Hi. It’s Mr. Andersen and this is AP Physics essentials video 62. It is on the force-time
graph, which is what it sounds like. It is a graph that shows the force applied and how
long that force is applied. And as an example I will use the Saturn 5 rocket which delivered
the Apollo astronauts to the moon. And so it is a three-stage rocket. And so stage 1
is the largest. It is 34 million newtons of force and it is applied for 165 seconds. That
will drop off and then you have stage 2 which is over 4 million newtons of force but it
is longer. It is 360 seconds. And then finally you have stage 3 which is 1 million newtons
of force and it will fire twice. The first one to get this escape velocity and the second
one to put it on a trajectory so it can intersect with the moon. And so if we were to draw a
force time graph of that first stage it would look like this. So we are applying a 34 million
newton force and it is for 165 seconds. And so this would be the force-time graph. And
so the area underneath that graph is equal to the impulse, which we use J to represent
that. So the force applied and how long it is applied. Now as we have learned in earlier
videos that is equivalent to the change in momentum or mass times the change in velocity.
And so if you can get the force-time graph you can figure out what the change in momentum
is and you could figure out the change in velocity. Now the second stage the force-time
graph would look like this. It is about 4 million newtons but it is longer and since
it is longer we are applying a force for a greater amount of time so we are going to
have a greater change in momentum just because we are applying it for a greater period of
time. And so the change in linear momentum is equal to mass times the change in velocity.
But it is also equal to the impulse which is force times time. And these two values
are equivalent. They are equivalent in units, change in momentum is kilogram meters per
second. And force-time is going newton seconds. But they are equivalent. We can move between
the two. Once we have one we can figure out the other. And they are also equivalent in
their directions, so that change in linear momentum is equal to that force which is going
to be a vector times the time. And so if you have a force-time graph like this, simply
graph the force over time and then inside that or underneath that graph is going to
give you the change in momentum. And so again to go back over what impulse is if we take
force equals mass times acceleration, remember Newton’s second law, we can say acceleration
is simply the change in velocity over time, if we multiply both sides times time then
we have the two things we are talking about. On the right side we have change in momentum
and on the left side we have impulse. And these are equivalent. They are exactly the
same. And so if we are looking at impulse we use J to represent that, and it is simply
force times time. That impulse, which is going to be a vector is equal to the force, which
is a vector and the time that it is being applied for. And so let me give you an example
of how you might use this force-time graph. And so a real example, from the Saturn 5 rocket,
if you apply a 34 million newton force to a 3.0 million kilogram rocket that is how
much that Saturn 5 weighed for 165 seconds, calculate the change in velocity? And so this
will be the formula that we are going to use right up here. So we will plug in everything
that we know. So force times time equals mass times change in velocity. Our force is going
to be 34 million newtons. That is right here, times the time, 165 seconds. That is equal
to the mass of the rocket which is 3 million kilograms times the change in velocity. And
so now we just have that one value change in velocity. So we could multiply everything
on the left side. Divide by everything on the right side and so we get a change in velocity
of around 1900 meters per second. So there is going to be a huge change in velocity.
Now when I looked this up and looked at what NASA released as the amount of change in velocity
during that time, they have a value that is greater. So 2756 meters per second. And so
where is the difference there? Well remember as that rocket is firing it is using up some
of that rocket fuel. What is that doing to the mass? The mass is changing. It is getting
lighter and lighter and lighter, so what is happening to our change in velocity? It is
getting greater. Now in AP Physics they will only ask you questions where the mass is going
to remain constant. Another way they could ask you that question is to give you the force-time
graph and then have you calculate the change in momentum. So let me give you an example
of one. Let’s say this is the change in force over the change in time and you need
to calculate the momentum change. All you are going to do remember is calculate the
area underneath that curve. That is going to be the impulse. And so we could break it
down into geometric shapes. And so the first one I see is going to be this rectangle right
here. It is a 30 newton force on this side times 30 seconds and so that is going to be
900 newton seconds. It is just base time height. I also see a triangle on the left and on the
right side. And so again geometrically that is 1/2 times base times height. So that is
30 newtons times 20 seconds. And again we have to take that in half. And so that is
going to be 300 newton seconds. And then the other side is going to be 300 newton seconds
as well. And so we can just break that up into different shapes and then we add them
up. So we are going to have an impulse of 1500 newton seconds. Now another question
they could ask you is similar to the question we just had about the rocket. So now we have
a change in momentum of 1500 kilogram meters per second. Could you calculate the change
in velocity if I give you the mass of the rocket to be 0.5 kilograms. Well try that
and I will put the answer in the video description down below. And so did you learn to mathematical
routines to calculate impulse which again is force times time? And do you know that
that is equivalent to the change in momentum? And finally could you preform data analysis
on a graph of the force-time graph to figure out not only the impulse but the change in
momentum? I hope so, and I hope that was helpful.