- Is it possible to witness on Earth two objects coming together
under the force of gravity? And before you comment "yes," obviously, it's easy to witness on Earth two objects coming together
under the force of gravity if one of those objects is the Earth, but what about just two objects in a room? It turns out it is possible. It's something I've wanted
to do for a long time, and I finally got to do
it, and it's amazing. The experiment was first conducted by Henry Cavendish in 1797. I wanted to
see if I
could recreate his setup, and goal one would be
to show that two objects in a room can be pulled
together by gravity in a way that's visible to the naked eye, and if it goes really well,
maybe goal number two can be to calculate the
gravitational constant, Big G. In Cavendish's setup, there
were two weights attached to each end of a bar suspended by a wire. This forms a twisting pendulum
or a torsion pendulum, that's because a wire
resists being twisted, so masses suspended in this
way
will twist back and forth. Cavendish would let that settle and then introduce two stationary masses near the suspended masses, the idea being that the force of gravity
would pull the suspended masses towards the stationary masses. If you know the stiffness of the wire, then you can figure out
the force of gravity between the masses based on how
much the pendulum is twisted from its equilibrium,
how much gravity pushes against the force of the torsion pendulum. And the cool thing is
once you've g
ot the force, you can rearrange this famous equation for the force of gravity to calculate the gravitational constant
of the universe, Big G. I assumed Cavendish's experiment just wouldn't be possible for
me to recreate in my studio. It just seems incredibly fiddly. Then I saw this video on
the "MrLundScience" Channel, and, look, on the time lapse,
it's a very clear effect. So I bought some really heavy balls. The stationary masses are wrought iron, and they weigh about 14 kilograms each. You ne
ed at least one of the masses in an attracting pair to be non-ferrous, either the stationary mass
or the suspended mass. That's because you don't want
the masses to be attracted to each other by anything
except the force of gravity, and if both the balls were ferrous, you would need to worry about magnetism. Like even a tiny bit of magnetism
would completely overwhelm the minuscule force of
gravity between them. So for the suspended
masses, I went with copper, and they're about five kilograms ea
ch. So here's a time lapse of the
suspended masses settling down and finding an equilibrium
about which to oscillate. And look what happens when I then introduce
the 14-kilogram masses. Absolutely nothing. What? (chuckling) Why not? Mr. Lund got it working? What's wrong with my setup? Maybe I'm doing something differently that just kind of ruins
the effect somehow. My first thought was that
maybe my wire is too stiff. You can get a sense of
how stiff the wire is from how quickly the pendulum
osc
illates back and forth. A stiffer pendulum will
oscillate more quickly just like how a stiffer spring
boi-oi-oings more quickly. But actually, if you
look at how long it takes for our two pendulums
to make one oscillation, well, they're about the same. That tells me that if Mr.
Lund's wire isn't too stiff, then neither is mine. The other difference is like
how close can the center of masses get to each other? By my estimation, Mr. Lund's
masses, when they're touching, their centers of mass are
a
bout 47 millimeters apart. The fact that they're on the ends of a meter ruler makes the calculation from a screenshot much easier, whereas the distance between the centers of my masses is about double that. And you probably know that
the force of gravity goes as the inverse square of distance, so that does have an effect. But even when Mr. Lund's
masses are really far apart from each other, you can see the effect. Look, this mass is supposed
to be going that way, but it just stops dead, turns ar
ound, and goes towards the lead block. And then I thought,
"Well, hold on a second. We actually do know the value of Big G." So given the parameters of the experiment, we should be able to calculate roughly how much we expect that
pendulum to twist around towards those stationary masses. In other words, we should
be able to figure out to what extent is the
force of gravity able to overcome the stiffness of the wire. And just to be clear, because the pendulum
is always oscillating, we're really t
alking about how much does the equilibrium position
of that oscillation move when the stationary masses are introduced. Instead of going into the
derivation of the equation, I'll leave a link to a video
that does that quite nicely. So here's the equation for Big G that you can get from
the Cavendish experiment, where L is the length of the rod separating
the suspended masses; R is the distance between
the centers of mass of the two masses in
the deflection position; M is the mass of the stationa
ry mass; theta is an angle, it's
how much the pendulum moves when the stationary mass are introduced; and T is the time taken for the pendulum to make one oscillation. That's there representing
the stiffness of the wire. Side note, you'll notice that the mass of the copper balls doesn't
come into the equation, and actually that's
something we should expect in the same way that the rate
at which an object accelerates towards the Earth is independent
of the mass of the object. It's always 9.8 mete
rs
per second per second. One consequence of that is I could have used much
lighter hanging masses, which would've meant I could have used thinner wire without its snapping, which would've made the
experiment more sensitive. But anyway, because we know Big G, we can rearrange this equation
to find what theta should be, and when you plug it all
in for my experiment, we should expect a deflection
of only about 0.1 degrees. And in fact, you expect
roughly the same amount for Mr. Lund's experiment.
