General Physics I - Space and Time

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Questions and Answers

What are the three dimensions that define space?

  • Length, weight, and time
  • Length, width, and height (correct)
  • Length, width, and temperature
  • Length, volume, and mass

According to Isaac Newton, how is space characterized?

  • As an unchanging, rigid structure (correct)
  • As a relative entity dependent on matter
  • As flexible and changing
  • As a non-existent concept

Which of the following statements reflects the view of Gottfried Leibniz on space?

  • Space is static and unchanging.
  • Space exists independently of objects.
  • Space only exists as the distance between objects. (correct)
  • Space can be measured with absolute precision.

What role does time play in physics?

<p>It quantifies the duration of events and intervals between them. (D)</p> Signup and view all the answers

How does general relativity describe the nature of space?

<p>Space can be curved by the presence of mass and energy. (A)</p> Signup and view all the answers

What is the significance of the Cartesian coordinate system in physics?

<p>It is used to represent the position of objects in a three-dimensional space. (C)</p> Signup and view all the answers

In what way is time considered a dimension in physics?

<p>It combines with spatial dimensions to form spacetime. (D)</p> Signup and view all the answers

Which of the following best describes one-dimensional space?

<p>Only one coordinate is needed to specify position (C)</p> Signup and view all the answers

What concept suggests that time can vary depending on an observer's velocity?

<p>Relative Time (B)</p> Signup and view all the answers

What is the term for the effect where time passes slower for fast-moving objects compared to stationary observers?

<p>Time Dilation (B)</p> Signup and view all the answers

What are the two postulates of Special Relativity?

<p>Uniformity of Physics and Constancy of Light Speed (D)</p> Signup and view all the answers

How does classical physics treat space and time?

<p>They are absolute and independent (B)</p> Signup and view all the answers

What is the four-dimensional construct that unifies space and time in Einstein's theory?

<p>Spacetime (A)</p> Signup and view all the answers

What happens to objects moving at high speeds regarding their perceived length?

<p>They appear shorter in the direction of motion (D)</p> Signup and view all the answers

Which transformation is straightforward in classical mechanics?

<p>Galilean Transformation (B)</p> Signup and view all the answers

At what speeds do Newtonian ideas about space and time break down?

<p>High speeds near the speed of light or in strong gravitational fields (A)</p> Signup and view all the answers

What is the correct formula to find the distance between two points in three-dimensional space?

<p>$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$ (C)</p> Signup and view all the answers

If an astronaut measures a proper time interval of 2 hours while traveling at 0.8c, how much time passes on Earth?

<p>4 hours (D)</p> Signup and view all the answers

According to the length contraction formula, how long does a spaceship traveling at 0.9c appear to an observer on Earth if it measures 100 meters in its own frame?

<p>77.78 meters (C)</p> Signup and view all the answers

Which of the following is a fundamental SI unit?

<p>Kilogram (C)</p> Signup and view all the answers

What is the unit of velocity in the SI system?

<p>m/s (B)</p> Signup and view all the answers

Which rule is true regarding the application of SI unit symbols?

<p>Unit symbols should be small letters unless named after a scientist. (B)</p> Signup and view all the answers

What does the symbol $k_b$ represent in the equation for gas velocity?

<p>Boltzmann constant (B)</p> Signup and view all the answers

In physics, what term describes units derived from combinations of basic units?

<p>Derived units (B)</p> Signup and view all the answers

What is the unit of the Boltzmann constant $k_b$?

<p>kg m$^2$ s$^{-2}$ K$^{-1}$ (B)</p> Signup and view all the answers

How many organisms can be formed in a chain of 0.60 km if each organism is 12 μm long?

<p>5000000 (B)</p> Signup and view all the answers

What is 3.2 x 10$^{-6}$ year expressed in seconds?

<p>1.68 min (B)</p> Signup and view all the answers

What is the SI prefix for $10^{-9}$?

<p>nano (n) (D)</p> Signup and view all the answers

What dimension represents density in dimensional analysis?

<p>M L$^{-3}$ (B)</p> Signup and view all the answers

Which of the following prefixes represents a factor of $10^{12}$?

<p>tera (T) (D)</p> Signup and view all the answers

Dimensional analysis is primarily used to do which of the following?

