Preliminary Physics I - Gravitation

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Questions and Answers

What does the minus sign in the gravitational force equation indicate?

  • The force is repulsive.
  • The force is attractive. (correct)
  • The force is constant.
  • The force varies with distance.

What is the value of the gravitational field strength (g) at the Earth's surface?

  • 10.00 N kg-1
  • 9.81 m/s2 (correct)
  • 6.67 N kg-1
  • 9.81 N kg-1 (correct)

How is gravitational field strength calculated at the Earth's surface?

  • F = mg (correct)
  • g = F/m (correct)
  • g = -Gm/r²
  • F = m/R

What represents the gravitational constant (G) in the gravitational force equation?

<p>6.67 x 10-11 m3 kg-1 s-2 (B)</p> Signup and view all the answers

What type of force is the gravitational force when considering planetary motion?

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

Which law relates gravitational force to the centripetal force in circular motion?

<p>Law of universal gravitation (C)</p> Signup and view all the answers

In the equation $g = -\frac{GM_E}{R_E^2}$, what does $R_E$ denote?

<p>Radius of the Earth (C)</p> Signup and view all the answers

What happens to gravitational force as the distance between two masses increases?

<p>It decreases rapidly. (D)</p> Signup and view all the answers

Why do a paper and a stone fall at the same rate in a vacuum?

<p>Their acceleration is independent of mass. (C)</p> Signup and view all the answers

What does the mass of an object measure?

<p>The amount of matter in the object. (B)</p> Signup and view all the answers

What happens to a cork and an iron nail of equal mass placed on the surface of water?

<p>The cork will float and the nail will sink. (D)</p> Signup and view all the answers

What is the upward force experienced by a body immersed in a fluid called?

<p>Buoyant force. (D)</p> Signup and view all the answers

How does the buoyant force relate to the weight of a submerged object?

<p>It is equal to the weight of the fluid displaced. (D)</p> Signup and view all the answers

Which object would float when placed in water?

<p>An object with a density of 0.5 g/cm³. (B)</p> Signup and view all the answers

What is Archimedes' Principle used for in practical applications?

<p>Designing ships and submarines. (B)</p> Signup and view all the answers

What describes the relationship between the density of an object and its ability to float?

<p>Objects with densities lower than the liquid will float. (D)</p> Signup and view all the answers

What is the formula for gravitational field strength, g?

<p>$g = \frac{W}{m}$ (A)</p> Signup and view all the answers

What keeps the moon in orbit around the Earth?

<p>Centripetal force provided by Earth (A)</p> Signup and view all the answers

According to Newton’s Law of Gravitation, the force of attraction between two bodies is directly proportional to what?

<p>The product of their masses (D)</p> Signup and view all the answers

What happens to an object if the centripetal force acting on it is removed?

<p>It will move in a straight line tangent to the circular path (D)</p> Signup and view all the answers

Why does the Earth not visibly move towards an apple when the apple falls?

<p>The apple has negligible mass compared to Earth (C)</p> Signup and view all the answers

What happens to an object placed in a gravitational field around a massive body?

<p>It experiences a force directed towards the center. (C)</p> Signup and view all the answers

According to Newton’s third law of motion, what can be said about the forces between two objects?

<p>They are equal and opposite (D)</p> Signup and view all the answers

How is gravitational field strength defined?

<p>The force per unit mass at a point in the field. (D)</p> Signup and view all the answers

Which of the following accurately describes the gravitational field lines around the Earth?

<p>Closer field lines indicate a stronger field. (C)</p> Signup and view all the answers

What type of motion does an object exhibit when released from circular motion without centripetal force?

<p>Linear motion along a tangent (C)</p> Signup and view all the answers

What is the approximate acceleration due to gravity on the surface of the Earth?

<p>$9.81 , m/s^2$ (A)</p> Signup and view all the answers

What is the relationship between mass and acceleration according to Newton's second law of motion?

<p>Acceleration is inversely proportional to mass (B)</p> Signup and view all the answers

What is the angular velocity of a geostationary satellite in rad/s?

<p>$7.27 \times 10^{-5}$ rad/s (B)</p> Signup and view all the answers

What does a radial gravitational field imply about the strength of the field?

<p>The strength decreases with distance from the mass. (C)</p> Signup and view all the answers

Which of the following is NOT a use of geostationary satellites?

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

What is the value of the gravitational constant G?

<p>$6.674 \times 10^{-11} \text{ N m}^2\text{ kg}^{-2}$ (A)</p> Signup and view all the answers

Which of the following statements regarding geostationary orbit is true?

