JULIE HOOD: I'm Dr. Julie Hood.
An AP Physics teacher from Mast Academy in Miami, Florida.
In today's video you're going to practice multiple choice
questions.
I've chosen questions that focus specifically on momentum.
Momentum is very powerful conservation law
and it's often overlooked.
Now, if you want to work through these problems with me,
click on the link over the video now.
And you can download the PDF of questions
featured in this session.
So momentum it's mass times velocity.
It's a vector, and it's conserved.
It's a beautiful thing that it's conserved.
But here's the deal.
You can change the momentum of a system
by adding an external force.
We call that an impulse.
And there's your change in momentum.
It depends how much force and for how much time.
And if the force is a function of time,
then you've got to do some calculus and integrate.
We use a J to represent impulse.
And because [AUDIO OUT] is the integral of F dt,
the force F is going to be the derivative of momentum
with respect to time.
And these are equations that I've boxed for you.
These equations are on your equation sheet.
Get familiar with your equation sheet.
So let's do some problems.
So we have a ball initially moving horizontally
with velocity vi.
It's struck by a stick.
After leaving the stick the ball moves vertically
with a velocity vf, vf smaller in magnitude than vi.
And the question is, which of the following vectors
best represents the direction of the average force
that the stick exerts on the ball?
Now, these are our choices for that vector of force.
We're looking for force.
Well, whenever I think of force I think of Newton's second law,
F equals ma.
And acceleration a is just the change in velocity with respect
to time.
So we're going to get a force that's parallel
to the change in velocity.
And the change in velocity it's just
going to be final velocity minus initial velocity.
And I don't know how to subtract vectors.
But I know how to make a negative vector.
You just simply change the direction
and keep the same magnitude as shown up there.
And now I can add vectors.
And I add them tip to tail.
And my result is a change in velocity
in that direction, which means the force has
to also be in that direction.
It can't be one of the choices I just checked out.
It's B, that's your answer.
Now, I've got another problem here.
I have an object with the initial momentum represented
by the vector that I'm showing there below the text,
and it strikes an object that's initially at rest.
And I'm going to give you several sets of vectors that
might represent the momenta of the two objects
after the collision.
Well, which one?
I'm looking for momentum after the collision.
Momentum is conserved.
So I need to add the two vectors in each of the five
potential answers and see if I get one that's
equal to what I started with.
In choice A, those two vectors cancel one another
that can't be the choice.
And choice B, those two vectors would add and make
a really, really long magnitude for final momentum.
So that's not going to be right.
Choice C, the vectors that vector moving to the left
is going to make the vector moving
to the right yeah, shorter in magnitude
but in the wrong direction.
So that can't work.
Choice D, well, if I add the two vectors together,
I'm going to get a vector that's not in the proper direction.
So let's look at choice E and make sure it works.
When I add the two vectors together sure enough,
I get a vector pointing to the right, and that's our answer.
These aren't so bad.
I think you're going to get a 5 on the exam.
Watch all these review videos and practice
and you've got this.
I have a good feeling about this.
So now I've got a problem where I've
got an object moving on a horizontal frictionless surface
and it makes a glancing collision with another object
that's initially at rest.
And we want to know which of the statements
is true about momentum and kinetic energy.
Well, momentum is always conserved.
So right away B and E cannot be the right choice.
And kinetic energy could be conserved
in a perfectly elastic collision,
but often it's not necessarily conserved.
So you don't want to use the word always
it's not going to work.
So B and are not choices.
And to say that kinetic energy is never conserved in choice C,
never say never, it could in fact
be conserved if your collision is perfectly elastic.
So A is the only choice that you can count on,
and that's why it's the answer.
So here's a great problem.
You've got a mass moving with the speed v naught
to the right on a frictionless surface,
and suddenly it explodes into two pieces.
One of the pieces, 2/5 of the original mass,
will move with half the original speed but to the left.
And we're asked to find the speed of the other piece.
And these are our choices.
Now, momentum is conserved.
And in an explosion, a lot of people
are really bothered by this.
But don't be momentum will still be concerned
because the explosion is internal to the system.
You're not adding an external force.
So momentum will remain conserved.
Initially, that's how much momentum you had.
Afterwards, 2/5 of the mass move to the left,
that means negative v0 over 2, velocities of vectors.
So you definitely want to have that negative sign in there.
And the other piece is 3/5 of the mass.
It's what's left.
And we want to find the velocity.
Notice the masses cancel out.
And if I do a bit of algebra, I'll
move that negative 1/5 to the other side
so then I can find B. Adding those together,
I get 6/5 of the knot, and that better equal 3/5 of B.
When you do the algebra, v is twice the original speed
of the entire mass.
Don't forget, you've got some other piece
of mass moving the other way.
So together, the total momentum is conserved.
These aren't the choices.
Here's your answer.
This is a two dimensional problem
and not only is it two dimensional
but you've got two questions associated with one stem.
So you've got two pucks moving on a frictionless air table,
they're about to collide.
We've got one of them moving directly East
and one of them moving North.
So we've got this coordinate system.
And we're asked first, to find the total kinetic energy
before the collision.
These are our choices, and we're looking for kinetic energy
before the collision.
