3.6.2 Thermal physics

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Last updated 5:30 PM on 10/7/24
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29 Terms

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Properties of Gravity/Gravitational force

  • Acts on objects with mass

  • Always attractive

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Newtons’s Laws of gravitation

  • Directly proportional to the product masses

  • Inversely proportional to the square of the distance between them

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Gravitational Force Equation

  • F = (G * m1 * m2) / r²

<ul><li><p>F = (G * m1 * m2) / r²</p></li></ul><p></p>
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Relationship between Mass and gravitational force

  • Larger masses exert greater gravitational force

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Relationship between distance and gravitational force

  • Greater distance results in weaker gravitational force

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Uniform Field

  • Same gravitational force everywhere

  • Represented by parallel, equally spaced field lines

<ul><li><p>Same gravitational force everywhere</p></li><li><p>Represented by parallel, equally spaced field lines</p></li></ul><p></p>
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Radial Field

  • Force varies with position

  • Field lines spread out as distance increases

<ul><li><p>Force varies with position</p></li><li><p>Field lines spread out as distance increases</p></li></ul><p></p>
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Field Lines

  • Direction of force on mass

  • Closer lines indicate stronger force

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Earth's Gravitational Field

  • Radial in nature

  • Nearly uniform close to the surface

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Gravitational Field Strength (g) (definition and variability)

  • Definition

    • Force per unit mass exerted by a gravitational field

  • Variability

    • Constant in uniform fields

    • Varies in radial fields

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Formulas for Gravitational Field Strength

  • General Formula

    • g = F / m

  • Radial Field Formula

    • g = (G * M) / r²

<ul><li><p><strong>General Formula</strong></p><ul><li><p>g = F / m</p></li></ul></li><li><p><strong>Radial Field Formula</strong></p><ul><li><p>g = (G * M) / r²</p></li></ul></li></ul><p></p>
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Gravitational Potential

  • Work done per unit mass

  • Moving an object from infinity to a point

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Gravitational potential at infinity

Zero

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Is the Gravitational Potential positive or negative

  • Always negative due to energy release

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Gravitational potential formula

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Gravitational Potential Difference (ΔV)

  • Energy needed to move a unit mass between two points

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Gravitational Potential Difference (ΔV) equation

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Equipotential Surfaces

  • Surfaces of equal gravitational potential

  • Constant potential across the surface

  • No work done when moving along these surfaces

    • since gravitational potential difference = 0

  • Visual representation: red lines in this diagrams

<ul><li><p>Surfaces of equal gravitational potential</p></li><li><p>Constant potential across the surface</p></li><li><p>No work done when moving along these surfaces</p><ul><li><p>since gravitational potential difference = 0</p></li></ul></li><li><p>Visual representation: red lines in this diagrams</p></li></ul><p></p>
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V vs r relationship

  • gravitational potential(V) Inversely proportional to the distance between the centres of the two objects (r)

<ul><li><p>gravitational potential(V) Inversely proportional to the distance between the centres of the two objects (r)</p></li></ul><p></p>
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area under g vs r graph

  • gravitational potential difference

  • Typically shows a decrease as distance increases.

<ul><li><p>gravitational potential difference</p></li><li><p>Typically shows a decrease as distance increases.</p></li></ul><p></p>
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Kepler’s Third Law

  • Square of orbital period (T) is directly proportional to the cube of radius (r)

<ul><li><p>Square of orbital period (T) is directly proportional to the cube of radius (r)</p></li></ul><p></p>
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How would you derive the equation

  • Centripetal Force = Gravitational Force

    • (mv² / r) = (GMm / r² )

  • Rearrangement to find velocity (v)

    • v² = GM / r

  • Substitute v² into gravitational equation

    • v = 2πr / T

      v² = 4π²r² / T²

    • 4π²r² / T² = GM / r

  • Final equation: T² = (4π² / GM) * r³

  • (4π² / GM) is a constant

<ul><li><p>Centripetal Force = Gravitational Force</p><ul><li><p>(mv² / r) = (GMm / r² )</p></li></ul></li><li><p>Rearrangement to find velocity (v)</p><ul><li><p>v² = GM / r</p></li></ul></li><li><p>Substitute v² into gravitational equation</p><ul><li><p>v = 2πr / T</p><p>v² = 4π²r² / T²</p></li><li><p>4π²r² / T² = GM / r</p></li></ul></li><li><p>Final equation: T² = (4π² / GM) * r³</p></li><li><p>(4π² / GM) is a constant</p></li></ul><p></p>
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What is the total energy of a satellite

  • Kinetic Energy + Potential Energy

  • Constant total energy in orbit

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Escape velocity

  • Minimum velocity to escape gravitational field

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Equation for escape velocity

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Synchronous Orbit

  • Orbital period equals rotational period of the planet

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Geostationary Satellites

  • Specific type of synchronous orbit

  • Always above the same point on Earth

  • Useful for communication (TV, telephone)

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Calculating Geostationary Orbit

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Low-Orbit Satellites features and uses

  • Lower orbits, faster travel

  • Smaller orbital periods

  • Require less powerful transmitters

  • Applications: Weather monitoring, scientific observations, military uses