<p>The satellite remains stationary relative to the surface of the Earth. (A)</p> Signup and view all the answers

Which equation correctly represents the balance of forces for a geostationary satellite?

<p>$F_{centripetal} = F_{gravitational}$ (D)</p> Signup and view all the answers

What is the relationship between gravitational field strength and weight?

<p>Weight is the force experienced by a mass in a gravitational field. (B)</p> Signup and view all the answers

What is the gravitational force between the Earth and the moon?

<p>-1.98 x 10^20 N (A)</p> Signup and view all the answers

Which of the following best describes a uniform gravitational field?

<p>Field lines that are evenly spaced. (D)</p> Signup and view all the answers

Which formula calculates the gravitational force between two masses?

<p>$F = G \frac{m_1 m_2}{r}$ (C)</p> Signup and view all the answers

What is the formula for the radius of a geostationary satellite's orbit?

<p>$r^3 = \frac{GM}{\omega^2}$ (B)</p> Signup and view all the answers

What does the variable 'g' represent in the equation $F = mg$?

<p>Acceleration due to gravity (D)</p> Signup and view all the answers

Which statement about the geostationary orbit is true?

<p>It remains fixed above one point on the Earth. (D)</p> Signup and view all the answers

Why does the paper take longer to reach the ground than the stone when dropped simultaneously?

<p>Air resistance affects the paper more than the stone. (A)</p> Signup and view all the answers

What type of force does the universal law of gravitation primarily describe?

<p>Gravitational force (D)</p> Signup and view all the answers

What does the gravitational force between two objects depend on?

<p>The product of their masses and inversely on the square of the distance (C)</p> Signup and view all the answers

If the radius of the Earth is considered to be R, how is the acceleration due to gravity 'g' related to mass M of the Earth?

<p>$g = G \frac{M}{R^2}$ (A)</p> Signup and view all the answers

What is the unit of acceleration due to gravity?

<p>m/s^2 (B)</p> Signup and view all the answers

Which of the following describes the state of an object in free fall?

<p>An object only influenced by gravitational force (B)</p> Signup and view all the answers

What calculations are needed to find the gravitational force if the masses and the distance are known?

<p>Multiply the masses and divide by the square of the distance. (D)</p> Signup and view all the answers

Flashcards

Geostationary Orbit Period

The time it takes for a satellite to complete one orbit around Earth, which is 24 hours.

Geostationary Orbit Angular Velocity

The rate at which a geostationary satellite rotates around Earth, equal to the Earth's rotation rate (2π/24 hrs).

Geostationary Orbit Radius

The distance from Earth's center to a geostationary satellite; calculated by setting the centripetal force equal to the gravitational force.

Universal Law of Gravitation

Every object attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

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Centripetal Force

The force that keeps an object moving in a circular path.

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Gravitational Force

The force of attraction between two objects with mass.

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Value of 'G'

The universal gravitational constant, a fundamental physical constant linking the gravitational force to the masses and distance between them.

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Use of Geostationary Satellites

Applications of stationary satellites include weather monitoring, television transmission, and phone communication.

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Gravitational Force

The force of attraction between any two objects with mass.

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Free Fall

Falling under the sole influence of gravity. No air resistance.

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Acceleration due to Gravity (g)

The rate at which an object's velocity changes due to gravity.

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Gravitational Constant (G)

A constant in the law of universal gravitation that determines the strength of gravity.

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Example of Gravitational Force

The calculation of the force between the Earth and the Moon.

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Air Resistance

The force that opposes the motion of an object through the air.

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Force of Gravity Formula

𝐹 = − 𝐺𝑀𝑚/𝑟^2

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Free fall experiment

Demonstrating that objects fall at the same rate in a vacuum, ignoring air resistance.

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Gravitational Field

A region around a massive object where a force acts on objects with mass.

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Gravitational Field Strength

Force per unit mass at a point in a gravitational field.

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Newton's Law of Universal Gravitation

The force of attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

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Gravitational Field Lines

Lines used to visualize a gravitational field. Closer lines mean a stronger field.

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Gravitational Field Strength Equation?

The equation is defined as F/m, where F is the force and m is the mass. Units are N/kg

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Earth's Gravitational Field

Radial and approximately uniform at the Earth's surface.

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Geostationary Orbit

An orbit where a satellite stays above the same point on Earth.

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Weight

Gravitational force on a mass near the surface of a planet.

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Gravitational Field Strength

The force per unit mass experienced by an object due to gravity.

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Gravitational Force

The force of attraction between any two objects with mass.

