Transcript 9.2 Conservation of Momentum

9.2 Conservation of Momentum
A collision is an interaction between two objects which
have made contact with each other
In a collision, there is
a force on both
objects which causes
an acceleration of
both objects.
9.2 Conservation of Momentum
The rightward moving seven-ball experiences a leftward
force which causes it to slow down; the eight-ball
experiences a rightward force which causes it to speed
up
9.2 Conservation of Momentum
under certain circumstances momentum is a conserved
quantity – a quantity that remains unchanged as a
system evolves.
• System – a set of objects
that interact with each other
• Closed system – a system that
does not gain or lose mass
• Two types of forces can act on
a system of objects
• Internal – forces the objects
in the system exert on each
other
• External – forces exerted on
the objects from a source
external to the system
9.2 Conservation of Momentum
isolated system - the net external force acting on the
system is zero (no system on Earth can be completely
isolated)
• The momentum of each ball may
change as a result of the collision
(each departing with a velocity
different than what it started with)
• The sum of their momenta is found
to be the same before as after the
collision
Sum of momenta before:
mAvAi + mBvBi
Sum of momenta after:
=
mAvAf + mBvBf
9.2 Conservation of Momentum
Law of Conservation of Momentum:
The total linear momentum of a closed, isolated
system remains constant (is conserved).
m1v1i + m2v2i = m1v1f + m2v2f
momentum before
=
momentum after
9.2 Conservation of Momentum
Frictionless Pool Table (Two-ball system)
There is no net external force during the collision.
The total momentum of this two-ball system IS conserved.
9.2 Conservation of Momentum
Frictionless Pool Table (Two-ball system)
The instant before the balls collide, a hole opens in the table beneath
them.
During the collision, an external force causes the balls to accelerate
downward causing a change in the total momentum.
Total momentum of this two-ball system is NOT conserved.
9.2 Conservation of Momentum
Frictionless Pool Table (One-ball system)
The force applied by ball 2 causes a net external force.
The total momentum of the system is NOT conserved.
9.2 Conservation of Momentum
Starting from rest, two
skaters push off against
each other on smooth level
ice, where friction is
negligible. As figure (a)
shows, one is a woman
(mw = 54 kg), and one is a
man (mm = 88 kg). Part (b)
of the drawing shows that
the woman moves away
with a velocity of vf1 = +2.5
m/s. Find the recoil
velocity vf2 of the man.
9.2 Conservation of Momentum
A rocket, containing fuel at rest in some reference frame.
In the same reference frame, the rocket fires and gases
are expelled at high speed out the rear. The total vector
momentum remains zero.
9.2 Conservation of Momentum
A gun recoils when it is fired. The recoil is the result of actionreaction force pairs. As the gases from the gunpowder explosion
expand, the gun is pushed backward and the bullet is pushed
forward. The acceleration of the recoiling gun is ...
a) greater than the acceleration of the bullet
b) smaller than the acceleration of the bullet
c) the same size as the acceleration of the bullet
9.2 Conservation of Momentum
Calculate the recoil velocity of a 5.0 kg rifle that
shoots a 0.050 kg bullet at a speed of 120 m/s.
9.2 Conservation of Momentum
Movies often show
someone firing a gun
loaded with blanks. In a
blank cartridge the lead
bullet is removed, and the
end of the shell casing is
crimped shut to prevent
the gunpowder from
spilling out. When a gun
fires a blank, is the recoil
greater than, the same as,
or less than when the gun
fires a standard bullet?
9.2 Conservation of Momentum
Momentum is conserved in two-dimensional collisions
as well
x-component momentum conserved
y-component momentum conserved
9.2 Conservation of Momentum
A 1325 kg car, C, moving
north at 27.0 m/s,
collides with a 2165 kg
car, D, moving east at
11.0 m/s. The two cars
are stuck together. In
what direction and with
what speed do they
move after the collision?
9.2 Conservation of Momentum
A 65.0 kg ice skater moving forward with a velocity of 2.50 m/s throws
a 0.150 kg snowball forward with a velocity of 32.0 m/s.
What is the velocity of the skater after throwing the snowball.
Disregard friction.
A second skater initially at rest with a mass of 60.0 kg catches the
snowball. What is the velocity of the second skater?
9.2 Chapter 9 Vocabulary
impulse
momentum
impulse-momentum theorem
closed system
isolated system
internal forces
external forces
law of conservation of momentum