And that was at first confusing
and then disheartening. Confusing because, well, look, this is what 0.1 degrees looks like. You can barely see that
there's an angle there with the naked eye. You'd certainly be hard pressed
to see a change like that in the experimental
setup that I have here. And although the suspended
masses in Mr. Lund's experiment never actually reached their
new equilibrium position because they collide with
the stationary masses first, it's still clear that the
deflection is
much greater than 0.1 degrees. Could there be something
else in this video that's attracting the
masses towards each other? The stationary masses are made of lead, so it can't be magnetism because
lead isn't very magnetic. Could it be electric charges
attracting each other? Well, I did some rough calculations, and it seems as though
you could get a force of attraction greater
than the force of gravity from a charge that is less
than the amount of charge you typically get from
a static electric
shock. So maybe that's what's going on. Maybe some charge was transferred to the masses inadvertently,
but then, again, that assumes that the two
masses have an opposite charge to each other, which seems like
an unlikely thing to happen. Like if you've got one charged object and one uncharged object,
they'll still be attracted to each other because the
uncharged object becomes polarized by the charged object, but
that's a smaller force, but generally it was difficult to find good quality
informa
tion about like, what is the typical amount
of charge you might find on a lump of metal in everyday life? So I'm not convinced by that idea at all. I'm really grateful to Mr. Lund, actually, for helping me think
through all this stuff. He was tempted to take his video down because it wasn't quantitative,
it was just qualitative, but after speaking to a
professor who was convinced that it did indeed show
the force of gravity, he decided to keep it up
because people were using it as an educational
aid. But anyway, assuming my
calculations are right, and the expected deflection is
just a fraction of a degree, then I made this whole setup for nothing. But Steve, you promised us
at the start of this video that we would see two
masses in a room moving towards each other under
the force of gravity. I did, and you will thanks to Simon Foster at Imperial College London
because it just so happens that they have this
beautiful lab bench example of the Cavendish experiment. It's much smaller than
my setup, but it's also much more precise, and it has some really clever features. You've got the long wire
thread coming down here, and you see it coming down there. You also have to spend ages making sure that the hanging masses
are centered enough that they won't bash into
the insides of the container when you introduce the stationary masses, which took another couple of hours. And then, look, these stationary masses, they're actually movable. So first you put the
masses in this position, and
you wait for the hanging
masses to settle down. Then you swing the stationary masses around to the other side and then let the hanging
masses settle again. But this is the really clever part. How do you measure theta? How do you measure the change in angle of the hanging masses due
to being pulled one way and then the other by
the stationary masses? Well, just here on the wire,
there's a little mirror, and you can see here we
also have a laser pointer. So look, with the laser
pointing at the mi
rror, you can see the reflection
on the wall there, and, of course, the reflection
is moving back and forth as this torsion pendulum,
that is the hanging masses, oscillates side to side. In the time-lapse, you can even see, look, it's settling down. By the way, each full oscillation
is about 10 minutes long. That's one of the ways
that this instrument is more sensitive than mine. That longer oscillation period tells us that there is a much
smaller restoring force from the twisting wire,
meaning
the position of the hanging masses
will be more affected by the gravity of the stationary masses. It also means that this whole thing takes a heck of a long time, so
I hope you'll forgive me for at this point deciding
that the equilibrium position is about here, marked in green. So then we switch the
stationary masses over to the other side, and in doing so, we disturbed the apparatus a little bit and set the pendulum oscillating again. And once again, here it is
settling down in the time-lapse.
Eventually you can see that
the new equilibrium position is different to the old one. How cool is that? We have witnessed gravity
acting on object in a room. And look, after I got bored, I decided that the new equilibrium
position was about here, and I measured the distance between the equilibrium positions and some other distances and
the period of oscillation, and put them all into this equation. You'll notice this is very similar to the equation we saw before. The only difference is that
the
ta has been replaced with this term here. That's just the distance that the laser point was deflected by, divided by the distance from
the screen to the apparatus. And if we make the small
angular approximation, that value is theta, but you
also have to divide by two because the deflection of
the laser is always going to be twice the deflection of the mirror. I could cancel out the 2's, but I wanted to show
you what was going on. And I get a value for Big G
of 7.4 times 10 to the -11. And, hey,
here's the real value
of G. That's not bad, is it? I just measured Big G in the
lab, and it wasn't terrible. I always thought I was
a bad experimentalist, but maybe after years of struggling to get things working for YouTube videos, I'm not so bad at it anymore, or maybe it was just a fluke. I don't know if this is
weird or not, but as a kid, I used to do these mathematics
workbooks in my spare time. Like, my dad would bring
home these problem books, and I just absolutely
devour them at the week
ends. And I really think it
made a difference actually because, well, it's well known that you learn better
through doing something than through passively
taking in information. So what about the contents of this video? If you want a fun and easy
way to learn about gravity and then retain what you've learned, I highly recommend the sponsor
of this video, Brilliant. Brilliant is really interactive,
so you are fully engaged, and actually now it's the
thing that I do on my phone when I would normal
ly be playing a game because it's really fun, and
it's the best way to learn about mathematics, science, data science, and computer science. Brilliant has thousands of lessons, all the way from basic up to advanced, and new lessons are added every month. Because it works on phones and tablets as well as laptops and desktops, it's easy to commit to 15 minutes a day, build up this habit for
learning, and before long, you're mastering these big concepts. And it's customized to your skill level. You
don't move on to the next level until you're really happy
with the previous level. As well as the course on gravitation, one that I really like is
the Thinking in Code course. It just really tickles that problem-solving part of my brain, and I'm learning a really
useful skill along the way. The great thing is you can try everything that Brilliant has to offer
for free for a full 30 days. Go to brilliant.org/stevemould. The first 200 people will get 20% off Brilliant's annual premium subscriptio
n. The link is also in the description. So check out Brilliant today. I hope you enjoyed this video. If you did, don't forget to hit Subscribe, and the algorithm thinks
you'll enjoy this video next. (upbeat music)
Comments