Does an apple exert a gravitational force on the earth? If so, how large a force? Consider an apple (a) Attached to a tree and (b) falling.
Yes, an apple does exert a gravitational force on the Earth. The magnitude of this force depends on the mass of the apple and the distance between the apple's center of mass and the center of mass of the Earth.
(a) When the apple is attached to a tree, it is not falling, but it still exerts a gravitational force on the Earth. This force is equal to the apple's mass multiplied by the gravitational acceleration constant (approximately 9.8 meters per second squared). However, the force is relatively small compared to the overall mass of the Earth and other significant gravitational forces, so it is not typically noticeable.
(b) When the apple falls, its gravitational force becomes more evident. As it falls, the force it exerts on the Earth remains the same, but now the force is balanced by the Earth's gravitational pull on the apple. The magnitude of the force is given by Newton's law of universal gravitation, which states that the force is proportional to the product of the masses of the objects (apple and Earth) and inversely proportional to the square of the distance between their centers of mass.
In practice, the force exerted by an apple falling from a tree is still relatively small due to the apple's small mass compared to the Earth's mass. However, the force is enough to cause the apple to accelerate toward the Earth and eventually hit the ground.
Yes, an apple does exert a gravitational force on the Earth. This force, known as the gravitational pull, is present between any two objects that have mass.
To calculate the gravitational force between the apple and the Earth, we can use Newton's law of universal gravitation. The formula is given as:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2),
m1 and m2 are the masses of the two objects involved (in this case, the apple and the Earth),
r is the distance between the center of masses of the two objects.
(a) When the apple is attached to a tree, it remains at a constant distance from the Earth's center. In this case, we assume the tree provides no upward force, so the apple experiences a net gravitational force towards the Earth's center. The gravitational force experienced by the apple is the weight of the apple, which can be calculated using the formula:
Weight = mass * gravitational acceleration
(b) When the apple falls from the tree, it accelerates towards the Earth due to the force of gravity. As it falls, its distance from the Earth's center decreases, which increases the gravitational force acting upon it.
The exact force exerted by the apple on the Earth is the same as the force exerted by the Earth on the apple but in the opposite direction, as stated by Newton's third law of motion. However, the gravitational force exerted by the apple on the Earth is incredibly small compared to the Earth's mass and other factors, such as the gravitational force from the Sun and other celestial objects, make it insignificant.
Therefore, even though the apple exerts a gravitational force on the Earth, the magnitude of this force is practically negligible in both cases (attached to a tree or falling). The overall effect of the apple's gravity on the Earth is virtually zero.