Download Linear Momentum

S-43
A. What is the relationship between the forces
when the two sumo wrestlers run into each
other?
B. What is the relationship between their
accelerations?
C. Is their a relationship
between their initial
velocities and their
final velocities?
Linear Momentum
AP Physics
Chapter 7
Linear Momentum
7.1 Momentum and Its Relation to Force
7.1 Momentum and Its Relation to Force
Linear momentum – product of an objects
mass and its velocity


p  mv
Unit is a kgm/s
The quantity is only useful when discussing
collisions
7-1
7.1 Momentum and Its Relation to Force
Impulse
F  ma
v
a
t
v
F m
t
7-1
7.1 Momentum and Its Relation to Force
Impulse
v
F m
t
p  mv
p
F
t
7-1
7.1 Momentum and Its Relation to Force
Impulse
p
F
t
Or
Ft  p
7-1
7.1 Momentum and Its Relation to Force
In a collision, to decrease force, we increase
time of the collision
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Consumer Report
7-1
Linear Momentum
7.2 Conservation of Momentum
7.2 Conservation of Momentum
Two kinds of collisions
1. Perfectly elastic – objects bounce apart
2. Perfectly inelastic – objects stick together
7-2
7.2 Conservation of Momentum
In reality collisions are a combination of the
two.
Law of Conservation of Momentum – in a
closed system, momentum is conserved in
a collision
p0  p
7-2
7.2 Conservation of Momentum
In an elastic collision
mAvA0  mB vA0  mAvA  mB vB
Direction of velocity is given by the sign of the
velocity.
7-2
7.2 Conservation of Momentum
In an inelastic collision
mAv A0  mB v A0  (mA  mB )v
7-2
7.2 Conservation of Momentum
In an explosion
The reverse of a
Inelastic collision
(mA  mB )v0  mAv A  mB vB
7-2
S-44
Bart and his friends are out for a drive in their
model T. The car and the passangers have a
total mass of 560 kg. They run into an angry
cow while driving at 6.08 m/s. If the car stops
in 0.44 s
• What is the change in momentum of the
car?
• What is the average
force exerted on the
cow?
S-45
Shortly after this picture was taken Mittens
drove into a wall. The car had a mass of
2500 kg, was traveling at 30.2 m/s, and
came to a stop in 1.9 m.
A. What was the
impulse on the car?
B. What was the
average force on
the car?
Linear Momentum
7.3 Conservation of Momentum in Collisions
7.3 Conservation of Energy and Momentum
Energy (mechanical) is conserved in an
elastic collision
So
mAvA0  mB vB0  mAvA  mB vB
1
2
mv  mv  mv  mv
2
A A0
1
2
2
B B0
1
2
2
A A
1
2
2
B B
7-3
7.3 Conservation of Energy and Momentum
Any collision in which energy is lost, is
considered inelastic.
7-3
Linear Momentum
7.4 Collisions in Two Dimensions
7.4 Collisions in Two Dimensions
inelastic collisions in two dimension
mAv A0 x  mB vB0 x  (mA  mB )vx
mAvA0 y  mB vB0 y  (mA  mB )v y
v v v
As always each dimension is treated
x
y
independently
Then use vector addition to calculate the final
answer
7-4
S-46
In what would later be called a
“really sucky play” Carlos came
running out of the goal at 5.6 m/s
and ran into the attacking Kanu.
The 65 kg Kanu was running
toward Carlos at 8.4 m/s. Carlos,
who is 84 kg, came to a dead
stop after the collision. What
was Kanu’s velocity after the collision? Did
you notice that Carlos missed the ball?
Linear Momentum
7.5 Center if Mass
7.5 Center of Mass
Even if an object rotates there is one point
that moves in the same that a particle
would move if subject to the same force.
7-5
7.5 Center of Mass
Center of mass – the point that does not
rotate
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Center of gravity – the point at which the force
of gravity can be considered to act
7-5