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
Comparing momentum and
kinetic energy
p = mv
# 1 If the velocity
triples, by what factor
will the momentum
change?
K = ½ mv2
# 2 If the velocity
triples, by what factor
will the kinetic
energy change?
Question # 3
Momentum = m∙v
Can a bullet have the
same momentum as
an Army tank?
Answer:
Y- yes
N- no
Question # 4
If the boulder and the
boy have the same
momentum,
will the boulder
crush the
boy?
(Hint: Which would
have the
larger speed?)
Answer
Y-yes
N- No
Problem Examples
What is the momentum of a 1500 kg race car
moving at 24 m/s ?
pcar = m∙v
p = 1500 kg x 24 m/s
p = 36,000 kg∙m/s
How fast would a 2 kg cat have to be moving to
have the same momentum as the race car?
pcat = m∙v = 36000 kg∙m/s
v = 36000 kg∙m/s ÷ 2 kg
v = 18,000 m/s!!!
Now, your turn…
#5
What is the momentum of a 10,000 kg
locomotive moving at 2 m/s?
#6
How fast would a 500 kg VW bug have to be
moving to have the same momentum as the
locomotive?
Momentum of a system of objects
Momentum is a vector and therefore has both
magnitude and direction.
If two objects are moving in opposite direction,
then one direction must be chosen as negative
and the other as positive before determining the
momentum of the system.
What is the momentum of this two-object system,
taking “right” to be the positive direction?
Question # 7
A 4 kg object moves to the right at 8 m/s.
A 12 kg object approaches it, moving to
the left at 4 m/s. Taking “right” to be the
positive direction, what is the momentum
of the two-object system?
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
Impulse = F∙t
#8
A truck that crashes into a wall experiences
a force of 20,000 N. If the truck comes to
a stop in 3 seconds, how much
impulse was imparted to the truck?
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.
Whether you drop an egg on the floor or on a
pillow, it loses all of its momentum.
The same impulse is applied in either case,
but the stopping time is so much less for the
floor, the force is proportionally greater.
Impulse = Force x time
The impulse given to an object is equal to the
change in momentum of the object.
F∙t = D mv = mvf – mvo
Impulse
Change in momentum
Question # 9
A boy pushed on a 8 kg crate at rest with a
net force of 20 N for 4 seconds. How fast
was the crate moving afterwards?
F∙t = Dmv = mvf – mvo
F∙t = mvf
Question #10
A boy pushed on a 8 kg crate initially moving
at 2 m/s with a net force of 20 N for
4 seconds. How fast was the crate
moving afterwards?
Ft = Dmv = mvf – mvo
Ft + mvo = mvf
Conservation of Momentum
System- a collection of objects that is being
observed.
Closed system- no objects enter or leave the
system
Isolated system- no external forces act on any
object in the system. The objects can exert
forces on one another.
In a closed, isolated system, the total momentum
will remain the same- it will be CONSERVED.
Recoil
Is this a closed, isolated system?
Momentum before = momentum after
Momentum
Before = 0
------------Momentum
After = 0
------------After firing,
the equal but
opposite
momenta
cancel.
=
Recoil is an application of Newton’s Third Law:
For every force there is an equal, but opposite force
Conservation of Momentum in
Collisions
•
•
•
Elastic collision- A collision in which objects
collide and bounce off each other with no
energy loss. (occurs very rarely)
Inelastic collision- A collision in which objects
collide and some of the kinetic energy is
transformed into heat energy. (almost all
collisions)
Completely inelastic collision- the objects
stick together after the collision- will result in
the maximum kinetic energy loss- in fact,
sometimes ALL kinetic energy is lost if the
objects stop completely.
Momentum before = momentum after
m1v1
=
(m1 + m2) v
Momentum
after a
completely
inelastic
collision
Three Examples of conservation of momentum in collisions with equations:
m1v1o = m2v2f
m1v1o + m2v2o
m1v1o - m2v2o = - m1v1f + m2v2f
= m1v1f + m2v2f
Conservation of momentum
Recoil:
m1v1 = m2v2
Completely (totally) Inelastic collisions:
m1vo + m2vo = (m1 + m2)vf
Other collisions
m1vo + m2vo = m1vf + m2vf