- Good morning.
Let's apply conservation of momentum to an explosion.
♫ Flipping Physics ♫
- That doesn't look like an explosion to me.
- It's a mechanical explosion.
Nice vintage athletic outfits, by the way.
- [All] Vintage Athletic Day!
- Can anyone guess which movie character
I decided to dress up as?
- I have no idea who you're supposed to be.
- He wears this awesome outfit through the entire movie.
- I like your bandana.
- What is that?
- Oh well, we may never know.
Okay, here's the situation.
I attached my nerd-a-pult to two momentum carts
and used it to launch a brass ball.
Notice how the nerd-a-pult moves to the right,
as it catapults the brass ball to the left.
Bo, why is that?
Why does the nerd-a-pult move to the right?
- [Bo] Uh, because of conservation of momentum.
The brass ball has negative momentum,
therefore the nerd-a-pult must have positive momentum.
- [Billy] And we know momentum is conserved
because this is an explosion
and momentum is conserved in all explosions.
- Absolutely, let's write down our known values.
The mass of the brass ball is 0.066 kilograms.
And the mass of the nerd-a-pult
plus the two momentum carts is 1.791 kilograms.
I overlayed a picture of a meter stick on the video
to show that after the explosion,
the ball goes from a position of 0.451 meters
to 0.015 meters in 0.11 seconds.
And the velocity of the ball after the explosion
equals the displacement of the ball
divided by it's change in time,
which works out to be negative 3.963,
with the 63 repeating, meters per second.
Again, that's the final velocity of the ball,
after the explosion.
Bobby, what is the equation for conservation of momentum?
- Conservation of momentum,
the sum of the initial momenta
equals the sum of the final momenta.
- This means the momentum of the ball initial
plus the momentum of the nerd-a-pult initial
is equal to the momentum of the ball final
plus the momentum of the nerd-a-pult final.
And because momentum equals mass times velocity,
we know the mass of the ball times
the velocity of the ball initial,
plus the mass of the nerd-a-pult
times the velocity of the nerd-a-pult initial
is equal to the mass of the ball times
the velocity of the ball final,
plus the mass of the nerd-a-pult
times the velocity of the nerd-a-pult final.
And class, what is the initial momentum of the system?
In other words, before the explosion,
what is the initial momentum of the ball
and the nerd-a-pult?
- [Class] Zero!
- And we can subtract the mass of the ball
times the velocity of the ball final from both sides
and then we can divide both sides by
the mass of the nerd-a-pult to get,
the velocity of the nerd-a-pult final
equals the negative of the mass of the ball
times the velocity of the ball final,
all divided by the mass of the nerd-a-pult.
Billy, could you please plug in some numbers?
- Sure, the velocity of the nerd-a-pult final
equals the negative of 0.066 times negative 3.963
with the 63 repeating, divided by 1.791,
which is 0.14606 meters per second.
And we are predicting that the nerd-a-pult should have
a final velocity of roughly 0.15 meters per second
to the right.
- Correct and now we can measure the displacement
and change in time for the nerd-a-pult
to determine its final velocity.
The nerd-a-pult starts at 0.400 meters
and after the same 0.11 seconds,
the nerd-a-pult is now at 0.416 meters.
Which means the final velocity of the nerd-a-pult
is positive 0.145 meters per second,
with the 45 repeating.
And let's use the relative error formula
to determine how far our prediction
is from the measured value.
Using our measured value as the observed value,
and our predicted value as the accepted value,
we get a relative error of negative 0.42%,
with two significant digits.
And you know what that means.
- [Class] The physics works!
- That's right.
♫ The physics works, the physics works, the physics works.
Thank you very much for learning with me today.
I enjoyed learning with you.
Just so you know, if instead of using a brass ball
with a mass of 0.066 kilograms,
you use a wooden ball with a mass of 0.004 kilograms,
the nerd-a-pult does not move to the right.
Do you think you could explain why?