Download Momentum and Impulse

Momentum and Impulse
Momentum:
A measure of how difficult it is to stop
a moving object.
Momentum = mass x velocity
p = mv
m
Unit for momentum: kg
s
Can a VW bug have
the same
momentum as an
ocean liner?
Can a bullet have the
same momentum as
an Army tank?
If the boulder and
the boy
have the same
momentum,
will the boulder
crush the
boy?
Hint: Which would
have the
larger speed?
Momentum of a system of particles
P   m i v i  Mv cm
i
Which also yields the formula to calculate
the velocity of the center of mass:
v cm
mv


i
M
i
Calculus Connection!

dv d mv d p

 F  ma  m 
dt
dt
dt
Kinetic Energy in terms of
momentum– MEMORIZE!!
2
mv
(mv )(mv )
K

2
2m
2
p
K
2m
Honestly, this could save you a lot of time on occasions!
How do you change the momentum of an
object?
PUSH on it for a period
of TIME.
Impulse: the product of
the force exerted on
an object and the time
interval during which
it acts.
Impulse = Force x time
J = Ft
Some texts symbolize impulse with “I”, but AP uses “J”
Example: Wall exerts
a force of 100,000 N.
The contact time is
0.2 s.
-----------------------------Impulse = F t
= 20000 N-s
The impulse given to an object is equal to the
change in momentum of the object.
Ft = D mv = mvf – mvo
Change in Momentum = Impulse
D(mv) = Ft
mv = Ft
The same change in momentum may be the
result of a SMALL force exerted for a LONG
time, or a LARGE force exerted for a SHORT
time.
Varying Forces
If the force exerted on an object is NOT a
constant force, finding the impulse/change
in momentum is a little more difficult.
As the saying goes,
“If the forces varies…
You must integrate!”
In most cases dealing with
collisions, the varying
force is shown to be a
function of time.
The impulse is defined as
the integral of the force
over the time interval
during which the force
acts. It equals the total
change in momentum of
the particle.
 F( t )dt  impulse  Dp
F
(
t
)
dt

D
p

For example:
If F(t) = 4t2 + 2,
J = 4/3 t3 + 2t (+ C)
Which will equal the CHANGE in momentum
And, of course, on a Force vs time graph,
The impulse/change in momentum,
Is the “area under the curve”