- Good morning.
We have a brass ball,
which is thrown into
and lands in a cart.
♫ Flipping Physics ♫
- [Mr. P.] Bobby, what type of collision is this?
- This is a perfectly inelastic collision,
because the two objects stick to one another.
- [Mr.P.] Bo, is momentum conserved
during this perfectly inelastic collision?
- Momentum is conserved in all collisions,
so yes.
- [Mr.P.] Billy, is kinetic energy conserved
during this perfectly inelastic collision?
- Kinetic energy is only conserved
during elastic conditions,
so, no.
- Great!
Let's see what we know.
The total mass of the cart is 0.599 kilograms,
and the mass of the brass ball is 0.066 kilograms.
I overlaid a picture of a meter stick on the video
to show that right before the collision with the cart,
the brass ball goes from a position of 0.566 meters
to 0.313 meters
in 0.16 seconds.
Therefore, the velocity of the ball before the collision
is negative 1.58125 meters per second.
Note that this is velocity of the ball
in the x direction,
because we are going to use conservation of momentum
to predict the velocity of the cart
and ball after the collision,
which will all be in the x direction.
Therefore, everything in this problem
is in the x direction.
Conservation of momentum states
that the sum of the initial momenta of the system
is equal to the sum of the final momenta of the system.
In other words,
the initial momentum of the ball
plus the initial momentum of the cart
is equal to the final momentum of the ball
plus the final momentum of the cart.
And, momentum equals mass times velocity,
therefore,
the mass of the ball
times the velocity of the ball, initial
plus the mass of the cart
times the velocity of the cart, initial
is equal to the mass of the ball
times the velocity of the ball, final
plus the mass of the cart
times the velocity of the cart, final.
However, we know the initial velocity of the cart
is equal to zero,
therefore that whole term
is equal to zero.
And because the-- - Mr. P.
- Yes, Bobby?
- Isn't the brass ball inside the cart
after the collision?
So don't the brass ball and the cart
have the same final velocity?
- [Mr.P.] Correct, Bobby.
Because the ball is in the cart after the collision,
the final velocity of the ball
and the final velocity of the cart
are the same.
Therefore, we can combine the masses to get...
The mass of the ball
times the velocity of the ball, initial
equals the total mass,
or the mass of the ball
plus the mass of the cart,
all times the final velocity of the ball-cart system.
And we can solve for that final velocity.
Bo, could you please plug in the numbers?
- The mass of the ball is 0.066 kilograms,
the initial velocity of the ball
is -1.58125 meters per second,
and the mass of the cart is 0.599 kilograms,
which means the predicted final velocity
of both the cart and the ball
is -0.15694,
or with two significant digits,
- 0.16 meters per second.
- [Mr.P.] And we can again overlay the meter stick
and show the cart goes
from 0.306 meters
to 0.267 meters
in 0.25 seconds,
which gives us an observed final velocity for the cart
of -0.156 meters per second,
which we can use to determine an error
between our predicted value and our observed value.
Using the relative error formula,
or the observed value minus the accepted value
divided by the accepted value times 100,
and substituting in our predicted value
for the accepted value,
we get an error of,
with two significant digits,
- 0.60%
between the predicted final velocity
and the measured final velocity.
Which means,
♫ The physics works
♫ Uh-Huh, uh-huh
♫ The physics works
Thank you very much for learning with me today.
I enjoyed learning with you.
Oh wait, I forgot!
It's fruit day!
- [Students] Fruit day.
- What kind of fruit are you guys?
- I'm a banana.
- I'm a pumpkin.
- I'm an eggplant.
- Oh, I get it.
Egg. Plant.
Nice.
Mr. P.,
What kind of...
What kind of fruit are you?
- I'm an apple.
See?
- [Billy] Am I the only one who actually dressed up
as a fruit?
- An apple is a fruit.
- So is a pumpkin.
- And so is in eggplant.
- I'm not so sure about that.
- All you did was wear yellow.
I had to carry this plant all the way here.
And this egg. - This was hard to find
all this yellow. - But I get to eat the egg
for lunch. - And I wore
the hat - That's cool I guess.
But then, - For the
stem. - Then I'll be just a plant.
- And everything.
I worked pretty hard
at this. - That's kinda weird.
- [Billy] Even my underwear is yellow.