Transcript momentum is conserved

Momentum
Crashing Cars
Water on Walls
Hitting Tennis Balls
Watching Skaters Fall
Newton’s Second Law, Redux
We have written ∑F = ma as Newton’s 2nd.
Newton:
 p
 F  t
where p = mv: momentum
Note if ∑F = 0, then Δp = 0.
Since Δp = pf – pi = 0, this means pf = pi and
momentum is conserved.
Conservation of Momentum
In a collision between two objects, we can
say that ∑F = 0 if the only force on object
one is from object two, and likewise the
only force on object two is from object one.
Then, Newton’s third law demands that
these forces add up to zero, and
momentum is conserved.
Simple example: inelastic collision
Car 1 (400 kg) moves to the right at 20 m/s; Car 2
(600 kg) moves to the left at 10 m/s. The cars
collide and stick together. What happens?
Only force on car 1 is from car 2, and vice versa,
so momentum is conserved.
pi = (400 × 20) – (600 × 10) = 2000 kg m/s.
pf = (600 + 400) × Vf = pi = 2000 => Vf = 2.0 m/s
Collision Definitions
Perfectly inelastic: objects collide and
stick together.
Inelastic: objects collide, don’t stick
together, but collision is not elastic.
Elastic: objects collide, and kinetic energy
is conserved [more on this (much) later].
Other momentum stuff: Impulse
Although momentum is probably most often
used in the conservation of momentum
theorem, it is also useful in situations
where ∑F ≠ 0 so that Δp = ∑F × Δt.
We’ll only consider one force, so Δp = F Δt,
or Change in momentum = Impulse
Impulse example
A 20 gram tennis ball is moving to the right
at 30 m/s; it is hit so that it moves to the
left at 25 m/s. The ball is in contact with
the tennis racket for 10 ms. What is the
average force on the ball while in contact
with the racket?
See board for the “real world” situation, and
our solution.
Moving Masses
We use

 p
v

 F  t  m t  m a with constant mass
We could also use
 p  m
 F  t  v t
This is useful for calculating the force on moving
masses of bulk material: see board for example.
Qualitative issue
Δp = F Δt can be used to qualitatively
analyze some situations.
A car is going to crash: big Δp for car, and
more importantly, for driver.
Two choices: Big F, small Δt or . . .
Small F, big Δt. Which would YOU want?
Examples
Bridge abutments
Airbags
metal vs. rubber hammer
Angular Momentum
Just as Linear Momentum is the product of
mass and velocity, angular momentum is
the product of moment of inertia and
angular momentum.
L = Iω
Conservation of Angular
Momentum
Just as Linear Momentum is conserved if
the sum of the external forces is zero,
Angular momentum is conserved if the
sum of the external torques is zero.
Li = Lf gives Iiωi = Ifωf see the board,
and maybe a demo ???