the video?

    -The British Physics Olympiad Senior Challenge problems serve as a practice for A-level multiple choice questions and are considered to be more challenging.

  • How can dimensional analysis be used to solve physics problems?

    -Dimensional analysis can be used to solve physics problems by ensuring that the units on both sides of an equation are equal, which helps in determining the correct form of the equation.

  • What is the correct equation that relates the mass of a boulder to the speed of the river, its density, and the gravitational field strength?

    -The correct equation is the one where the units on the right-hand side, after simplification, equal the units of the mass on the left-hand side, which is kilograms.

  • What is Avogadro's number and what is its approximate value?

    -Avogadro's number, symbolized as 'NA', is the number of constituent particles (usually atoms or molecules) in one mole of a substance, and its approximate value is 6.0 × 10^23.

  • Why does a plate of food often land upside down when knocked off a table?

    -The plate often lands upside down due to the turning force applied by gravity as the plate slides off the edge of the table.

  • Why is the weight of the food on the plate not a reason for it turning over when knocked off a table?

    -The weight of the food acts straight downwards and does not create a turning moment, so it is not the reason for the plate turning over.

  • Why is air drag not a likely reason for a plate turning over when knocked off a table?

    -Air drag would oppose the motion and act directly upwards, which is not conducive to turning the plate over.

  • What is the recommendation for viewers watching the video on the British Physics Olympiad Senior Challenge problems?

    -The recommendation for viewers is to pause the video, attempt the questions independently, and then check with the solutions provided in the video.

Outlines
00:00
📚 Introduction to 2019 British Physics Olympiad Problems

The video script begins with a warm welcome and an introduction to the 2019 British Physics Olympiad Senior Challenge problems. The narrator suggests these problems as excellent practice for A-Level multiple-choice questions, acknowledging their potential difficulty. The audience is encouraged to pause the video to attempt the problems independently before checking the solutions. The first problem involves calculating the mass of a car in kilograms, leading to a correct answer of 1,000 kg. The script emphasizes the importance of understanding base units and their conversions, particularly when dealing with Planck's constant in different unit systems.

05:02
🔍 Analyzing Units and Dimensional Analysis in Physics

The second paragraph delves into the concept of dimensional analysis, which is crucial for solving physics problems where units must balance on both sides of an equation. The narrator explains the process of converting units from the International System (SI) to the centimeter-gram-second (CGS) system, using Planck's constant as an example. The explanation includes converting kilograms to grams and meters to centimeters, which results in a significant increase in the numerical value of Planck's constant. The paragraph also discusses the incorrect options for a question related to a boulder in a riverbed, before identifying the correct dimensionally consistent equation.

10:02
🍬 Estimating Molecules in a Teaspoon of Sugar

In the third paragraph, the script addresses an estimation problem regarding the number of molecules in a teaspoon of sugar. It introduces Avogadro's number as a reference point, which is approximately 6.0 x 10^23 particles per mole of a substance. The narrator suggests that the number of molecules in a teaspoon of sugar would be around Avogadro's number, providing an estimate of 10^23 for the problem.

🍽️ The Physics of a Plate Falling Upside Down

The final paragraph discusses a common occurrence of a plate falling off a table and landing upside down. The narrator refutes the first two options related to the weight of the food and air drag as causes for the plate's rotation. The correct explanation involves the turning force applied by gravity as the plate slides off the edge of the table, creating a moment that results in the plate landing upside down. The script concludes with a call to action for feedback on whether to create more Physics Olympiad videos and provides a link to the actual Senior Physics Olympiad Challenge in the video description.

