So in last video we figured out. How to solve
The projectile motion of this example we said we had a person standing up on a cliff
50 meters high it threw a ball at 20 meters per second at an angle of 30 degrees from horizontal and
we figured out that flight path
by the way here's the graph laid over our original
Diagram here how cool is that i couldn't resist now in this one i want to
figure out an example where we assign a mass to this ball and then we figured out the actual
kinetic energy and potential energy and graph that as well
So here's kind of where we left off we had our graph that we figured out
how to graph the entire flight path and then
we can change anything in here
And the graph will update automatically and it'll always end at zero thanks to some calculations that we built into this
now like i said we want to add in some columns
So how do we do that let me just kind of clean things up first of all so
What, we want to do is add some columns here and we'll add the velocity in the x-direction the
velocity in the y-direction
and let's just solve those for naught
And this switches back to 50 meters just so our graph looks right so if you remember
we are solving this considering
or not considering air resistance so
The velocity in the x direction is going to be constant it's not going
To slow down over time so the x component of this velocity
Vector at that 30 degree angle is never going to change so?
what we can do is
just, say
equals and then select our
initial x velocity there lockette it and then that will populate down then for the y velocity
We need to do a little bit more of a calculation
We need to say
our
initial y velocity
lock that plus gravity
lock that times our time
So we can see that velocity is decreasing by 9.8
meters per second squared so every second that velocity is decreasing
9.8, meters per second
So if we look at one second it
decreased roughly 9.8
and that the reason that it's not exactly point two is because of a rounding error
So if i increase that you can see that's not exactly one second?
let's figure out how much kinetic and potential energy is in the ball at
Any given second along the flight path so in order to do that let's type in pe and
ke
So this would be our potential energy and our kinetic energy so the equation for potential energy is
going, to be
draw, over here on the right potential energy
equals
mass times
gravity times the height of the
object from the ground and
kinetic energy
is
going, to equal
1/2
ohmygosh 1/2
The mass
times the velocity squared
So now that we know that we can calculate?
Both, of those at any given point so to calculate the potential energy well first of all we're gonna need a mass so let's
just, drop that in here i'm gonna
right click insert
shift cells down okay so our mass let's assign that a mass of five kilograms
and
So now we can use that to calculate the potential energy so we take our
five kilogram mass lock that times our
gravity lock that
times our height and our height is going to be our y-value
So the distance our ball is from the ground is going to
Allow us to calculate the potential energy that's in that ball at any given point
through this flight path so
If we hit enter there that calculates and this is giving us a negative value because our gravity is negative so we'll just put
absolute value
in front of that so we can already see that our potential energy starts at this number
2,450 joules that would be in and then it slowly increases as
The height of the ball increases and then it starts to come back down as the ball comes back down and
the interesting thing is that the kinetic energy it'll actually
Do the exact opposite so the kinetic energy is going to
Start higher and then go down as
The ball slows down
Toward the peak of the arch and then it will increase as the ball accelerates back toward the ground
So let's see what that looks like, so we're gonna do oh point five times
again the mass of our ball
times our
Velocity squared so actually what we need to do is go square root of
the velocity and x
squared
plus the velocity
whoops plus the velocity in the y squared and
that will all be squared as well
So if we were to add yet another column
just, say total energy and we're gonna say that equals this plus this
we can see that it's equal all the way through and that's actually
the
conservation of energy the law of conservation of energy saying that the
potential energy plus the kinetic energy of an object
no matter
what the velocity the height the
Acceleration all that that always has to be equal so that's pretty cool now
what we can do is
let's just
grab all this and
insert
The graph and it'll just be a nice visual and i only grab the whole thing because it's the easiest way to do that and
Then oops
right there
so that is a graph comparing our potential energy and our kinetic energy over time
So just another cool visual to help understand some of these kind of complex
Topics if i just zoom out here and i changed some of our variables again let's say hundred meters and let's go
60 degrees and
this is where it'll get
you, can see our graphs
Update so let's say 0 that'll change a lot so we can see
now our potential energy when the ball is
Sitting on the ground right at 0 seconds so the moment it's launched the potential energy there is zero
Because the ball can't be accelerated it can't be moved downward at that exact point it has nowhere to go
but the kinetic energy because it's just been
accelerated and an absolute instant all the way up to our
velocity our initial velocity there are 20 meters per second the kinetic energy at that point is
All the way up to a thousand ten thousand
joules and then as the
ball goes through its flight path right at the peak here we can see the potential energy
maxes out and
the kinetic energy is at a minimum and
what's
important to note here
is that the kinetic energy never reaches zero
because and i'll switch to draw mode again to kind of explain this
i'll switch draw mode here
Because even at the peak of the arch when the ball is right here it still has an x vector
There's there's no y velocity to it
so
that's where the kinetic energy is lost and its lowest because there's an
why velocity
but there is still an x velocity so the kinetic energy will never reach zero through the the flight path
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