KRISTIN GONZALEZ-VEGA: Welcome to AP Daily practice sessions.
My name is Kristin Gonzalez-Vega,
and I teach at Centennial High School in Frisco, Texas.
Today we're going to be going over some multiple-choice
questions and strategies how to answer them,
tips to get through them, and how
to weed out important information,
and to get you the best score possible.
So we're going to dig right in.
Some things I just wanted to mention are that we do have--
all of our sessions will have the problems available
for you to download in PDF form.
But I also do suggest that you get out some paper,
your formula chart so that you can
get used to using that, and something to write with,
and a calculator.
Today we won't be really doing any set calculations,
but in our future sessions, we will.
So if you're watching a few at a time,
then it's good to have handy.
What I'd like you to do for each of these questions
is to take a second to pause your video
and read through them and try to answer it on your own
and then come back.
And we're just going to talk it out and go over it together.
So our first question here, I'll just put up,
and I'll give you a chance to read it.
Since you guys are all excellent readers,
I don't have to read the question to you.
But like I said, go through it, answer it, and then come back.
So what do we have going on in this question?
The first thing I see when I look at this
is I feel super overwhelmed because it
is so much information.
The question has a huge paragraph.
All the answers have sentences to them.
And there's this diagram.
There's so much going on.
So what should we do?
Well, you're going to take your pencil.
And at the exam, you're going to just start picking out
the important things.
So on this one, the things that I just
were noticing when I was reading it
is there was a whole bunch of stuff, all of this green stuff
that was really just describing what
the diagram was showing me.
So, yes, we have this block that has a mass M.
It compresses a spring.
It's on an incline at an angle.
And then it's released and goes up to some distance
D where it's going to come to a rest.
That's probably important right it
is starting compressing the spring and it's ending at rest
and then also there's this thing that
says frictional forces are considered
to be non-negligible.
What does that mean?
Well, that just means there is friction.
Generally, the rule on the AP exam is that if we don't say
there is friction in AP Physics 1, then there is no friction.
Same thing with air resistance.
But here, they're telling me there's definitely friction.
There also might say that it's a rough ramp,
and that would tell us that there's friction.
But that is our hint here that there is friction.
The other thing we want to know is what's really the question.
We want to know which of the following systems
under consideration will--
which the following claims correctly describes
the energy of the system under consideration
from when the block is compressed against the spring
until it travels a distance D?
And this happens to be a question that
has two answer choices.
So let's go through those answer choices.
The whole system thing is really what our focus is today.
In energy and in momentum, it's really important
to know what you're looking at because
if you have things that are inside your system,
then they're not affecting the system as a whole.
They affect each other but not the system,
meaning the center of mass.
And if we have things external to our system,
then they can apply forces to make changes to our system.
Remember, forces can change energy.
They can change momentum.
They can change motion and cause acceleration.
So looking at what your system is.
So in our first part, our system was
consisting of just the spring.
Well, if we're looking at the spring only,
well, the spring can store elastic potential energy.
In the second example, our system
is consisting of only the block.
Well, single objects like the block
can only store energy kinetically in the motion.
And then if we take the block and Earth as our system,
well, now we can store energy gravitationally.
It's that interaction between the block and the Earth,
that gravitational field that is allowing
us to store that gravitational potential energy.
And so if the Earth isn't in our system,
we cannot say that the system is storing energy in gravitational
potential energy.
And then lastly, the system consisting of the spring,
the block, and the Earth, well, now we can have
all of those types of energy.
We can have our spring potential energy,
our gravitational potential energy.
And there can be the block in motion, which
means we have kinetic energy.
So looking at what's in your system
and what energies are possible for that system
is super important here.
So what's the right answer?
Well, B and C. So why?
Let's look at the ones that aren't right.
A, the mechanical energy of the system consisting of the spring
increases by one-half kx squared.
Well, as that spring is uncompressing and pushing
the block, that spring potential energy
is actually decreasing by one-half kx squared.
And our last one, the mechanical energy
of the system consisting of the spring, block, and Earth
increases by one-half kx squared.
Well, if everything is in our system except there's friction,
well, that tells me that our total energy of the system
is going to be slightly decreasing but not very much.
We're pretty much starting with the same amount of energy
that we began with, which was that one-half kx squared
minus a little bit because of friction.
So let's look at why the right answers are right.
So for B, the mechanical energy, again,
of the system consisting of the block isn't changing.
It's starting from rest.
It's ending at rest.
And so if we're looking at just the block,
it's starting at rest, so no kinetic energy,
and it's ending at rest, so no kinetic energy.
And if we look at the mechanical energy of the system consisting
of the block and Earth increases by more than zero
but less than one-half kx squared,
well, we've still got that friction to think about.
So what I suggest you do when working problems with energy
is to draw what we call an energy bar
chart or LOL diagram.
So if we do that for this example, the way they work
is you draw LOL.
And on the left side, we're going
to represent the energy that is our initial condition energy.
So that would be when our block is
compressed against the spring.
