Understanding gravitational force is key to comprehending weight and the acceleration due to gravity (g). This force is what we feel as weight, calculated by the formula F = m * g. The value of g changes with altitude and geographical location, affecting an object's weight. The text explores how g varies with altitude above and below Earth's surface, its maximum at the surface, and its decrease with depth and distance.
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Gravitational force is the force of attraction that the Earth exerts on any object with mass, pulling it toward the planet's center
Formula for Force
According to Newton's second law of motion, force is the product of mass (m) and acceleration (a), given by the formula F = m * a
Weight as a Result of Gravitational Force
In the context of weight, the acceleration due to gravity (g) replaces a, leading to the equation F = m * g, which defines the weight (W) of an object
Weight is measured in Newtons (N) and varies slightly depending on geographical location and altitude
The acceleration due to gravity (g) is the rate at which the velocity of an object increases as it falls freely under the influence of Earth's gravity
Inverse Proportionality with Square of Distance
The acceleration due to gravity is inversely proportional to the square of the distance (r) from the Earth's center, as described by the equation g ∝ 1/r²
Direct Proportionality with Earth's Mass
The value of g is also directly proportional to the mass (M) of the Earth, leading to the relationship g ∝ M
The strength of gravity decreases with increasing altitude above the Earth's surface
Weight is the product of an object's mass and the acceleration due to gravity, measured in Newtons (N)
As altitude increases, the distance from the Earth's center (r) increases, leading to a decrease in the acceleration due to gravity (g) and a decrease in an object's weight
A graph of weight vs. altitude typically shows a linear increase in weight within the Earth, reaching a maximum at the surface, and then decreasing in a parabolic fashion for r > R
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Gravitational force definition
Attraction force Earth exerts on objects with mass towards its center.
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Newton's second law formula
Force equals mass times acceleration (F = m * a).
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Weight measurement unit
Weight measured in Newtons (N), equivalent to kg * m/s².
