The equation "force times mass equals acceleration" (F = ma) comes into play when we consider the factors that affect the motion of an object. In the case of objects falling in a vacuum with no air resistance, the force acting on each object is the force of gravity. According to Newton's second law of motion, the force acting on an object is equal to its mass multiplied by its acceleration. Thus, we can write:
F = mg
Where:
- F is the force acting on the object (force of gravity)
- m is the mass of the object
- g is the acceleration due to gravity
In the case of objects falling near the Earth's surface, the acceleration due to gravity (g) is approximately constant and equal to about 9.8 meters per second squared (m/s^2).
When two objects are dropped at the same time, assuming no air resistance, both objects experience the same acceleration due to gravity. Since the mass of each object does not affect the acceleration in this scenario, the equation F = ma simplifies to F = mg for both objects.
Therefore, even though the force acting on each object is proportional to its mass, the acceleration experienced by both objects is the same. As a result, both objects will hit the ground at the same time, regardless of their mass. This principle was famously demonstrated by Galileo in his experiments with falling objects, challenging the prevailing belief at the time.