We're going to draw what is in our system inside our circle
and what is outside our system outside the circle.
And then we're going to draw what our final energy
conditions are on the right-hand side in that L. So for this,
we're looking at just the block and the Earth.
What's not in my system?
The spring.
The spring is pushing, increasing
the energy of the block because it's
pushing in the same direction that it's being displaced.
Since work is force times distance,
it's doing positive work, increasing the energy
of the block-Earth system.
But then we have that friction, which
is going to take a little bit of energy out.
It's doing negative work.
The force is down the ramp while the block
is displaced up the ramp.
Negative work.
What do we end with?
We end with a little bit of energy
dissipated as thermal energy in the friction.
And then we have that gravitational potential energy
because the block did raise to a height.
All right.
One question down.
Let's take a look at another one.
So, again, you're going to read it, see if you can answer it,
and then come back.
Again, this problem is pretty wordy.
So let's pick out some important things.
One thing that I highlighted here
is that here, all frictional forces are
considered to be negligible.
So here, we don't have friction.
If we look through our answer choices,
let's look at number one.
If the block is released from a height of 2h1,
the block will land at a distance
2D away from the end of the track.
So they're saying that there's a direct relationship
between the starting height of the block
and how far it travels from the table.
So we need to do some math.
So we're going to get out our formula charts.
What relationships would we use here?
Well, when I think about it, I know
that I need to know what the velocity
at the bottom of the track is.
So we're starting with gravitational energy.
We're leaving with kinetic energy of the block.
And if we rearrange that, if I had twice the height, really,
that's only going to give me the square root
of two times the velocity.
And then since we're using kinematics and projectile
motion to see how far it lands away from the table,
if we're using the x equation, x is v-knot t,
then if I have square root of two times the velocity, that
means it's going to go square root of two times the distance,
which is not double.
If we look at B, if the block's mass is increased to 2M,
then it would land a distance of 2D away.
Well, if we look at our energy equation again,
mgh equals one-half mv squared, our masses
are going to cancel out.
So it doesn't matter what the mass of the block is.
It's going to reach the same velocity
at the bottom of the ramp.
At C, the total mechanical energy
of the system consisting only the block
increases from the moment of release
to the moment it strikes the ground.
Well, again, what's our system?
This time, our system is only the block.
As the block goes down the ramp if there's no friction,
it's speeding up that whole time.
And then when it's in the air, it's
speeding up on the way to the ground because
of the gravitational force all the time
pulling it towards the ground.
So since it's speeding up, our kinetic energy
is going to increase.
And then lastly, the total mechanical energy
of the block-Earth system remains constant.
Again, we've got the block and the Earth in our system.
So we're changing from gravitational energy
to kinetic energy.
And since there's no friction, we have no work being done.
The ramp can't do work because the normal force is
perpendicular to the ramp and the motion is parallel.
So even if the ramp is in our system,
the ramp can't do work, especially
if there's no friction.
Last question here, guys.
Read through it and then come back
and let me know what your answer is.
All right.
So this time, we've got a little bit of a collision with energy
here.
We got a few different principles involved here.
So we've got this clay ball that's
moving towards the block attached to a string.
It's going to collide and do what?
Stick to it.
So that should be a clue of it's colliding, it's sticking,
there's some momentum going on.
We want to know which of the following quantities
is the same immediately after the collision and the instant
the block reaches that height h-knot,
which is the maximum height.
So first one says linear momentum
of the clay-block system.
So, again, clay-block is our system.
Well, hey, what's not in our system that is acting
on the block and the clay?
That's the Earth.
The Earth is exerting an external force,
which is going to cause a change in momentum.
Forces cause change.
So not A. B, what about the angular momentum
of the clay-block system?
Well, again, we have the Earth that
is going to exert a torque.
Remember, angular momentum only stays constant
if there's no external torques.
The Earth's not in my system, so we have an external torque.
And then the total mechanical energy
of the clay-block system.
The energy.
Is the energy constant of the clay-block system?
Well, no, because we don't have the Earth in the system.
So the Earth is going to do work.
What's going to decrease the energy?
So while if the Earth was in my system,
yes, we have kinetic energy that's
going to be then stored as gravitational energy.
But if the Earth is not in my system,
then our energy is actually going to be decreasing.
So what are we left with?
We've got D, the total mechanical energy
of the clay-block-Earth system.
Since now everything's within my system,
there's no external forces, no work being done on the system.
Now we do have a constant mechanical energy.
So I hope that helps you a little bit
with systems and with energy and how to approach those problems.
Number one, what is in your system?
Always going back checking, what's in my system?
Then what kinds of energy can my system be storing?
Is it spring energy, kinetic energy, gravitational energy?
What's in my system, and what can it store?
And then lastly, looking at, well, what's not in my system?
If there's any external forces, can those forces do work?
Remember, for work to be done, the force
has to be parallel or have a parallel component
to the displacement of the object.
So thanks so much for tuning in and come back
for more practice.