Gravitational acceleration

Examples of Gravitational acceleration in the following topics:

• Gravity

  • Gravitational energy is the potential energy associated with gravitational force, as work is required to move objects against gravity.
  • Gravitational energy is the potential energy associated with gravitational force (a conservative force), as work is required to elevate objects against Earth's gravity.
  • where PE = potential energy measured in joules (J), m = mass of the object (measured in kg), and h = perpendicular height from the reference point (measured in m); g = gravitational acceleration (9.8m/s2).
  • Using that definition, the gravitational potential energy of a system of masses m and M at a distance r using gravitational constant G is:
  • Hoover dam uses the stored gravitational potential energy to generate electricity.

• Winds

  • At the surface of the star we know that the centripetal acceleration must be less than the gravitational acceleration, so
  • The ratio of the centripetal acceleration to the gravitational acceleration decreases as

• Weight of the Earth

  • When the bodies have spatial extent, gravitational force is calculated by summing the contributions of point masses which constitute them.
  • For points inside a spherically-symmetric distribution of matter, Newton's Shell theorem can be used to find the gravitational force.
  • The portion of the mass that is located at radii $r>r_0$ exerts no net gravitational force at the distance $r_0$ from the center.
  • As a consequence, for example, within a shell of uniform thickness and density there is no net gravitational acceleration anywhere within the hollow sphere.
  • Describe how gravitational force is calculated for the bodies with spatial extent

• Defining Graviational Potential Energy

  • Gravitational energy is the potential energy associated with gravitational force, such as elevating objects against the Earth's gravity.
  • Since this problem takes place near the surface of the earth, gravitational acceleration is taken to be the constant $g = 9.8 \text{m/}\text{s}^2$, and the gravitational potential energy is $mgh$.
  • Thus, if the book falls off the table, this potential energy goes to accelerate the mass of the book and is converted into kinetic energy.
  • Near the surface of the Earth, for example, we assume that the acceleration due to gravity is a constant $g = 9.8 \text{m/}\text{s}^2$ ("standard gravity").
  • where $U$ is the potential energy of the object relative to its being on the Earth's surface, $m$ is the mass of the object, $g$ is the acceleration due to gravity, and $h$ is the altitude of the object.

• Tides

  • Given this, in order to figure out the force observed, we must subtract the acceleration of the (Earth) frame itself.
  • The tidal force produced by the moon on a small particle located on Earth is the vector difference between the gravitational force exerted by the moon on the particle, and the gravitational force that would be exerted if it were located at the Earth's center of mass.
  • Thus, the tidal force depends not on the strength of the lunar gravitational field, but on its gradient (which falls off approximately as the inverse cube of the distance to the originating gravitational body).
  • More precisely, the lunar tidal acceleration (along the moon-Earth axis, at the Earth's surface) is about $1.1 \cdot 10^{-7}$ g, while the solar tidal acceleration (along the sun-Earth axis, at the Earth's surface) is about $0.52\cdot 10^{-7}$ g, where g is the gravitational acceleration at the Earth's surface.
  • This is the acceleration "felt" by an observer living on Earth.

• Rocket Propulsion, Changing Mass, and Momentum

  • shows a rocket accelerating straight up.
  • A rocket's acceleration depends on three major factors, consistent with the equation for acceleration of a rocket.
  • The faster the rocket burns its fuel, the greater its thrust, and the greater its acceleration.
  • The smaller the mass is (all other factors being the same), the greater the acceleration.
  • The reaction force on the rocket is what overcomes the gravitational force and accelerates it upward.

• Mass

  • Mass is the quantity of matter that an object contains, as measured by its resistance to acceleration.
  • Mass, specifically inertial mass, is a quantitative measure of an object's resistance to acceleration.
  • In scientific terms, 'weight' refers to the gravitational force acting on a given body.
  • This measurement changes depending on the gravitational pull of the opposing body.
  • In contrast, the mass of an object is an intrinsic property and remains the same regardless of gravitational fields.

• Newton and His Laws

  • There are three laws of motion that describe the relationship between forces, mass, and acceleration.
  • For example, if you push the car with a greater force it will accelerate more.
  • But, if the car is more massive $$($m$ is larger) then it won't accelerate as much from the same size force as a lighter car.
  • Gravitational Force: a massive body is attracted downward by the gravitational force practiced by the Earth
  • Apply three Newton's laws of motion to relate forces, mass, and acceleration

• Circular Motion

  • An object in circular motion undergoes acceleration due to centripetal force in the direction of the center of rotation.
  • In this case, it is the gravitational force from the Earth.
  • Since the velocity vector of the object is changing, an acceleration is occurring.
  • Therefore, the force (and therefore the acceleration) in uniform direction motion is in the radial direction.
  • The equation for the acceleration $a$ required to sustain uniform circular motion is:

• Mass

  • The problem is complicated by the fact that the notion of mass is strongly related to the gravitational interaction but a theory of the latter has not been yet reconciled with the currently popular model of particle physics, known as the Standard Model.
  • Mass is defined as a quantitative measure of an object's resistance to acceleration.
  • Weight is a different property of matter that, while related to mass, is not mass, but rather the amount of gravitational force acting on a given body of matter.
  • Newtons Second Law relates force f, exerted in a body of mass m, to the body's acceleration a:F=ma