- Good morning, today we are going
to talk about kinetic energy.
Bo, could you please tell me what the word, "Kinetic" means?
♫ Flipping Physics ♫
- Kinetic is like having to do with motion, right?
- Like kinetic friction.
- Correct, kinetic energy is the energy
associated with the motion of an object.
The equation for kinetic energy is KE= 1/2 mv².
Where m is the mass of the object and
v is the velocity of the object.
Billy, could you please determine
the units for kinetic energy?
- Kinetic energy is in joules, just like work.
- [Mr. P.] That may be correct, however I asked
you to determine the units for kinetic energy.
- OK, mass is in kilograms and velocity
is in meters per second, but I
don't see how that is joules.
- Well, that works out to be kilograms
times meters squared divided by seconds squared,
which is the same thing as kilograms times
meters per second squared times meters.
- Right and newtons are kilograms
times meters per second squared,
so kinetic energy is in newtons
times meters, which is joules.
Thanks Bobby.
- You are welcome.
- So yes, kinetic energy is in joules.
Bobby, can kinetic energy ever be negative?
- Well, mass cannot be negative
but velocity can be negative.
Oh, but velocity is squared in kinetic energy
and the square of a negative number is always positive,
so kinetic energy can never be negative.
- Also kinetic energy, just like work, is a scalar.
Let's do a short example problem.
Let's say I'm riding my bike at 25 miles per hour.
How fast would I need to drive my Prius
in order to have the same amount of kinetic energy?
Bo, please solve this problem.
- Don't we need to know the masses of the objects?
- [Mr. P.] Yeah, OK.
The mass of the bike with me on it
is 86 kilograms, and the mass of the Prius
with me in it is 1,400 kilograms.
- Let's see, we know the masses,
we know the speed of the bike is 25 miles per hour and
we know we are trying to solve for the speed of the Prius.
- Don't we need the velocity of the bike,
because it's velocity, not speed,
in the kinetic energy equation?
- Not really, remember that velocity is squared,
so we really only need the magnitude
of the velocity and instantaneous speed
is the magnitude of the instantaneous velocity.
- Uh, sure.
- Bobby, please keep going.
- Well, we know the two kinetic energies
need to be equal, so the kinetic energy
of the bike equals the kinetic energy
of the Prius, so one half mass times
velocity squared equals one half
mass times velocity squared...
Oh, everybody brought mass to the party.
♫ Everybody brought mass ♫
- That's not right.
- It's not the same mass.
Mass doesn't cancel out, it's one half
times the mass of the bike times
the velocity of the bike squared equals
one half times the mass of the Prius
times the velocity of the Prius squared.
- Subscripts, we always have to remember subscripts.
- Everybody brought one half to the party.
- That's not as fun.
- [Bobby] Nope. - [Bo] No.
- Billy, please finish.
- Divide both sides by the mass of the Prius
and then take the square root of the whole equation
to get to the velocity of the Prius
equals the velocity of the bike
times the square root of the quantity,
the mass of the bike divided by the mass of the Prius.
Substituting in values gives us
25 miles per hour times the square
root of 86 kilograms divided by
1,400 kilograms.
We forgot to convert from miles
per hour to meters per second.
- Actually, we don't need to because
the kilograms cancel out and we are
left with 6.1962, or 6 miles per hour.
- OK, but shouldn't our answer have two significant digits?
- Yes, however the Prius' speedometer
does not display tenths of a mile per hour.
- OK, that makes sense.
- [Mr. P.] And this is what the bike
and the Prius look like when they
are moving with the same amount of kinetic energy.
Jimmy: Two Dollars!
Thank you very much for learning with me today.
I enjoyed learning with you.