Interactive physics simulator
Free Fall
Explore gravity in its purest form—where acceleration is uniform and independent of mass. Drop multiple bodies side-by-side in planetary vacuums, launch projectiles straight up to solve kinematic equations, and invert the famous Leaning Tower coin & feather tube under variable vacuum conditions.
Free Fall Laboratory
Select planetary gravity, adjust release heights or initial launch speeds, then run the simulation to monitor equations and plots.
Live Telemetry
- Planet gravity (g)
- 9.81 m/s²
- Drop Height (y₀)
- 50 m
- Fall Time (t)
- 0.00 s
- Object A Speed
- 0.0 m/s
- Object B Speed
- 0.0 m/s
- Time Difference
- 0.00 s
What is Free Fall?
An object is in free fall whenever it is moving solely under the influence of gravitational force, with all other external forces, such as air resistance, being completely zero or neglected. Under these pure conditions, any falling object experiences a uniform downward acceleration equal to the local gravitational acceleration constant (g).
Because acceleration is uniform, the position and velocity of the object are governed exactly by the standard kinematic equations of motion, substituting -g for acceleration (where upward is defined as the positive direction):
In a vacuum, free fall is completely independent of mass. A heavy anvil and a feather dropped together will fall at the same rate, accelerating continuously and hitting the ground at the exact same instant.
Uniform Acceleration
Gravity creates constant rates of speed increase in vacuums:
- Earth surface gravity: g ≈ 9.81 m/s². For every second of fall, an object's speed increases by about 9.8 m/s.
- Directional Sign: Downward gravity is negative (-g). While falling, velocity becomes increasingly negative.
- Symmetric Flight: Objects thrown upward slow down at rate g, stop briefly at peak height, and speed up at rate g when falling back.
Kinematic Launch Math
Predicting trajectory telemetry under gravity:
- Rise Time to Peak: Calculated by setting v = 0 ⇒ t_peak = v₀ / g.
- Peak Height reached: Calculated using v² equation ⇒ h_max = y₀ + v₀² / (2g).
- Quadratic Position: Landing time is found by setting y = 0 and solving the quadratic formula.
Air Resistance Offsets
Why atmospheric drops diverge from perfect free fall:
- Fluid Resistance: Falling through air pushes gas molecules aside, creating an upward drag force opposing gravity.
- Mass-Area Ratio: Large, light shapes (like feathers) experience drag equal to their weight quickly, stopping acceleration.
- Vacuum Tubes: Evacuating air molecules eliminates fluid drag. Coin and feather fall at identical rates.
Weightlessness in Orbit
Weightlessness is not caused by lack of gravity:
- Orbit Free Fall: Satellites drop continuously towards the Earth. Sideways speed keeps them falling "around" the planet.
- Microgravity: Since spacecraft and astronauts fall at the same rate, no normal support force acts between them.
- Zero-G Aircraft: Planes flying parabolic paths drop in free fall for 20-30 seconds, simulating astronaut weightlessness.
Solved Examples
A heavy steel bolt is dropped from the top of a skyscraper. If it takes exactly 4.5 seconds to strike the ground in a vacuum, calculate the height of the skyscraper and the impact velocity of the bolt just before landing. (g = 9.81 m/s²)
- Identify the given initial values: initial velocity v₀ = 0 m/s (dropped from rest), time of flight t = 4.5 s, acceleration a = -g = -9.81 m/s².
- Apply the position kinematic equation: y = y₀ + v₀*t - 0.5*g*t².
- Set ground level as y = 0, so height is y₀. ⇒ 0 = y₀ + 0 - 0.5 * 9.81 * (4.5)².
- Calculate: y₀ = 0.5 * 9.81 * 20.25 = 4.905 * 20.25 ≈ 99.33 meters.
- Apply the velocity equation to find impact speed: v = v₀ - g*t.
- Substitute values: v = 0 - 9.81 * 4.5 = -44.15 m/s. (The negative sign indicates downward direction).
