14.6
因地球重力而产生的加速度
根据牛顿万有引力定律，物体所受的引力与其质量成正比。 根据牛顿第二运动定律，外力产生的加速度与力成反比。 因此，物体在外引力作用下的加速度与其质量无关。
靠近地球的物体，由于地球引力的作用而产生的加速度，称为重力加速度。 它始终指向地球中心。
当然，任何物体都会对地球施加相等且相反的拉力。 然而，由…
当一个物体仅受到地球引力作用时，该物体被视为自由下落。这种自由下落物体的加速度称为重力加速度，用 g 表示。
根据牛顿第二运动定律，作用在物体上的力的大小等于其质量乘以加速度。该力也被称为物体的重量。
将 mg 与重力公式相等，可得物体因重力产生的加速度等于引力常数与地球质量的乘积，除以物体到地心距离的平方。
在地球表面附近测得的g 的平均值为9.8 m/s2。由于g 与物体的质量无关，因此所有物体在地球表面附近自由下落时都具有相同的加速度。
因此，将重力加速度、引力常数以及距离（取地球半径）的数值代入公式，可估算出地球的质量为 5.97 × 1024 千克。
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Q1: What is acceleration due to gravity and how is it defined?
Acceleration due to gravity, denoted by g, is the acceleration of an object when only Earth's gravitational force acts on it during free-fall. According to Newton's second law, this acceleration equals the gravitational constant multiplied by Earth's mass, divided by the square of the distance from Earth's center. The average measured value near Earth's surface is 9.8 m/s².
Q2: Why do all objects fall with the same acceleration regardless of their mass?
According to Newton's law of gravitation, gravitational force is proportional to an object's mass. However, Newton's second law shows acceleration is inversely proportional to mass. These effects cancel out, making acceleration independent of mass. Therefore, all objects near Earth's surface experience the same gravitational acceleration of 9.8 m/s².
Q3: How does Earth's rotation affect the acceleration due to gravity?
The acceleration due to gravity varies from the equator to the poles because of Earth's rotation about its axis. This rotational effect causes measurable differences in g at different latitudes. However, for most practical purposes near Earth's surface, such as on Mount Everest, these variations are negligible and g can be treated as constant.
Q4: How can Earth's mass be calculated from the acceleration due to gravity?
Since Earth's mass and average radius are related to the gravitational constant and acceleration due to gravity, one can be estimated if the other is known. By substituting measured values of g, the gravitational constant, and Earth's radius into the gravitational equation, Earth's mass is calculated to be approximately 5.97 × 10²⁴ kilograms.
Q5: Does the acceleration due to gravity change significantly at high altitudes?
Near Earth's surface, g remains approximately constant at 9.8 m/s². However, at distances hundreds of kilometers above Earth's surface, the value of g becomes considerably different. This occurs because g depends on the square of the distance from Earth's center, so greater altitudes produce measurable reductions in gravitational acceleration.
Q6: What is the relationship between weight and acceleration due to gravity?
An object's weight is the gravitational force acting on it, calculated as mass times acceleration due to gravity (mg). According to Newton's second law, this force equals mass multiplied by acceleration. Since g is independent of an object's mass, weight is directly proportional to mass, with g serving as the proportionality constant.
Q7: Why is Earth considered an inertial frame of reference for studying gravity?
Although every object applies an equal and opposite gravitational pull on Earth according to Newton's third law, Earth's acceleration is negligible because its mass is vastly larger than ordinary objects near it. This makes Earth an appropriate inertial frame of reference for studying the dynamics of objects placed on or near its surface.