Transcript Review - Worth County Schools

Momentum
• A measure of how hard it is to
stop a moving object.
• Related to both mass and
velocity.
• Possessed by all moving
objects.
Calculating Momentum
• For one particle
p = mv
• For a system of multiple
particles
P = pi = mivi
• Momentum is a vector!
Which has the most
momentum?
Impulse (J)
The product of an external
force and time, which results
in a change in momentum
•J = F t
•J = P
•Units: N s or kg m/s
Impulse (J)
F(N)
3000
2000
area under curve
1000
0
0
1
2
3
4
t (ms)
Law of Conservation of
Momentum
pb = pa
If the resultant external force on
a system is zero, then the vector
sum of the momenta of the
objects will remain constant.
Collisions
• Collisions are governed by Newton's
laws.
• Newton’s Third Law tells us that the
force exerted by body A on body B in a
collision is equal and opposite to the
force exerted on body B by body A.
Collisions
During a collision, external forces are
ignored.
The time frame of the collision is very
short.
The forces are impulsive forces (high
force, short duration).
Collision Types
• Elastic (hard, no deformation)
– P is conserved, K is conserved
• Inelastic (soft; deformation)
– P is conserved, K is NOT conserved
• Perfectly Inelastic (stick together)
– P is conserved, K is NOT conserved
Golf and Momentum
Consider the
elastic collision
between the
club head and
the golf ball in
the sport of golf.
Golf and Momentum
Forces are on
the clubhead
and ball are
equal and
opposite.
Golf and Momentum
The acceleration
of the ball is
greater because
its mass is
smaller.
Pool and Momentum
Consider the
elastic collision
between a
moving ball and a
ball that is at rest
in the sport of
billiards.
Pool and Momentum
The balls
experience forces
which are equal
in magnitude and
opposite in
direction.
Pool and Momentum
Since the balls
have equal
masses, they
experience equal
accelerations.
Explosion
• When an object separates suddenly, this is
the reverse of a perfectly inelastic
collision.
• Mathematically, it is handled just like an
ordinary inelastic collision.
• Momentum is conserved, kinetic energy is
not.
• Examples:
– Cannons, Guns, Explosions, Radioactive
decay.
Perfectly Inelastic Collision #1
An 80 kg roller skating grandma collides
inelastically with a 40 kg kid as shown.
What is their velocity after the collision?
Perfectly Inelastic Collisions #2
A train of mass
4m moving 5
km/hr couples
with a flatcar of
mass m at rest.
What is the
velocity of the
cars after they
couple?
Perfectly Inelastic Collisions #3
A fish moving at 2
m/s swallows a
stationary fish
which is 1/3 its
mass. What is the
velocity of the big
fish and after
dinner?
Recoil Problem #1
A gun recoils when it is fired. The
recoil is the result of action-reaction
force pairs. As the gases from the
gunpowder explosion expand, the
gun pushes the bullet forwards and
the bullet pushes the gun backwards.
Sample Problem
Suppose three equally strong, equally
massive astronauts decide to play a game
as follows: The first astronaut throws the
second astronaut towards the third
astronaut and the game begins. Describe
the motion of the astronauts as the game
proceeds. Assume each toss results from
the same-sized "push." How long will the
game last?
Announcements
4/1/2016
• Tomorrow -- Graded Quiz
• Lunch Bunch Wednesday this week!
• Lunch Bunch HW due Wednesday.
• Exam Thursday on Momentum.
• Energy Exam corrections M,Tue,Thu
• Makeup lab on Friday.
Center of Mass
• Physicist like to deal with particles
because it is relatively easy to deal with
an object that has position and mass,
but no real size.
• But what do you do if you have a real
object with a non-zero size? Or if you
have a collection of particles?
• You turn the object into a particle by
pretending all the mass resides at the
center of mass.
Calculate momentum of the balls before
and after the collision.
2 m/s
3 m/s
2 kg
0 m/s
8 kg
Before
2 kg
50o
8 kg
V?
After
Center of Mass
The point at which all of
the mass of an object or
system may be considered
to be concentrated.
Center of Mass for solid
objects
Pick the
geometric center
of the object
x
x
x
Center of Mass for
collection of points
xcm =  mixi / M
ycm=  miyi / M
zcm=  mizi / M
Center of Mass Problem
(SOS 8.10)
A system consists of the
following masses in the x,y
plane: 4 kg at (0, 5m), 7 kg
at (3m, 8m), and 5 kg at (-3
m, -6m). Find the position of
its center of mass.