A question that has boggled the minds of us all at one time or another: Do heavier objects
fall faster than lighter ones?
Take a bowling ball and basketball to the top of the Empire State Building and drop
them off,
which one do you think will hit the ground first?
Despite what you might have seen or what you believe the science says, the actual answer
will surprise you and your intuition may be right or wrong!
I’m Stu, and welcome to Debunked, where we sort the truths from the myths and the
facts from the misconceptions.
Like, subscribe and leave us a comment now about which ball you think would hit the ground
first
Before we go dropping things off of one of the World’s highest buildings, let’s first
take ourselves to a more familiar height: the roof of your house.
And from here we’re also going to drop two balls.
But to make sure the falling race is fair, we’ll use 2 bowling balls, a kid’s 6-pound
ball (2.7 kg) and our 16-pound (7.3 kg) competition ball.
Because the balls are the same size and shape, and the distance to the ground is quite small,
we only really need to consider their mass; 1 heavy and 1 light.
So which will hit the ground first?
The heavier ball feels more eager to drop, right?
Let’s drop them and see.
The heavy ball hits the ground at the same time as the lighter ball.
You may be thinking well this doesn’t prove anything it’s an animation, so we tried
it out for real
As you might have guessed, dropping bowling balls from the roof of my house was a logistical
nightmare so here we are for a real life experiment.
So, what’s happened?
Why doesn’t the heavier ball hit the ground first as our intuition would suggest?
To understand what’s happened, let's have a word with gravity enthusiast Isaac Newton.
He laid out a few Laws Of Motion.
An object at rest stays at rest,
and an object in motion stays in motion,
unless an external force acts on it.
This property of all objects is known as 'inertia', and is essentially a resistance to a change
in their state of motion.
The heavier an object, the higher the inertia
and the more force is needed to change its motion
This applies to all movement, and is why it’s harder to move a heavier object than a lighter
one.
Newton also gave us a Law Of Universal Gravitation.
This tells us that the more mass an object has, the stronger the gravitational force
acting on it.
Our 16lb ball is heavier, so the force of gravity acting on it is stronger.
But here's the key: while the heavier ball has a greater inertia and so resists changes
in its motion more than the lighter one, the increased gravitational force on the heavier
ball exactly compensates for this greater inertia.
The result is that both balls, despite their different masses and inertias, accelerate
towards the Earth at the same rate, 9.81 meters per second squared.
The two balls fall at the same rate, and hit the ground at the same time.
So, if the acceleration due to gravity is the same for all objects, why, if we climb
back on your roof and drop a bowling ball and feather at the same time, would the bowling
ball leave a crater in your lawn long before the feather had finished falling?
It’s because of the component that we didn’t need to consider in the double bowling ball
experiment: air resistance.
Air resistance, or ‘drag’, is an interaction between a moving object and the molecules
in the air, and it opposes the downward motion of a falling object.
Shape, surface texture, cross-sectional area and velocity all affect the degree of air
resistance an object experiences.
A feather has a large surface area relative to its mass, and the fine filaments it’s
made up of create turbulence and friction as the feather falls.
As a result, our dropped feather is subject to a much greater degree of air resistance
than our bowling ball, and its descent to earth from the roof is significantly slowed.
Without air resistance, then, would the feather and the bowling ball hit the ground at the
same time?
In 2014, a headline-grabbing experiment took place inside a vacuum chamber –
essentially a big room that has had all the air sucked out.
No air means no air resistance, which means we’re only seeing the effects of the acceleration
due to gravity.
The experimenters simultaneously dropped some feathers and a bowling ball from the top of
the vacuum chamber,
and [drum roll, please!] the feathers and the ball hit the ground at the very same moment.
This experiment beautifully illustrates what the science has already told us – the mass
of an object has no effect on the rate at which it accelerates under gravity, and without
the effects of air resistance, two dropped objects will hit the ground at the same time,
regardless of their mass.
Under normal conditions, though – that is, non-vacuum conditions – falling objects,
be they feathers, basketballs, or bowling balls, do experience air resistance, and,
if the height from which an object is dropped is large enough, we need to factor in both
air resistance and terminal velocity.
As we’ve already established, the force of gravity causes objects to accelerate.
In air, though, this acceleration doesn’t continue indefinitely.
For a ball dropped from a height, air resistance increases as velocity increases, and, eventually,
if the ball is dropped from a high enough height, the force of air resistance (acting
upwards) increases until it is equal to the force of gravity (acting downwards).
At this point, the ball stops accelerating, and the rest of its fall continues at a constant
velocity, known as its terminal velocity.
Let’s get a little more ambitious than the roof of our hypothetical house, and drop some
stuff from the observation deck at the top of the Empire State Building.
We’re keen to drop a basketball and a bowling ball, but the two balls have different sizes
and different surface properties.