Answer: Height = 99.3 meters, Impact Velocity = 44.2 m/s downward
A tennis ball is thrown straight upward from a balcony 30.0 meters above the ground with an initial velocity of 15.0 m/s. Calculate the maximum height reached by the ball relative to the ground and the total elapsed time before it strikes the street below. (g = 9.81 m/s²)
- Identify initial values: initial height y₀ = 30.0 m, initial velocity v₀ = 15.0 m/s, acceleration due to gravity g = 9.81 m/s².
- Determine height above balcony to peak: at peak height, final velocity v = 0. Use v² = v₀² - 2g*Δy.
- Substitute: 0 = (15.0)² - 2 * 9.81 * Δy ⇒ 225 = 19.62 * Δy ⇒ Δy = 225 / 19.62 ≈ 11.47 meters.
- Calculate total maximum height from the ground: y_max = y₀ + Δy = 30.0 + 11.47 = 41.47 meters.
- Apply position equation to find total flight time to ground (y = 0): 0 = 30.0 + 15.0*t - 0.5 * 9.81 * t².
- Rearrange into standard quadratic equation: 4.905*t² - 15.0*t - 30.0 = 0.
- Solve using quadratic formula: t = [15.0 ± √((-15.0)² - 4 * 4.905 * (-30.0))] / (2 * 4.905).
- Calculate discriminant: D = 225 + 588.6 = 813.6. √D ≈ 28.52.
- Solve for positive t: t = (15.0 + 28.52) / 9.81 ≈ 43.52 / 9.81 ≈ 4.44 seconds.
Answer: Max Height = 41.5 meters, Total Time of Flight = 4.44 seconds
A scientific probe is dropped from rest inside a test shaft on Mars (g = 3.71 m/s²). If the probe falls for 6.0 seconds, how far has it descended, and what is its average speed during this interval?
- Identify Mars values: gravity g = 3.71 m/s², time t = 6.0 s, initial velocity v₀ = 0 m/s.
- Calculate distance fallen: d = 0.5 * g * t².
- Substitute values: d = 0.5 * 3.71 * (6.0)² = 0.5 * 3.71 * 36 = 18 * 3.71 = 66.78 meters.
- Calculate average speed: v_avg = total distance / total time = 66.78 / 6.0 = 11.13 m/s.
- Verify average speed formula for constant acceleration: v_avg = (v₀ + v_final) / 2.
- Calculate final speed: v_final = g * t = 3.71 * 6.0 = 22.26 m/s. ⇒ v_avg = (0 + 22.26) / 2 = 11.13 m/s.
Answer: Distance Fallen = 66.8 meters, Average Speed = 11.1 m/s
Common Misconceptions
- "Heavy objects fall faster in vacuums": False. In a vacuum, acceleration is strictly g. Mass cancels out of the force equations.
- "Free fall only means moving downwards": False. An object thrown upward is in free fall from the instant it leaves the hand, as gravity is the only force acting on it.
- "Acceleration is zero at the peak height": False. Velocity is zero at the peak, but acceleration is still -9.81 m/s² downward. If acceleration were zero, it would float at the peak!
Practice Questions
1. Describe Galileo Galilei's Leaning Tower of Pisa experiments and explain how they challenged Aristotelian physics.
Aristotelian physics stated that the speed at which an object falls is directly proportional to its weight (i.e., a 10 kg object should fall ten times faster than a 1 kg object). According to historical accounts, Galileo Galilei challenged this by dropping two spheres of different masses (such as a heavy cannonball and a light musket ball) from the Leaning Tower of Pisa. He demonstrated that both objects struck the ground at virtually the same instant. This experiment proved that, in the absence of significant air resistance, the acceleration of free fall is a constant value independent of mass, laying the foundation for modern kinematics and classical mechanics.
2. Explain why skydivers experience a sensation of weightlessness when they first step out of an aircraft, and how this sensation changes as their descent continues.
When a skydiver first jumps from an aircraft, their initial velocity relative to vertical drop is zero, meaning air resistance is negligible. In these first few seconds, gravity is the only substantial force acting on them, placing them in a state of near-perfect free fall. Since all parts of their body and their clothing accelerate downward at the same rate (g), there are no normal support forces compressing their bones or muscles, creating the sensation of weightlessness. As they speed up, however, upward air drag increases. This drag counters gravity, reducing net acceleration. When terminal velocity is reached, acceleration is zero, and they feel their full weight supported by the upward pressure of the air rushing past.
