Acceleration Due to Gravity

Free fall — motion under the influence of gravity alone, with no other force acting. Strictly this requires a vacuum; in practice it means air resistance is small enough to ignore.

g — the acceleration of a freely falling object near the Earth's surface, about 9.81 m s⁻². It acts vertically downwards, and for a freely falling object it is constant.

Why mass makes no difference — a heavier object is pulled harder, but it also has more inertia to overcome. The weight is mg and Newton's second law gives a = F/m = mg/m = g. The mass cancels, so a feather and a hammer released together in a vacuum land together.

Example: this is genuinely counter-intuitive, and worth being clear about. In air the feather loses, but not because gravity pulls it less — because air resistance is large compared with its weight. Remove the air and the difference vanishes entirely.

Applying the suvat equations — for free fall, substitute a = g. Taking downwards as positive for a dropped object keeps every quantity positive and avoids sign errors.

Example: an object released from rest falls for 2.0 s. Taking down as positive, u = 0 and a = 9.81 m s⁻², so s = ut + ½at² = ½ × 9.81 × 2.0² = 19.6 m.

Objects thrown upwards — the acceleration is the same throughout, on the way up, at the top and on the way down. At the highest point the velocity is momentarily zero but the acceleration is still g downwards. If it were not, the object would hang there.

Measuring g — a common method times a ball falling through a known height using light gates or a trapdoor and electromagnet, then applies s = ½gt². Better still, vary the height and plot s against t²: the graph should be a straight line through the origin of gradient ½g, and using a gradient rather than a single pair of readings averages out random error and exposes any systematic one.

Why measured values of g often come out low — air resistance opposes the fall, reducing the acceleration slightly. Timing errors that lengthen the recorded time also reduce the calculated value. Using a dense, small object minimises the first.