Why isn’t it possible to add enough mass to double the acceleration?
Wouldn't this depend on what you were doing?
To understand why it is not possible to double the acceleration by adding mass, let's consider Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. The equation representing this relationship is:
F = m × a
Where F is the net force acting on the object, m is the mass of the object, and a is the acceleration.
From this equation, it becomes clear that if we want to double the acceleration (2a), we would need to double the net force as well (2F), assuming the mass stays the same. However, if we increase the mass by adding more mass (2m), the equation becomes:
2F = 2m × a
The equation remains balanced because the net force is doubled, but the acceleration remains unchanged at a. This is because the increase in mass counteracts the increase in force, resulting in the same acceleration as before.
To summarize, doubling the mass of an object does not double its acceleration because the net force required to achieve that acceleration also needs to be doubled. Adding more mass only results in an equal and opposite increase in force, keeping the acceleration the same.