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Centripetal Force

The force that keeps an object moving in a circular path.

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Newton's Law of Gravitation

The force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.

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Gravitational Force: Earth and Apple

Earth pulls on an apple, but the apple also pulls on the Earth.

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Gravitational Force and Circular Motion

The force that keeps planets in orbit, such as the moon around Earth.

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Newton's Theory of Gravity

Explanation of the force of attraction between objects.

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Force in Circular Motion

Force required for an object's motion in a curve.

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Gravitational Force Formula

The force of attraction between two masses (m1 and m2) is calculated as F = -G * m1 * m2 / r^2, where G is the gravitational constant and r is the distance between the centers of the masses.

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Gravitational Constant (G)

A fundamental constant in physics that determines the strength of the gravitational force between two objects.

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Gravitational Field Strength (g)

The gravitational force experienced by a unit mass at a point in space.

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Earth's Surface g

The gravitational field strength at the Earth's surface, approximately 9.81 N/kg.

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Radial Fields

Gravitational fields that emanate outward from a central point of mass.

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Planetary Motion

The motion of planets around a star (e.g., the Earth around the Sun) due to gravitational forces.

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Centripetal Force & Gravitational Force

The centripetal force needed for circular motion is provided by the gravitational force in planetary orbits.

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Gravitational Force & Attraction

A force of attraction that exists between any two objects with mass.

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Air Resistance

The force that opposes the movement of an object through the air.

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Free Fall

Falling only under the influence of gravity (no air resistance).

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Buoyancy

The upward force exerted by a fluid (like water) on an object.

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Upthrust

Another name for the buoyant force.

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Object Density

How much mass is in a given volume of an object.

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Floating

An object floats if its density is less than the density of the fluid it's in.

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Sinking

An object sinks if its density is greater than the density of the fluid it's in.

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Object Acceleration

Independent of mass; all objects fall at the same rate in a vacuum.

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Study Notes

Preliminary Physics I - Gravitation

  • Gravitational Field: A region surrounding a massive body where another mass experiences a gravitational force.
  • Gravitational Field Strength: Force per unit mass at a specific point in the field (N/kg). A vector quantity.
  • Gravitational Field Strength Equation: g = F/m, where g is the gravitational field strength, F is the force, and m is the mass.
  • Uniform Gravitational Field: A field with equally spaced field lines, which is the approximate condition near the Earth's surface.
  • Gravitational Field on Earth's Surface: Acceleration due to gravity (g) is approximately constant, equal to -9.81 m/s². The negative sign indicates the direction is downwards.
  • Newton's Law of Universal Gravitation: The force of attraction between any two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
  • Newton's Law of Universal Gravitation Equation: F = G * m₁ * m₂ / r², where F is the gravitational force, G is the gravitational constant (6.67 x 10⁻¹¹ N m² kg⁻²), m₁ and m₂ are the masses of the two bodies, and r is the distance between their centers.
  • Gravitational Constant (G): A constant of proportionality in Newton's Law of Universal Gravitation. Expressed in N m² kg⁻².
  • Gravitational Potential Energy (U): The energy an object possesses due to its position in a gravitational field. A negative value for objects near earth. This equation is valid for objects far from Earth's surface.
  • Gravitational Potential (Φ): Work done in moving a unit mass from infinity to a point in a gravitational field (J/kg).
  • Equipotential Lines: Lines connecting points with the same gravitational potential. These are perpendicular to the gravitational field lines.
  • Geostationary Orbit: An orbit where the satellite remains above the same point on the Earth's equator, due to the satellite matching the Earth's rotation speed.
    • Conditions required for geostationary orbit:
      • Orbital period of 24 hours
      • Circular orbit above the equator
      • Orbiting in the same direction as Earth's rotation
  • Geostationary Orbit Properties:
    • Period (T): 24 hours (86400 s)
    • Angular velocity (ω): 2π / T = 7.27 × 10⁻⁵ rad/s.
    • Radius of orbit (r): 4.22 × 10⁷ m.
  • Uses of Geostationary Satellites: Weather monitoring, television transmission, telephone communication.
  • Free Fall: Objects falling towards the Earth under the influence of gravity only. Acceleration due to gravity is constant throughout.
  • Buoyancy: The upward force exerted on an object immersed in a fluid. Equal to the weight of the fluid displaced.

Other

  • Activity: Methods to demonstrate gravitational and buoyancy principles (different experiments involving throwing stones, placing objects in water, etc.).
  • Recall: Summary and key definitions of mass, weight, and their relation to gravity.

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