If we really want to know how mass affects the rate at which these balls plummet towards
the streets of New York, they need to be the exact same size and shape.
So, in addition to our regular basketball, let’s engineer ourselves a replica basketball
with the exact same weight as our 16lb bowling ball,
plus a steel basketball weighing in at a whopping 125lbs.
We’ve somehow got our basketball, our bowling-ball-weight basketball and our steel basketball to the
top of the Empire State Building.
It’s time to drop them simultaneously from the viewing platform.
Which one will hit the ground first?
Your instinct may be to say ‘the heavier ball’.
But recalling our earlier observation that a falling object’s mass doesn’t affect
the rate at which it accelerates, you might also be tempted to wager that they’ll hit
the ground at the same time.
But then again, what about terminal velocity?!
A falling ball’s terminal velocity depends on five things:
its mass its area.
it’s acceleration.
the density of the air, or medium, through which the ball is falling
the drag, or air resistance
Only one of these factors varies between our regular basketball, our 16-lb basketball and
our 125-lb steel basketball
– mass.
So how long does it take before each ball hits the sidewalk?
The steel basketball won’t actually reach its terminal velocity from the height of the
Empire State Building, but it will reach the ground first, after a speedy 8.9s, at a velocity
of 81.89 m/s.
The bowling-ball weight basketball also won’t reach terminal velocity from this height,
but it will have accelerated to a lower velocity of 61.67 m/s and will impact the ground after
10s.
The regular basketball will reach its terminal velocity of 19.72 m/s after 10s and will eventually
reach the ground after a total of 20.7 s.
This thought experiment illustrates something you might not have expected to see.
If neither of the heavier balls managed to reach terminal velocity,
why did they not hit the ground at the same time?
This was something that baffled us at first –
the balls are the same size and shape, they have the same surface texture,
and, they are falling under identical conditions.
Surely, we thought, it’s pretty straightforward:
they fall at the same rate.
If they’re falling for long enough,
the lightest ball reaches its terminal velocity first,
and the heavier balls continue to accelerate at the same rate for a while longer.
Then, once the middle weight ball hits its terminal velocity the heaviest ball overtakes.
If none of them reach terminal velocity, they hit the ground at the same time.
That’s all there is to it, right?
To our surprise, as our physics professor explains, it’s not quite that simple.
For a start, when we’re talking about the forces acting on a falling object, we need
to think about the object’s weight, which isn’t quite the same as its mass.
‘Mass’ tells us how much matter an object is made up of.
Weight (on Earth) is the force exerted by gravity on the object,
which results in a falling acceleration of 9.81 m/s^2 when unimpeded by other forces
– like air resistance.
When an object falls a long distance through air, though, we obviously do need to consider
air resistance.
If we consider all the forces involved, we can work out a sort of ‘overall’ force
– also known as the ‘resultant force’ – acting on a falling object.
Time for a thought experiment:
Imagine a falling ball with a weight of 500 Newtons (roughly the weight of an adult male
bullmastiff).
With an air resistance of 3 N opposing its downward motion,
the resultant downward force would be 497 N – air resistance has reduced the downward
force, and hence the acceleration of the ball, by a measly 0.6%.
The ball accelerates at 9.75m/s^2 until it reaches terminal velocity.
Now imagine the other ball of identical size, shape and smoothness weighs only 6 Newtons
(about the weight of a 5-6 week old kitten).
With the same air resistance of 3 N opposing its downward motion,
we get a resultant force of only 3 N – a reduction of 50% –
for an acceleration of 4.9m/s^2.
In our Empire State experiment, the difference in weight values is less extreme, and neither
the 16lb bowling ball nor the steel bowling ball is light enough that air resistance would
affect their acceleration quite so profoundly.
Over such a large distance, though, the effect is measurable.
And we can clearly see that the acceleration of the lighter ball is impeded more than the
steel ball.
And the steel ball would hit the sidewalk first.
Whilst the Empire State is high enough to demonstrate a variation in falling speeds,
we don't yet know the terminal velocities that these two balls will achieve.
So from what altitude would these need to be dropped?
Well, our bowling ball weighted basketball would need 36 seconds of falling time to achieve
69.17 m/s.
For our steel basketball to reach its terminal velocity of 193.32 m/s, it would need around
150s of falling time which would mean increasing our altitude all the way to 26,000 meters,
that’s over 85,000 feet! (85,300) for our steel basketball.
This would mean dropping it from the Stratosphere, so we’d technically need to factor in a
whole bunch of other atmospheric changes like air density and humidity, but for our point
in question this illustrates the physics at play well enough.
We’ve covered a lot of ground in this video, but I think there are a couple of key, stand-out
points – I shouldn’t be allowed anywhere near the Empire State Building, or my local
bowling alley.
I hope you learnt something new, we certainly did!