#### Transcript What do you know about momentum?

```What do you know about momentum?
Which has more momentum?
A hummingbird zipping down the street (v = 1 m/s)?
A bus stopped at a stop sign?
A bus barreling down the road (v = 10 m/s)?
A hummingbird hovering at a feeder?
What does
momentum
depend on?
Definition
Linear momentum (p) is defined as the product of an
object’s mass and its velocity.
p=mv
Momentum is a vector quantity and the direction of
the momentum vector is the same as the velocity
vector.
The units for momentum are
Notice that in all
the examples the
typically kg-m/s
mass is multiplied
Other acceptable units:
kg*mi/hr, kg*km/hr, and g*cm/s
by the velocity.
Since Momentum is a Vector Quantity....
….You must include the direction
for the velocity vector in the calculation
Mass = 10 kg
v = 10 m/s
P = 100 kgxm/s
Mass = 10 kg
v = 10 m/s
P = -100 kgxm/s
Use the established sign convention: right & up is positive
while left & down is negative.
Changing Momentum
To change momentum, either mass or velocity
changes, but usually it is caused by a change
in velocity:
Δp = mvf-mvi
Or
Δp =m (vf –vi)...if same mass
m = 10 kg
v = 10 m/s
pi = mvi= 0
pf = mvf = 100 kg·m/s
Δp = 10 kg ( 10 m/s – 0) = 100 kg ·m/s
Changing DIRECTION changes momentum
(since it is a change in velocity).
m = 10 kg
v = 10 m/s
m = 10 kg
v = 10 m/s
pi = mvi = 100 kg·m/s
pf = mvf = 100 kg·m/s
Δp = -100 kg·m/s – 100 kg ·m/s
Δp = -200 kg·m/s
Remember:
Subtracting vectors
negative vector
Rebounding causes a greater
change in momentum than stopping

Bouncing off an object is known as
rebounding.
(J) Impulse = changing
momentum (p)


To change an objects velocity, it is necessary to
apply a force against its motion for a given
period of time.
The more momentum, the greater the force
needed to stop the object or the force will need
to be applied for a greater time period.
Impulse –force applied through time
Formula: J =F  Δt Unit: N s
Force and Momentum
Remember, an unbalanced force causes
acceleration. F = ma
Remember, acceleration is a change in
velocity.
a = v/  t
So:
F = m v /  t
Therefore, a force acting for a given amount
of time will change an object's momentum.
F  t = m v


If the force acts opposite the object's motion, it
slows the object down.
If a force acts in the same direction as the object's
motion, it speeds the object up.
Impulse-Momentum Theorem
Since a force applied through time changes
momentum, Impulse is a change in
momentum, and is therefore a vector quantity.
J=Δp
F * Δt = mvf-mvi
Or
F * Δt =m (vf –vi) ...if same mass
Notice: If I = p, then the units equal each other, and can
be interchanged, ie. Kg-m/s = N s
Applying Theorem
Greatest velocity change?
Greatest acceleration?
Greatest momentum change?
Greatest Impulse?
Case B (-28 m/s – 30 m/s) = - 58
m/s
Case B, acceleration depends on
velocity
Case B, momentum depends on
velocity
Case B, impulse depends on
change in momentum
Why do we use airbags in cars?
Airbags apply less force over a greater time when
there is a change in momentum.
p = F t
A given impulse... say a car going from 60 mph
to 0... can be achieved by:
p =
F t = F t
=BIG FORCE
Crash test
short time
= small force longer time
Using the ImpulseMomentum Theorem:
A 1400-kg car traveling west with a family of crash test
dummies has a velocity of 15 m/s when it collides with a utility
pole and is brought to rest in 0.30 seconds. Find the magnitude
of the net force exerted on the car during the collision.
pi=mvi=1400 kg (15 m/s)
pf=mvf=0
p = F t
1400 kg (0-15 m/s) = F (0.30 s)
F = 7.0 x 104 N (to the east)
Conservation of Momentum
and Collisions
So long as the unbalanced forces exerted
on a system are internal to the system…
meaning they’re exerted by other parts of
the system, the momentum of a system is
conserved (will not change).
Conservation of Momentum
Total initial momentum = total final momentum
pi = p f
m1 v1i + m2 v2i = m1 v1f + m2 v2f
Linear momentum is conserved
when the net force on an isolated
system is zero.
Linear= straight line or
curves but NOT repeat
the motion
Isolated= internal forces
only—NO friction
System= all initial
interacting
objects/particles
Which of the following is an example of
an isolated system?
1. Two cars collide on a gravel roadway
on which frictional forces are large.
2. Hans Full is doing the annual
vacuuming. Hans is pushing the Hoover
vacuum cleaner across the living room
carpet.
* 3. Two air track gliders collide
on a friction-free air track.
COLLISIONS
Perfectly ELASTIC Collisions – 2 objects collide
and bounce off of each other
Total Momentum and
total kinetic energy is
+v when object
conserved (as long as
moves right, -v
when object
system is isolated)
moves left
m1 v1i + m2 v2i = m1 v1f + m2 v2f
Collisions applet
Car Rear Ends Truck
The animation below portrays the elastic collision between a
1000-kg car and a 3000-kg truck.
In this elastic collision, the total kinetic energy in the system is
conserved.
Collisions
Perfectly Inelastic Collisions –
the objects stick together after impact;
Kinetic energy is not conserved since
some of the energy is converted to
sound, heat and objects are deformed.
Total momentum is
still conserved
Inelastic Collisions
You are hovering next to the space and your buddy of
equal mass who is moving 4 m/s (with respect to the
ship) bumps into you. If she holds onto you, then how
fast do the two of you move after the collision?
Since there is twice as
much mass in motion after
the collision, it must be
moving at one-half the
velocity 2m/s.
m1 v1i + m2 v2i = ( m1 + m2)vf
Little Fish in Motion is Caught by Big
Fish
Big Fish in Motion Catches Little Fish
The animation below portrays the collision
between a 1.0-kg cart and a 2-kg dropped brick.
In the collision between the cart and the
dropped brick, total system momentum is
conserved. The momentum lost by the loaded
cart (40 kg*cm/s) is gained by the dropped
brick.
In an EXPLOSION, two objects at the same
velocity (usually at rest and therefore 0 m/s)
separate into two objects at separate
velocities, each with the same momentum.
Pfinal bullet = mbvb
Pfinal man/gun = mmgvmg
Pinitial = Pfinal
( m1 + m2) v0i = m1v1f + m2v2f
m1v1f = m2v2f
Since the initial momentum is zero, so is the final, with
the two vectors canceling each other out.
Explosions
A 100 kg cannon recoils 1 m/s when firing
a 5 kg cannon ball. What is the velocity of
the cannon ball fired?
( m1 + m2) 0vi = m1v1f + m2v2f
m1v1f = m2v2f
100 kg (1 m/s) = (5 kg) v2f
V2f = 50 m/s
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