<p>Check equations and derive relationships (A)</p> Signup and view all the answers

In the context of prefixes, what does 'milli (m)' represent?

<p>$10^{-3}$ (A)</p> Signup and view all the answers

What are the values of the indices x, y, and z in the relation T = k a^x ρ^y γ^z?

<p>x = 3/2, y = 1/2, z = -1/2 (A)</p> Signup and view all the answers

In the formula F = k m^a v^b r^c, which of the following corresponds to the dimensions of velocity?

<p>L^1 T^-1 (C)</p> Signup and view all the answers

What is the dimensional formula of electrical resistance (R)?

<p>M^0 L^2 T^-3 I^-2 (B)</p> Signup and view all the answers

What does Hooke's law state about the force in a spring extended by a length x?

<p>F = -kx (A)</p> Signup and view all the answers

What is the value of 'c' in the dimensional formula of force derived from the relation F = k m^a v^b r^c?

<p>-1 (B)</p> Signup and view all the answers

In the expression F = k I1 I2 / d, which of the following describes the dimensions of the constant k?

<p>M^1 L^1 T^-2 I^-2 (C)</p> Signup and view all the answers

If the period of vibration T has a dimension of time, what must the dimensions of the right-hand side of the relation T = k a^x ρ^y γ^z equal?

<p>L^0 M^0 T^1 (A)</p> Signup and view all the answers

What is the relationship expressed in the formula F = km^1 v^2 r^(-1)?

<p>Force is dependent on the square of the velocity and inversely proportional to radius. (A)</p> Signup and view all the answers

Flashcards

Space dimensions

Space has three independent directions: length, width, and height (or depth).

1D space

Space with only one direction to specify a point.

2D space

Space that requires two coordinates (like x and y) for a point.

3D space

Space requiring three coordinates (x, y, and z) for a point.

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Cartesian coordinate system

A system to describe positions in 3D space using (x, y, z).

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Absolute space

A fixed, unchanging space that's the backdrop for events, according to Newton.

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Relative space

Space exists only as relationships between objects, per Leibniz.

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Non-Euclidean geometry

Space that isn't perfectly flat; it can curve due to mass and energy.

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Time

The ongoing sequence of events from the past to the future.

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Spacetime

The four-dimensional continuum including space and time.

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Absolute Time

The idea that time flows at a constant rate, independent of any observer.

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Relative Time

Einstein's concept where the flow of time can vary depending on the observer's speed and gravity field.

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Time Dilation

The phenomenon where time passes slower for a moving object compared to a stationary one.

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Galilean Transformation

The way coordinates are transformed between observers moving at a constant velocity in classical mechanics, assuming time flows at the same rate for all.

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Spacetime

A four-dimensional concept that combines space and time into a single entity.

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Spacetime Interval

The distance between two events in spacetime, comprising both spatial and temporal differences.

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Event in Spacetime

A specific point in spacetime, described by four coordinates (x, y, z, t).

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Length Contraction

The apparent shortening of an object moving relative to an observer.

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Boltzmann Constant (kb)

A physical constant that relates temperature to the average kinetic energy of particles in a substance.

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Units of kb

kg m^2 s^-2 K^-1

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SI prefixes

Standard units used in the International System of Units (SI) for representing large and small multiples of units.

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Micro-organism chain length (μm)

A measurement of length in micrometers expressed as 10^-6 meters.

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Dimensional Analysis

A method to check equations and derive relationships based on physical quantity dimensions (like mass, length, and time).

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Acceleration

The rate at which velocity changes over time.

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Force

A push or pull that can change the motion of an object.

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Work

The energy transferred by a force.

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Power

The rate at which work is done.

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Distance between 3D points

The length of a straight line segment connecting two points in three-dimensional space. Calculated using the distance formula.

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Time dilation (formula)

The difference in elapsed time between two events as measured by observers moving relative to each other. Proper time is the shortest time interval.

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Time Dilation Formula

Δt = Δt0/√(1 - v²/c²)

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Length contraction

The apparent shortening of an object moving relative to an observer along its direction of motion.

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Length contraction formula

L = L0 √(1 - v²/c²)

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SI Units

International System of Units, based on powers of ten, fundamental units (meter, kilogram, second) and derived units (like velocity).

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Fundamental Units

Independent units in the SI system. Examples include meter for length, kilogram for mass, and second for time.

