Free fall is motion in which gravity is the only force acting on an object. Near Earth's surface, all freely falling objects have nearly the same downward acceleration, called g, regardless of their mass. This idea explains why a feather and a metal ball fall together in a vacuum.
Free fall is important because it connects forces, acceleration, and motion in a clear and testable way.
When air resistance is small or removed, the only force on the object is its weight, Fg = mg, so Newton's second law gives a = Fg/m = g. The mass cancels, which is why heavier objects do not fall faster in a vacuum. Free fall problems use constant acceleration kinematics with a = g downward, whether the object is dropped, thrown upward, or thrown downward.
Choosing a sign convention carefully is the key to solving these problems correctly.
Understanding Physics: Free Fall and g
Acceleration describes how velocity changes over time, not how fast something is moving at one instant. A ball released from rest has zero starting velocity, yet it immediately begins gaining downward velocity. During each second near Earth, its downward velocity increases by about nine point eight metres per second.
This means the distances covered in equal time intervals grow larger. After one second it has fallen much less far than it will during the next second. A motion diagram with dots at equal time intervals shows the gaps between dots getting wider.
Objects thrown upward follow the same acceleration throughout the trip. While the object moves upward, gravity reduces its upward velocity. At the highest point, its velocity is briefly zero, but its acceleration is still downward.
It does not pause because gravity has stopped. It turns around because its velocity has changed direction. On the way down, its downward speed increases.
If air effects are tiny and the object returns to its launch height, its speed on arrival matches its launch speed, though the direction is opposite. This result helps students check whether an answer makes physical sense.
Real drops through air are often not ideal models. Air resistance points opposite to the direction of motion. A falling object then has gravity pulling down and air resistance pushing up.
As speed rises, air resistance usually becomes stronger. Eventually the upward resistance can equal the downward weight. The net force then becomes zero, so acceleration becomes zero and the object continues at a steady speed called terminal velocity.
A skydiver experiences this clearly. Opening a parachute greatly increases air resistance, which reduces the terminal velocity to a safer value.
The value of g is close to constant only over ordinary distances near the ground. It becomes slightly smaller at higher altitude because an object is farther from Earth’s centre. It varies a little from place to place because Earth is not a perfect sphere and because Earth rotates.
On the Moon, gravity is much weaker, so a jump lasts longer and a dropped object accelerates more slowly. Mass still matters for weight, but it does not create a different gravitational acceleration at the same location when other forces can be ignored.
When solving vertical motion problems, first choose one direction as positive and keep that choice for every velocity, displacement, and acceleration. Draw a simple sketch showing the starting point, direction of motion, and known times or heights. Separate velocity from speed.
Velocity includes direction, while speed does not. Check units carefully. Acceleration in metres per second squared means a change in velocity each second.
Graphs provide another useful check. On a velocity versus time graph, constant gravitational acceleration makes a straight sloping line. On a position versus time graph, the curved shape becomes steeper as the object gains speed.
Key Facts
- Free fall means motion under the influence of gravity alone.
- Near Earth's surface, g = 9.8 m/s^2 downward.
- Weight is the gravitational force: Fg = mg.
- In a vacuum, all objects at the same location fall with the same acceleration, regardless of mass.
- For vertical motion with constant acceleration: y = y0 + v0t + 1/2 at^2.
- Velocity during free fall follows: v = v0 + at, with a = -9.8 m/s^2 if upward is positive.
Vocabulary
- Free fall
- Motion in which gravity is the only force acting on an object.
- Gravitational acceleration
- The acceleration caused by gravity, approximately 9.8 m/s^2 downward near Earth's surface.
- Weight
- The force of gravity on an object, given by Fg = mg.
- Air resistance
- A force from air that acts opposite an object's motion through the air.
- Vacuum
- A region with little or no matter, so air resistance is absent or nearly absent.
Common Mistakes to Avoid
- Thinking heavier objects fall faster in a vacuum. This is wrong because both weight and inertia increase with mass, so the acceleration remains g.
- Using g as an upward acceleration for a falling object. This is wrong unless your chosen coordinate system defines downward as positive.
- Forgetting air resistance in real-world drops. This is wrong because objects like feathers, paper, and parachutes can have large upward drag forces in air.
- Assuming velocity and acceleration must point in the same direction. This is wrong because an object thrown upward has upward velocity but downward acceleration.
Practice Questions
- 1 A ball is dropped from rest from a height of 45 m. Ignore air resistance. How long does it take to hit the ground, and what is its impact speed?
- 2 A stone is thrown downward from a bridge with an initial speed of 6.0 m/s. If it falls for 3.0 s, how far below the release point is it after that time?
- 3 A feather and a metal ball are released from rest at the same height inside a vacuum chamber. Explain why they hit the bottom at the same time even though their weights are different.