Hey guys welcome to this Mometrix video over the acceleration of gravity.
Now, before we jump into “the acceleration of gravity,” let’s talk about acceleration
real quick before we move on to the phenomenon of gravity.
In general, acceleration refers to anytime there is a change in velocity.
So, if you speed up you are accelerating.
This may sound like common sense, because of the way that we use acceleration in our language.
If you are driving in the car, and someone says “accelerate”, we generally
think “oh, they are asking me to go faster.”
But here is why this may be potentially confusing for someone who is very much in tune with
the precise definition of accelerate:
slowing down is also accelerating.
So, you are accelerating when you are speeding up, slowing down, and/or changing direction;
because, remember, acceleration just refers to the change in velocity.
So, if velocity is not changing then you are not accelerating.
For example, when you driving down a straight highway and you set your car on cruise control at 65 mi/ hr.
The car is going at a constant velocity of 65 mi/hr, and is therefore not accelerating.
It’s not changing in speed or direction.
Pay attention to this, an object may be at a constant speed,
but if it changes direction, then it is acceleration.
An example of this is the orbiting of a satellite around a planet.
It’s speed is constant, but it’s constantly accelerating due to the constant change of direction.
Acceleration is specifically defined by the rate of change of velocity.
So, in equation form that looks like this: a = (△v/△t)
Now, let’s break this down a little further.
So, acceleration is equal to the change in velocity over the change in time.
Well, “change in velocity” specifically means: the difference in initial and final velocity.
So, you started at “this” velocity, and that velocity changes to “this other” velocity,
and this all happens within “this” specific time frame.
So, that is acceleration in a nutshell.
Now, let’s look at acceleration of gravity.
Gravity is, actually, still kind of an enigma to physicists and scientists,
but we still we have some numbers that give us a little insight into this mystery.
Here is what we know.
When we have an object that is free falling, so let’s say something has been dropped from high up,
well this falling object has an acceleration of 9.8 m/s^2.
This number came from a lot of other really intelligent people who discovered that the
acceleration of any object, because of the force of gravity,
anywhere on the earth is 9.8 m/s^2.
And that’s basically what we know.
But, this one bit of information has lots of useful application for us to be able to solve problems.
To start, let’s look at a few laws.
Newton's 1st Law of motion (also called the law of inertia) states this:
an object at rest remains at rest, and an object in motion stays in motion with the exact same speed
and in the same direction unless it is acted on by an unbalanced force.
An unbalanced force literally just means that the force is greater than or less than the
force being exerted by that specific object.
If the force acting on the object was equal to the force being exerted by the object then
they would just cancel each other out… and therefore stay in rest.
Now, the reason this law is relevant to us learning about the acceleration of gravity
is because this unbalanced force that acts on this object is the very thing that causes acceleration.
The force causes a change in something’s velocity, which if you recall, is the definition of acceleration.
So, like in our example of a satellite orbiting around a planet.
The reason that it orbits (and doesn't just float off) is because of the force of gravity
from that planet is pulling it towards itself and causing the satellite to constantly accelerate.
That’s Newton’s 1st law, it gives us the idea of when something will accelerate or
what it is specifically that causes things to accelerate.
However, Newton didn’t stop there.
He told us that in order for something to accelerate it needs to have an unbalanced
force acting on it in his first law,
but he goes on to explain just how much force is
need in order to cause an object to accelerate in his second law.
So, you can think of Newton’s first law as qualitative, and his second law as quantitative.
Here is what Newton said in his second law:
The acceleration of an object depends directly
upon the net force acting upon the object and inversely upon the mass of the object.
So, mass basically refers to how much material an object is made up of and allows us to determine
the inertia of that object.
Newton’s second law tells us that if I take an object with a relatively small mass (lets say a bottle of water)
and an object with a relatively large mass (lets say a water tank),
and apply an equal force to them, then the acceleration of the object with the larger
mass (in this case the water tank) will be smaller than the acceleration of the object
with the smaller mass (in this case the water bottle).
So, if the same force that is applied to the water tower to make it move is then applied
to the water bottle, then the water bottle will go pretty stinkin’ fast!
So, if the mass of an object increases, then the acceleration of that object is decreased.
Now, here is the kicker, and why acceleration of gravity is kind of its own category of acceleration (kind of):
Despite the mass of an object, all objects free fall with the same acceleration -which is 9.8m/s^2.
The term free fall just means that an object is falling with no other force acting on or
against it, except gravity.
No air resistance, nothing.
Just gravity.
Let’s take the two objects that we’ve already looked at, and insert them into our free fall scenario.
So, we have our water tank with a mass of 19,000kg, and a let’s say we have a 1 liter water bottle,
so it has a mass of 1kg.
Well, if we considered Newton's second law of gravity and implemented it into this problem
then it would seem as though the water tank would have a greater force of gravity acting on it,
causing it to hit the ground before the water bottle.
If this consideration seems correct to you, then you are halfway right.
The object with the greater mass is experiencing a greater force of gravity,
but it does not cause it to hit the ground before the object with a lesser mass.
Confused?
That’s okay.
Let’s look closely at Newton's second law.
It states that the acceleration of an object depends directly upon the net force acting
upon the object and inversely upon the mass of the object.
Well when examining the acceleration of object, you must consider two factors -
the objects force and the object's mass.
When implemented into to the water tank-water bottle scenario, it would be accurate to say
that the water tank experiences a far greater force (which often leads to increased accelerations.
Nonetheless, an object's mass resists acceleration.
Therefore, the water tank’s greater mass (which often leads to decreased acceleration)
counteracts the effect of the greater force.
It is the force/mass ratio which determines the acceleration.
So, even though the water tank encounters way more force than a water bottle, it also
has way more mass than the water bottle.
The force/mass ratio is the same for each.
The greater mass of the water tank demands the greater force so that it can maintain
the same acceleration as the water bottle.
And that is why they both reach the ground at the same time.
I hope that this video over Acceleration of Gravity was helpful to you.
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See you guys next time!