Download AP Momentum 9_05

Do Now (9/23/13):

Show that the kinetic energy of a particle
of mass m is related to the magnitude of
the momentum p of that particle by
2
p
KE 
2m
Momentum
Linear Momentum

Momentum depends on the mass of an
object and the speed it is going.
p = mv


Because velocity is a vector then
momentum is, also.
Units of momentum are kg-m/s
Changes in Momentum
The rate of change of momentum of a body is
equal to the net force applied to it.
∑ F = ∆p / ∆t
= (mv – mv0)/∆t
= (m(v-v0))/∆t
∑ means “sum of”
= m ∆v / ∆t
= ma
 The force definition of change in momentum
includes cases in which the mass may change
(e.g., rockets)

Impulse
• Net force on an object is equal to the rate of
change of momentum
F = ∆p / ∆t
• Therefore, we can define:
Impulse = F ∆t = ∆p
• A force acting for a length of time
produces a change in momentum
Impulse-Momentum Problems #1




Tennis ball (0.06 kg) travels at 10 m/s
Hit by racket and goes 36 m/s in opposite
direction
What is change in momentum of ball?
If ball is in contact with racket for 0.02 s,
what is the average force applied?
Impulse-Momentum Problems #1


Dp = m(vf - vi) = (0.06 kg)[36 m/s –(-10 m/s)]
= 2.8 kg-m/s
F = mDv/ Dt where Dv = 46 m/s
= (0.06 kg)(46 m/s)/ (0.02 s) = 140 N
Impulse-Momentum Problems #2

Pellet (0.001 kg) from gun travels at 100 m/s
and embeds 0.02 m in target. What average
force is exerted on the pellet by the target?

Vav = (vf + vi)/2 = (0 m/s + 100 m/s)/2 = 50 m/s
Dd = vDt therefore Dt = Dd/v = 0.02 m/50 m/s = 0.0004 s
F = mDv/Dt = [(0.001 kg)(100 m/s)]/(0.0004 s) = 250 N


Conservation of Momentum


When two objects collide, the momentum before
the collision must be equal to the momentum
after the collision
m1v1 + m2 v2 = m1v1' + m2v2'
The total momentum of any group of objects
remains the same unless outside forces act on
the objects.

The total momentum of an isolated system of bodies
remains constant
Collision Problems


Elastic or inelastic
Elastic:
m1v1 + m2 v2 = m1v1' + m2v2’ where one or
more of the v’s are usually zero

Inelastic
m1v1 + m2 v2 = (m1 + m2) v
Collisions
system momentum
before a collision
= system momentum after collision
Two Kinds of Collisions

Elastic


Objects “bounce” off of each other without
permanent changes
Inelastic


Objects “stick” to one another after collision
May involve changes in shape, but not mass
Elastic Collisions
m
v
v
m
m
m
v
v
m
m
Elastic Collisions Transfer
Momentum with No Loses
Inelastic Collisions
Initial
Final
m
v m/s
m
m
m
P = mv
v/2 m/s
P = (2m)(v/2)
= mv
Momentum is a Vector—It has
Direction!
y
x
“y” value of momentum
must add to zero after
collision. Why?
Total Momentum After a Collision Must
Be Equal to Momentum After the
Collision
Notice that the small ball reverses direction after
the collision. When this happens, the “negative”
momentum of the small ball adds to the “positive”
momentum of the large ball.
Center of Mass



The center of mass is the point in space that would move
in the same path as a particle containing the mass of an
object would if subjected to the same forces.
For calculations, one can assume that all the mass of an
object is concentrated at the center of mass
In general the center of mass and the center of gravity are
the same
Path of CM is Path of a Projectile
Locating the Center of Mass (CM)

In a two particle system, the CM lies on a
line joining the two masses
x1
x
x2
xCM
xCM = m1x1 + m2x2
m1 + m2
Center of Mass in Car Crashes
Can you use the concept of center of mass to explain
why SUVs roll more easily than regular cars?
Center of Mass in Car Crashes
•
•
SUV is tall compared with its
width
At tip angle shown CM falls
outside of vehicle body and it tips
over
•
•
Car is wider compared to
height
At tip angle shown CM falls
inside of vehicle body and it
does NOT tip over
The Old Way of High Jumping—
The Straddle
Why is this easier than
the straddle from a
physics perspective?
The Modern Fosbury Flop
Flop vs Straddle
Center of mass
below bar
Center of mass
above bar
Height of
center of
mass
Height of
center of
mass
Straddle
•
•
•
Flop
Remember that: Potential Energy = mass x acceleration of gravity x height
Less energy is required to raise the center of mass a smaller distance
The flop requires less energy than the straddle
Do Now (9/24/13):

At an intersection, a 1500 kg car
traveling east at 25 m/s collides with a
2500 kg van traveling north at 20 m/s.
Find the velocity of the wreckage
immediately after the collision.
Practice:


Complete the multiple choice questions on
p. 168. Show work/reasoning in addition to
picking a letter
Brainstorm answers to conceptual
questions