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Derived Units

Units formed from combinations of fundamental units. Examples include velocity (m/s) and volume (m³).

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Gas velocity formula

V=γkbT/m

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Dimensional formula for period (T)

T has dimensions of time, represented as [T].

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Dimensional formula for radius (a)

Radius has dimensions of length, represented as [L].

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Dimensional formula for density (ρ)

Density has dimensions of mass per unit volume, represented as [M L-3].

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Dimensional formula for surface tension (γ)

Surface tension has dimensions of force per unit length, represented as [M L0 T-2].

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Finding indices in relation T=kaxρyγz

The exponents x, y, and z are determined by equating the dimensions of each quantity in the equation.

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Procedure to determine the indices

To solve the equation T=kaxρyγz dimensionally equate [M], [L], [T], to get three simultaneous equations.

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Dimensional formula for force (F)

Force is mass times acceleration, and acceleration is the change in velocity over time, resulting in the formula [M L T-2].

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Relation between centripetal force and variables.

Centripetal force is directly proportional to the mass, velocity squared, and inversely proportional to the radius: F ∝ mv²/r.

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Dimensional analysis of electrical resistance

Determine the dimensions of electrical resistance (R) using known dimensions of other related quantities.

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Study Notes

Course Information

  • Course Title: General Physics I (Mechanics and Properties of Matter)
  • Course Code: PHY111
  • Units: 2

Introduction to Physics

  • Physics is the science of describing matter, energy, space, and time as they affect the universe.
  • Physics aims to find fundamental laws governing these occurrences and express them precisely and simply.

Objectives

  • Understand space and time.
  • Grasp fundamental and derived units.
  • Understand dimensions as algebraic quantities.

Space and Time

  • Space is three-dimensional (length, width, height/depth).

    • 1D space: Uses one coordinate (e.g., a straight line)
    • 2D space: Uses two coordinates (e.g., x and y on a plane)
    • 3D space: Uses three coordinates (e.g., x, y, and z)
  • Spacetime: A four-dimensional continuum combining space and time.

  • Time refers to the sequence of events (past, present, future).

  • Absolute time: Time flows at a constant rate for all.

  • Relative time: Time can vary based on velocity and gravity. Time dilation occurs.

  • Absolute Space: Space is unchanging and provides a backdrop for processes.

  • Relative Space: Space exists as the distance between objects.

  • Non-Euclidean Geometry: Space isn't always perfectly flat; gravity can curve it.

Special Relativity and Spacetime

  • Special Relativity: Physics rules are consistent for all observers in non-accelerating reference frames.
  • Speed of light is constant.
  • Space and time unified as spacetime.

Time Dilation and Length Contraction

  • Time Dilation: Time slows for a moving object when compared to a stationary one.
    • Example: Moving spaceship's clock ticks slower than a stationary Earth-based clock.
  • Length Contraction: A moving object appears shorter in the direction of motion to a stationary observer.
    • Example: A fast-moving train appears shorter to someone watching from the side.

Examples of calculations

  • Calculations for distance between points in 3-D space.
  • Calculations involving time dilation (e.g., astronaut on a spaceship).
  • Calculations involving length contraction (e.g., spaceship's length as seen from Earth)

Units of Measurement

  • Units quantify physical parameters.
  • SI units: The standard international system of units, based on powers of 10.
  • Fundamental Units: Independent units, (e.g., meter, kilogram, second).
  • Derived Units: Formulated from combinations of fundamental units (e.g., velocity is measured in m/s).

SI Prefixes

  • Prefixes used to indicate multiples or fractions of SI units.
  • Many examples given.

Dimensional Analysis

  • A tool to check calculations and relationships between quantities.
  • Example: Units of velocity, area, volume, and density.
  • Calculating dimensions for acceleration, force, work, and power is provided in examples.

Dimensional Analysis Examples

  • Working through various examples involving the calculation of dimensions.
  • Derivation of a formula for the period of vibration of a string.
  • Derivation of a formula for centripetal force (involving mass, velocity, and radius).

Assignment Examples

  • Examples of calculations to perform using information above.
  • Calculating dimensional formulas for electrical resistance, Hooke's Law (spring constant).
  • Calculating units and dimensions for forces between wires, and for various formulas involving common physics concepts.

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