Hi. It's Mr. Andersen and this is AP Physics essentials video 11. It is on the equivalence
principle. What is equivalent? It is the two different types of mass. And so how do we
figure out the mass of this apple? I could use a balance and compare it to a known 1
kilogram mass to figure out its mass, like on a triple beam balance. Or I could apply
a force to the apple, measure its acceleration and then using Newton's second law work back
to find its mass. And scientists have noted that you could measure it in two different
ways but you always get the same answer. And so the first person to do that was Galileo,
followed by Newton. And even Einstein measured this and thought it was interesting that the
two were equivalent. And he figured out a theory of relativity that kind of explained
that. And so mass again can be inertial mass or gravitational mass. Inertial mass is taking
a mass, applying a force to it and measuring the acceleration to work back and find the
inertial mass. It is based on the inertia of an object. Gravitational mass, however,
we are taking a mass and putting it inside a gravitational field and measuring the force
of gravity on that mass. Now we have found, scientists have found that these are equivalent.
If you do it in those two different ways you are going to get the same number. And that
eventually led to the general theory of relativity. And so I wanted to measure inertial mass and
gravitational mass. And I used a ruler to do it. So what I essentially did was tape
a rule to the side of my desk. I gave it a flick and then I recorded it with video and
slowed down that video. And so we are going to count four oscillations. So there is 1,
2, 3, 4. Okay. So it went back and forth 4 times. And so we are really using the ruler
almost as a spring. And so it took 3.0 seconds to do that. In the second trial what I did
is added mass to that ruler and you will see that it goes much lower. And so this would
be 1 oscillation, 2, 3 oscillations, and then 4 oscillations. Now you can see that it went
much slower, the overall time is 7.4 seconds. Why is it taking longer? It is because that
weight has more inertia. And so it takes a slower acceleration with a given spring constant
in this case. Now, what do you think the next one is going to be? I put 20 grams on the
weight. So I started with 0, then 10 grams and then 20 grams. So you might be thinking,
well it is going to be slower for sure. What is the number going to be? Well, if it is
linear we would see an increase of 4.4 seconds, so it would be around 11.8 seconds. And so
let's see what the time is. So it is 10.4 seconds. And so it does not look like it is
linear. I graphed this data and it looked like that. And so on my graph I got the mass
across the bottom. So we started with a 0 gram mass. Then a 10 gram mass. And then a
20 gram mass. You can see that the period is dropping off like that. And so if I wanted
to measure the inertial mass of an object, I then taped a penny to the ruler and gave
it a flick. I would just measure that. So I have to figure out the time of this unknown.
And so if this case it took 4.6 seconds. And so if I want to figure out the inertial mass
of the penny what I would do is find the period of 4.6. Read that over across to my graph.
And you can see that it is going to be somewhere around 3 or 4 grams is what a penny is using
an inertial mass. Again, not super precise method but it seems to work. If we were to
use the gravitational mass, how would we do that? Well I used a ruler again. I put a 10
gram mass on this side. I put the penny on the other side and I tried to get it to balance.
I could never get it perfectly balanced and then take a photo. But this is pretty close
to being balanced. And so now how do you figure out the mass of the penny this way? Well you
could use 1 unit, in other words the distance from the fulcrum right here we will say is
1 unit. And so how many units are we going to have on the other side of the ruler? Well
if we kind of expand that out I have got around 3.5 units on the right side. And so how do
I solve the gravitational mass? I just set a ratio up where on the left side I have my
mass and the distance. Same on the right side. And so I could solve it for that unknown.
In this case the unknown is going to be the mass 2. And so if I multiply this, it is 10
on this side. 3.5 on that side. And so I get a mass of around 2.8 grams. And so again on
the last inertial mass experiment I said it is around 3 or 4 grams and now we get kind
of a similar answer. And so we are seeing equivalence. They are the same value, even
though there is no reason that they should be the same value. And the first person to
note this was Galileo. Now he did not just drop objects off the Leaning Tower of Pisa.
He was doing really detailed experimentation with inclined planes. And what he was able
to do is measure this inertial mass, also gravitational mass. And he found there was
equivalence. Newton did similar things with pendulums. And so scientists always thought
that was very interesting. And it took Albert Einstein to kind of explain why those are
the same thing. And he built his theory of relativity on top of that. And so again, that
is outside the scope of Physics I and II, but it is interesting to talk about it for
just a second. And so he said imagine the following two situations. We have got a rocket
that is here on the earth. And so what is the force that is acting on that? That force
is going to be the force of gravity pulling down on that person. And now let's say we
give universal or constant acceleration to a rocket as it is traveling through space.
And let's set that acceleration equal to the acceleration due to gravity on our planet.
What he said is there is no way you would be able to discriminate between those two
events. If I take an object for example and I drop an object from here it is going to
fall down acted on by gravity. And the same thing is going to occur here as we accelerate
away from it. And so he really tied together that equivalence principle and he used it
to build his general theory of relativity. And so did you learn to design a plan for
collecting data to measure gravitational mass? So we could use a balance to do that. An inertial
mass, which again is using the acceleration based on an applied force. I hope so. And
I hope that was helpful.