3. Derive the algebraic equations for the peak height (h_max) and the total time of flight (t_flight) of an object launched vertically upward from ground level with an initial velocity v0 in a vacuum.
At the peak of its trajectory, the final velocity of the object is zero (v = 0).
1. Peak Height: Using the kinematic formula v² = v₀² - 2g*h, we set v = 0 ⇒ 0 = v₀² - 2g*h_max. Solving for height gives: h_max = v₀² / (2g).
2. Time to Peak: Using v = v₀ - gt, we set v = 0 ⇒ 0 = v₀ - g*t_peak ⇒ t_peak = v₀ / g.
3. Total Flight Time: In a vacuum, the motion is perfectly symmetric. The time to fall back to the ground equals the time to rise. Therefore, the total flight time is double the rise time: t_flight = 2 * v₀ / g.
4. Describe the physical conditions of the "Coin and Feather" demonstration, comparing the results in atmospheric conditions versus a high vacuum.
In a glass tube filled with normal air, a coin falls rapidly while a feather drifts down slowly. This occurs because the feather is light with a large surface area, meaning air drag quickly becomes equal to its weight, reaching a low terminal velocity. The coin has a high mass-to-surface-area ratio, meaning air drag has a negligible effect over short heights. When a vacuum pump extracts the air molecules, creating a high vacuum, there is no fluid medium to exert drag. In this state, gravity is the sole force acting on both objects. According to the equivalence principle, both accelerate downward at the exact same rate (g) and strike the bottom of the tube simultaneously.
FAQ
Frequently Asked Questions
What is free fall in physics?
Free fall is the state of motion of an object falling solely under the influence of gravity, with all other forces (such as air resistance) being completely absent or neglected.
Does the mass of an object affect its acceleration in free fall?
No. In a vacuum, all objects in free fall accelerate at the exact same rate regardless of their mass, shape, or composition. This is a consequence of the equivalence principle.
What is the value of acceleration due to gravity (g) on Earth?
On Earth's surface, the standard acceleration due to gravity is approximately 9.81 m/s² (pointing vertically downward toward the Earth's center).
How do the equations of motion change for an object in free fall?
For free fall, the standard kinematic equations are simplified by setting acceleration a = -g (using downward as negative): v = v0 - gt, y = y0 + v0*t - 0.5*g*t², and v² = v0² - 2g(y - y0).
Why do a coin and a feather fall at different rates in air?
In air, the feather experiences a significant upward drag force relative to its small weight, which rapidly counteracts gravity. The coin experiences very little drag relative to its weight, so it falls much faster.
What happens to a coin and a feather in a vacuum?
In a vacuum tube, there is no air molecules to create resistance. When dropped, the coin and the feather fall at the exact same rate of acceleration and strike the bottom at the exact same millisecond.
Is an object thrown upward still in free fall?
Yes. As long as gravity is the only force acting on it, the object is in free fall during its entire flight—both while rising, at the peak, and while falling back down.
Why do astronauts feel weightless in space if there is gravity?
Astronauts in orbit are in a continuous state of free fall. They are falling toward the Earth, but because of their high tangential speed, the Earth's surface curves away at the same rate. Since both they and their spacecraft fall together, they float relative to each other, creating weightlessness.
Who experimentally proved that all masses fall at the same rate?
Galileo Galilei conceptually argued and experimentally demonstrated (using inclined planes and balls of different masses) that objects of different weights fall at the same rate. This was later famously confirmed by Apollo 15 astronaut David Scott on the Moon using a hammer and a feather.
What is the difference between free fall and terminal velocity?
Free fall occurs when gravity is the only force acting on an object, resulting in constant acceleration. Terminal velocity is reached when air resistance equals the object's weight, balancing the forces so that the net acceleration drops to zero and the object falls at a constant speed.
Can free fall occur on other planets?
Yes. Free fall can occur on any celestial body. The only difference is the local acceleration constant. For example, in a lunar vacuum, objects free fall at 1.62 m/s², while on Jupiter, they fall at 24.79 m/s².