Step-by-step explanation:
The force with which the Earth attracts the apple can be calculated using Newton's second law of motion, which states that the force F acting on an object is equal to its mass m multiplied by its acceleration a. In this case, the apple is not accelerating, so its acceleration is zero. Therefore, the force acting on the apple is equal to zero.
However, the Earth is still attracting the apple with a force known as gravitational force. This force is given by Newton's law of universal gravitation, which states that every mass in the universe attracts every other mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
In this case, the mass of the apple is 200g = 0.2kg, and the acceleration due to gravity is g = 9.8 N/kg. The distance between the apple and the Earth's center is the radius of the Earth, which is approximately 6,371 km.
Using these values and Newton's law of universal gravitation, we can calculate the force with which the Earth attracts the apple as follows:
F = G x (m1 x m2) / r^2
where:
G is the gravitational constant, which has a value of 6.674 x 10^-11 N(m/kg)^2
m1 is the mass of the apple, which is 0.2 kg
m2 is the mass of the Earth, which is approximately 5.97 x 10^24 kg
r is the distance between the apple and the Earth's center, which is approximately 6,371 km or 6,371,000 m.
Substituting these values into the formula, we get:
F = (6.674 x 10^-11 N(m/kg)^2) x (0.2 kg x 5.97 x 10^24 kg) / (6,371,000 m)^2
F ≈ 1.96 N
Therefore, the Earth attracts the apple with a force of approximately 1.96 N.