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.
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.