- Good morning.
Today we are going to solve Free Response Question
number 4 from the 2015 AP Physics 1 exam.
♫ Flipping Physics ♫
All right, we have two identical spheres, A and B,
which are released from the same height, capital H,
at the same time, t equals zero.
Sphere A has no initial velocity,
and Sphere B is given an initial horizontal velocity
with a magnitude V-not, and Sphere B travels
a horizontal distance, capital D,
before it reaches the ground.
Even though Sphere B has to go farther
before landing on the ground,
both spheres reach the ground at the same time.
Air resistance is negligible.
- Hold up, Mr. P.
- [Mr. P.] Yes, Bo?
- I feel like we've done this before.
- [Mr. P.] Bo, I am glad to see you recognize that.
- Yes, we did a demonstration of this concept,
and, actually, proved that the two spheres would land
at the same time, and demonstrated it.
- We are going to solve this Free Response question,
though, right?
- Absolutely, it is always good to review.
Part a asks us to draw free-body diagrams
of all the forces acting on each sphere
after they have taken half the time it takes
to reach the ground.
Bobby, could you please do that?
- Both spheres just have one force acting on them.
It's just the force of gravity,
and both spheres have the same mass.
So, the force of gravity should be of the same magnitude.
- That is true that the only force acting
on each sphere is the force of gravity.
However, could you please also explain
why all the other forces are not
in the free-body diagram?
- Okay, there is no string or rope,
so no force of tension.
There's nothing pushing on the spheres
while they are in the vacuum that you can breathe,
so no force applied.
The spheres are not touching a surface,
so no force normal, or friction force.
And there's no air resistance, so no force of drag.
That's all I can think of.
- Why don't we add V-not to the right
on Sphere B?
- Because the velocity is not a force.
- Oh yeah, right.
My bad, dog.
- That's great Bobby.
Bo, part B asks for a graph
of the horizontal components
of the velocities of each sphere as a function of time.
Could you please do that?
- Well, Sphere A has no velocity in the x-direction,
so draw a horizontal line at zero,
and Sphere B has an initial velocity, V-not,
which does not change in the x-direction.
So, draw a horizontal line at some positive value
and label it V-not.
- Remember to clearly identify which line goes
with which sphere.
I have used a legend.
And in order to make straight lines straight,
please use a straight edge.
Bobby, please read part c.
- In a clear, coherent, paragraph-length response,
explain why the spheres reach the ground
at the same time even though
they travel different distances.
Include references to your answers to parts a and b.
- So, Billy, give me a paragraph-length response, please.
- Okay.
As shown in part a, the only force acting on each sphere
is the force of gravity.
Therefore each sphere will have an acceleration
in the y-direction which will equal the negative
of the acceleration due to gravity.
There is no force in the x-direction on either sphere,
so, as shown in part b, both spheres will have
zero acceleration in the x-direction.
And any motion in the x-direction will not affect
how long it takes the spheres to reach the ground.
The initial velocity in the y-direction
for both spheres is zero.
The displacement in the y-direction
for both spheres is negative H.
Therefore, we can use the uniformly
accelerated motion equation
displacement in the y-direction equals
velocity initial in the y-direction times change in time
plus one-half times acceleration in the y-direction
times change in time squared
to show that both spheres will reach the ground
at the same time.
We have shown that, other than the change in time,
all of the variables in this equation are the same
for both spheres.
Therefore, the remaining variable, change in time,
must be the same.
- Sorry, I couldn't resist,
but I had to solve for the change in time
for both spheres.
Thank you very much for learning with me today.
I enjoyed learning with you.