What else effects the Acceleration?

Galileo appreciated that heavy objects have the same free-fall acceleration as lighter ones, provided that they are not affected by air resistance. You can confirm this by releasing two different-sized coins side-by-side; at low speeds, air resistance has little effect so you see and hear them reaching the ground together.

In vertical motion the mass of an object affects the force causing the acceleration; the heavier the object, the greater the force pulling it down. Doubling the mass doubles the pulling force (since W = m × g) but does not affect the acceleration.

Galileo’s insistence that heavy objects do not fall faster than lighter ones cost him his job as professor of mathematics at the University of Pisa.

This is not the case in horizontal motion, where increasing the mass of an object has no effect on the force causing it to accelerate, but does affect the acceleration. As the number of passengers on a bus increases, its acceleration away from the bus stop decreases.

Results of experiments using a constant force to accelerate different masses show that: the acceleration of an object is inversely proportional to its mass

If the mass of an object is doubled, its acceleration is halved for the same pulling force.

The dependence of acceleration on both the resultant force and the mass is summarised by the relationship:

resultant force = mass × acceleration
∑ F = ma

Where the unit of force, the newton, is defined as the force required to cause a mass of 1 kg to accelerate at 1 m s^–2.

The symbol ∑, meaning ‘sum of’ is used here to emphasise that the relationship applies to the resultant force on an object, and not to individual forces.