Definition and Conditions
Free fall motion: Free fall motion is when an object falls straight down only because of gravity pulling it. This means no other forces like air or wind are slowing it down. We imagine the object is falling in a place with no air, so gravity is the only thing acting on it.
Vacuum condition: In a vacuum, which is a space with no air at all, all objects fall at exactly the same rate, no matter how heavy or light they are. That means a feather and a rock would fall and hit the ground at the same time because nothing is slowing them down.
Gravitational Acceleration
Definition: Gravitational acceleration is how quickly an object speeds up when it’s falling because of gravity. We use the symbol g to show this. It tells us how fast something gains speed every second while it falls.
Standard value: On Earth, the value of g is about 9.81 m/s². That means every second, a falling object’s speed increases by 9.81 metres per second.
Geographical variation: The value of g is not the same everywhere on Earth. At the equator (near the middle of the Earth), it’s around 9.78 m/s², and near the North or South Pole, it’s around 9.83 m/s². This small difference happens because Earth is not perfectly round.
Direction: Gravitational acceleration always pulls objects downward, toward the centre of the Earth. No matter where you are, gravity pulls straight down.
Constancy near surface: Even though g changes a little in different places, we usually treat it as a constant value near the Earth’s surface when doing science calculations to make things simpler.
Gravitational field strength: This tells us how strong the gravity is at a certain place. It means how much force is pulling on each kilogram of mass. The number is the same as g, and it’s measured in N/kg or m/s².
Effects of Air Resistance
Definition: Air resistance is a force that pushes against an object when it moves through the air. It tries to slow the object down and make it fall more slowly.
Impact: Air resistance reduces how fast an object falls. It makes the object fall slower than it would in a vacuum. It has a bigger effect on objects that are light or have a large surface area, like a piece of paper.
Increasing resistance: As an object falls faster, it bumps into more air, and the air pushes back harder. So, the faster the object goes, the stronger the air resistance becomes.
Terminal velocity: When air resistance becomes exactly equal to the force of gravity pulling down, the object stops speeding up. It then falls at a steady speed called terminal velocity. It keeps falling, but no faster than that.
Surface area and mass: Objects that are big and light—like a balloon—reach terminal velocity quickly and fall slowly. Small and heavy objects—like a metal ball—can fall faster before they reach their terminal velocity.
Negligible resistance: For short falls or objects that are heavy and shaped to go through air easily (like a rock or a metal ball), we can ignore air resistance because it doesn’t make much difference.
Equations of Motion for Free Fall
Applicability: We can use the same equations that describe regular motion with constant acceleration to solve free fall problems—as long as we ignore air resistance and only think about gravity.
Direction convention: When solving problems, we have to choose which direction is positive:
- If we say upward is positive, then gravity acts downward, so g = -9.81 m/s².
- If we say downward is positive, then gravity helps the object fall, so g = +9.81 m/s².
Equations:
- v = u + gt — This equation gives the final speed after falling for a certain time.
- s = ut + ½ gt² — This one tells us how far something has fallen.
- v² = u² + 2gs — Use this when we know the distance but not the time.
Variable meanings:
- v = final velocity (how fast the object is going at the end)
- u = initial velocity (how fast the object started going, often 0 if dropped)
- g = gravitational acceleration (9.81 m/s²)
- t = time (how long the object has been falling)
- s = displacement (how far the object has fallen)
Assumptions: We use these formulas only when we are sure that gravity is the only force acting on the object, which means no air resistance at all.
Uses of Free Fall Equations
Final velocity: We can use the formula to find out how fast something is going after it has been falling for a few seconds.
Displacement: We can figure out how far something has dropped from its starting point during a fall.
Time of fall: We can work out how long it takes for an object to fall a certain distance to the ground.
Maximum height: If you throw something straight up into the air, the equations can help you find how high it goes before it stops and comes back down.
Key Points to Remember
Ideal assumption: In free fall, we pretend the only force is gravity and ignore air resistance. This makes solving problems easier and lets us focus just on the effect of gravity.
g value on Earth: We usually use 9.81 m/s² for g, but remember that the value can change a little depending on where you are on Earth.
Air resistance effect: Air resistance can have a big effect, especially for things that are big and light. It slows them down and changes their motion.
Equation origin: The formulas we use for free fall come from the same equations we use for regular motion with constant acceleration, but we use g for gravity instead of the general letter a.