Through experiments by Galileo and Newton, we can understand why all objects in free-fall experience the same acceleration, ”g”. We can also see why air resistance affects a falling object’s velocity and how this can lead to a falling object reaching a terminal velocity.
What Is Free Fall?
When Galileo Galilei discovered the concept of acceleration, which is the rate of change of velocity, he was trying to study falling objects. But because he lived long ago, he didn’t have a stopwatch or a smart phone to time falling objects. So instead, he used balls and rolled them down inclined ramps set at various angles to increase or decrease their acceleration.What he found was very interesting indeed! As he angled the ramps more vertically, the acceleration of the balls increased. If he set the ramp so that it was directly vertical, the ball accelerated toward the ground at free fall acceleration.
This is the falling of an object that is only under the influence of gravity, or, quite simply, the object’s weight. During free fall, other forces like air resistance, which is the friction due to air, do not affect the object’s motion.Galileo was really smart. Not only did he describe acceleration, but he also realized that free-fall acceleration doesn’t depend on the object’s mass. This means that when dropped from the same place, a tiny rock that fits in your hand and a giant boulder as big as you will fall together and hit the ground at the same time.
More massive objects don’t fall faster than less massive ones – this was really heavy news!
The Ratio of Force and Mass
Galileo got us this far, but we needed Isaac Newton to take it one step further. Galileo was very interested in how things worked, while Newton was more interested in the why. His second law of motion states that acceleration is directly proportional to the net force and inversely proportional to the mass of the object.Since acceleration is proportional to force, an increase in one will result in an increase in the other. More force, more acceleration. Less force, less acceleration. But because acceleration and mass are inversely proportional, this means that an increase in one will decrease the other.
More mass means less acceleration, and less mass means more acceleration.So if we write this law as an equation, we get a = F/m, where a is the acceleration (usually in meters/second^2), F is net force in Newton, and m is mass in kilogram.This equation tells us that if the net force acting on an object is doubled, the acceleration of the object will also double. But if the mass is doubled, the acceleration will be halved. Finally, if both the net force and the mass are doubled, there will be no change in acceleration because the ratio of force to mass stays the same. 1/1 is the same as 2/2 – they both equal 1!What does this have to do with free-fall? Well, it explains why in the absence of air resistance, heavier objects fall with the same acceleration as light ones. In fact, we even have a value for this acceleration: g, or 9.
8 m/s^2. This is often rounded up to 10 m/s^2, and we’ll use that for our calculations in this lesson for simplicity.Where does this value come from? Say, for example, that we have a 1 kg person and a 1000 kg elephant. Ignoring that this is a very small person, it’s a big difference in mass between the two, right? 1 kg is about 10 N, so when the 1000 kg elephant falls, the force due to gravity (its weight) is 10,000 N.
For the 1 kg person, its weight is 10 N. The force is far greater for the elephant than the person, but its mass is also much greater. If we return to Newton’s second law, we find that the acceleration for the elephant is 10,000 N / 1000 kg, which equals 10 m/s^2 (the unit of Newton can also be written as kg*m/s^2 so the kg of the force and mass cancel out).
What about the 1 kg person? If we do the math, we find that 10 N / 1 kg = 10 m/s^2 as well!Can you see how the proportional force increases the acceleration while at the same time the inversely proportional mass decreases it? It’s because of this relationship between force and mass that both objects will have the same acceleration in free-fall.
This value of g applies to all objects falling without air resistance acting on them, but in the real world this is usually not the case.When air resistance acts, acceleration during a fall will be less than g because air resistance affects the motion of the falling objects by slowing it down. Air resistance depends on two important factors – the speed of the object and its surface area. Increasing the surface area of an object decreases its speed. You’ve seen this with a skydiver – initially she falls quite fast through the air but as soon as her parachute opens she slows down very quickly!But air resistance is also building up before the parachute opens. During free-fall, the skydiver would only experience the force due to gravity since air resistance would be negligible.
But in the real world, her net force is different. Now, instead of just her weight being the downward net force, it’s her weight minus air resistance. As the diver falls she picks up speed, but air resistance works against that speed so her acceleration decreases. Eventually, the air resistance may equal her weight, meaning that there is zero net force.When this happens, the diver experiences zero acceleration – which is not the same as zero velocity! She reaches a point where her velocity doesn’t change but you better believe she’s still falling through the air. Since acceleration is a change in velocity, we can in fact have velocity without acceleration.
When a falling object no longer accelerates we say it has reached terminal velocity. It’s still falling, just at constant velocity.Unlike g, terminal velocity is not the same for every falling object. A heavier person has to fall faster through the air to reach that balance between air resistance and weight. Essentially, it takes more air resistance to cancel out the object’s weight, and that resistance increases as the object’s velocity increases. Terminal velocity can also be adjusted by surface area.
Our skydiver’s parachute eventually reduces the acceleration to zero, allowing for a much safer terminal velocity for landing.
Through experimentation, Galileo was the first to describe acceleration, the rate of change of velocity. Newton further refined this concept it in his second law of motion by saying that the acceleration of an object is directly proportional to the net force and is inversely proportional to the mass of the object.
This understanding allows us to see why all objects in free fall have the same acceleration: g, or 9.8 m/s^2. Free fall occurs for falling objects that are only under the influence of gravity. During free fall, other forces such as air resistance do not affect the object’s movement.In the real world, though, air resistance is often a factor.
Air resistance slows acceleration to less than g. The net force on the falling object is now its weight minus air resistance. As an object falls faster and faster, air resistance builds up more and more.
Eventually, acceleration stops, but that doesn’t mean that movement stops! The object is falling at constant velocity so there is no change in direction or speed, which also means no acceleration. Once acceleration is zero, the object has reached terminal velocity, which is different for each falling object. Heavier objects have to fall faster than lighter ones to counter their weight with air resistance. But increasing your surface area will increase the effect of air resistance, making for a slower terminal velocity and much safer landing.
Watch and complete this video lesson so that you can:
- Explain the importance of Galileo’s experiments with falling objects
- State Newton’s second law of motion
- Recall the equation for acceleration
- Explain the effect of air resistance on acceleration
- Provide the meaning of terminal velocity