Mindmap
Keywords
💡Physics Olympiad
The Physics Olympiad is a competitive exam that challenges students on their understanding of advanced physics concepts. In the video, the problems are sourced from the 2019 British Physics Olympiad Senior Challenge, which serves as practice for high-level physics students preparing for exams like A-levels. The Olympiad questions tend to be more challenging, pushing students to think critically and apply their knowledge in complex ways.
💡Dimensional Analysis
Dimensional analysis is a method used in physics to check the consistency of equations by comparing the dimensions on both sides. In the video, this technique is used to determine whether the units of different physical quantities in an equation are consistent. The process ensures that the equations used in solving physics problems are mathematically and physically valid.
💡Planck's Constant (h)
Planck's constant is a fundamental constant in physics, symbolized by 'h', representing the quantum of electromagnetic action that relates a photon's energy to its frequency. In the video, the discussion involves how the numerical value of Planck's constant would change if measured in different units (centimeter-gram-second system) instead of the standard SI units. Understanding Planck's constant is crucial for topics in quantum mechanics and energy quantization.
💡Base Units
Base units are the fundamental units of measurement defined by the International System of Units (SI), such as meters, kilograms, and seconds. These units are the building blocks for all other measurements in physics. The video highlights the importance of converting base units (e.g., kilograms to grams, meters to centimeters) and how these conversions affect the calculations and the final numerical values in physics problems.
💡Avogadro's Number
Avogadro's number, approximately 6.022 x 10^23, represents the number of atoms or molecules in one mole of a substance. In the video, it is used to estimate the number of molecules in a teaspoon of sugar, illustrating the concept of molar quantities in chemistry and physics. This constant is essential for understanding the scale of atomic and molecular interactions in substances.
💡Gravitational Force
Gravitational force is the attractive force that acts between any two masses. In the context of the video, it is discussed as the force responsible for the turning moment when a plate slides off a table. Understanding how gravity influences motion and forces is a fundamental concept in mechanics and physics as a whole.
💡Joule
A joule is the SI unit of energy, equivalent to the energy transferred when applying a force of one newton over a distance of one meter. In the video, the joule is used in the discussion of Planck's constant and energy units. Understanding how energy is measured and calculated is essential for solving a wide range of physics problems.
💡Kinetic Energy
Kinetic energy is the energy an object possesses due to its motion, calculated using the formula \( KE = \frac{1}{2}mv^2 \). In the video, the concept is used to explain the base units of energy, helping to illustrate how the units of joules are derived. Kinetic energy is a key concept in both classical mechanics and various fields of physics.
💡Turning Moment
A turning moment, or torque, is the rotational equivalent of force, which causes an object to rotate around an axis. In the video, it is explained as the reason why a plate flips when it falls off a table, due to gravity acting at a distance from the pivot point (the edge of the table). Understanding turning moments is critical for analyzing rotational dynamics and stability in physical systems.
💡Density
Density is a measure of mass per unit volume, typically expressed in kilograms per cubic meter (kg/m³). In the video, density is part of the dimensional analysis in one of the physics problems. It's a crucial concept in understanding how mass is distributed in a given volume, affecting buoyancy, pressure, and other physical properties in different contexts.
Highlights

Introduction to solving 2019 British Physics Olympiad Senior Challenge problems.

These problems serve as excellent practice for A-level multiple-choice questions.

The mass of a car is approximately 1000 kg, leading to the correct answer being 10^3 kg.

Planck's constant is measured in joule seconds, which equals kg m^2 s^-1 in base units.

Converting from meters to centimeters and kilograms to grams changes units, affecting numerical values.

Converting Planck's constant units results in a factor change of 10^7.

Dimensional analysis helps solve problems by ensuring units on both sides of equations match.

Density has units kg/m^3, velocity v has units m/s, and gravitational acceleration g has units m/s^2.

Correct equation for mass of boulder involves dimensional analysis leading to answer C.

Estimating the number of molecules in a teaspoon of sugar using Avogadro's number.

A mole of a substance contains approximately Avogadro's number, 6.0 x 10^23 particles.

Estimate of sugar molecules in a teaspoon is 10^23.

Analyzing why a plate of food lands upside down when knocked off a table.

Gravity provides a turning moment as the plate slides off the table edge, leading to answer D.

Conclusion and encouragement to watch more Physics Olympiad videos for practice.

Transcripts

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Physics OlympiadA-LevelZed PhysicsProblem SolvingEducationalBritish ChallengeScience EducationDimensional AnalysisMolecular EstimationPlate Dynamics