That's kinetic energy.
But there are two objects.
So you need to consider the kinetic energy for both.
Energy is a scalar.
You're squaring the velocity.
So don't worry about directions.
They add up.
Its scalar amounts.
So you substitute the values in, do the math,
and 5 joules is your answer.
And the next part of this question
asks you to find the magnitude of the total momentum
of the two puck system after the collision.
And these are your choices.
Total momentum after the collision,
there's the first object, the second object,
the coordinate system, and the key here, once again,
is that momentum is conserved.
And initially, you've got some momentum
going to the East and some to the North.
And so it's a two dimensional vector.
But that's what your total momentum
has to be after the collision, not
necessarily in the same direction with the same speeds.
But here's what you had initially.
Puck one and puck two gave you this much initial momentum.
And we're trying to find the final momentum
after the collision.
The total momentum is just going to be-- we're
looking for the magnitudes.
So we're just looking for the length.
And you literally just have Pythagorean theorem.
So 3 squared plus 4 squared, square root.
Hey, it's a 3, 4, 5 triangle.
So these are not correct.
And there's your answer.
Now, here's a great question.
If one only knows the constant resultant force acting
on an object and the time during which this force acts,
what can we determine?
Lots of choices.
But one of-- we all know what the constant result
of forces that acts on the object and we'll
also know the time.
And when you have force and time, I think of momentum.
Let's look at all those equations
for momentum and impulse.
Well, I don't know mass without knowing velocity.
So B and D don't work.
And if I don't mass and I don't know velocity,
I certainly can't find the kinetic energy.
And this is not a Newton's law problem.
This is a problem for momentum.
I've got force.
I've got time, that means I can find the change in momentum.
Choice A is your answer.
Here's another problem.
You've got a 5 kilo object propelled
starting at rest at time t, and we apply a force.
And that force is a function of time.
And we want to know what the speed of the object
will be after 4 seconds.
Well, we want to find speed, and these
are our choices for the answer.
We are given the force and times involved,
that means oh, I'm going to use a momentum problem
and I'm applying an external force.
So I'm finding an impulse.
An impulse is the change in momentum,
which is going to be mass times a change in velocity.
And that will be equal to the integral of the force function.
There it is.
And we're starting at time 0, and we're
going to integrate that force function until we get to time
equals 4 seconds.
You know how to integrate that, and then
you just evaluate it at the limits,
and you find that the change in momentum is for momentum units.
And the change in velocity.
Well, initially the object's at rest.
So v sub 1 is 0.
So if the change in velocity is the speed of the object at 4
seconds, and that means we just have
to take the impulse change in momentum and divide by mass.
We already found the change in momentum it was 4, A,
and we're given the mass up there it's 5 kilograms.
So there's our final speed.
Not one of these, B's our answer.
Now, this is a fun one.
We've got a person holding a portable fire extinguisher.
And the extinguisher ejects 1 kilogram of water per second.
What does that mean?
Horizontally at a speed of 6 meters per second,
what horizontal force in newtons must the person
exert on the extinguisher to keep
the system from accelerating?
We need a net force equal to zero.
But we're looking for the horizontal force
that the person needs to exert.
So don't quickly say, oh, A, no.
That's not the right answer.
We have a kilogram of water moving
at a rate of 1 kilogram per second at that speed,
and I have to find force and in newtons.
And what do I do.
What do I do.
Oh, I remember, how about some dimensional analysis?
F is equals ma.
So 1 Newton of force, that's what's
needed to accelerate a kilogram of mass
at a rate of 1 meter per second squared.
So I can break up those units into kilograms per second times
meters per second.
And now I'm starting to see the light go on because I'm
given that information.
The force is going to be the rate of what mass of water
injecting at times the speed that that water is spewing out
of the extinguisher.
And that leaves us with 6 newtons.
That's how much force I would need
to exert on the extinguisher to keep it from accelerating.
So 6 newtons is your answer, dimensional analysis
very powerful.
The graph below is another one shows
the force of an object of mass m as a function of time.
For the time interval from 0 to 4 seconds,
and we want to find the total change
in the momentum of the object or applying an external force.
We want to find the change in momentum
and these are our potential answers.
Change in momentum.
Oh, that's just the integral of the force function with respect
to time, which means all you have to do
is find the area under the curve.
This is not some fancy curve.
You don't need to use calculus.
You just need to use the idea of calculus.
I have to find the area of each of these rectangles.
Now, area base times height, 2 seconds,
10 newtons that's 20 Newton seconds.
Now, area 2 is don't forget the force is negative 10 newtons
so we're going to get negative 20 newtons
seconds and the entire from 0 to 4 seconds the integral,
the total area would be the sum of the two,
and they cancel, and you're left with 0.
So you have no change in momentum.
So certainly we did determine it.
So B is not the answer but it's 0.
So B don't work, and C is your answer.
Now, I think we've had a great time.
So why don't we go over the takeaways.
First of all, is there a collusion in the problem?
The news momentum.
That's momentum.
And it's conserved unless you have an external force acting
on the system, then you can change momentum.
We call that an impulse.
There it is.
And thank you so much.
I wish you the best.