Conservation of
Momentum
• From Newton’s
Third Law
• Action force =
reaction force
• FA = FR
• (ma)A = (ma)R
ONLY
WHEN NO
EXTERNAL
FORCES ARE
INVOLVED!!!
Inelastic collisions:
objects stick together after the collision
Inelastic collisions:
objects stick together after the collision
Inelastic collisions:
objects stick together after the collision
Inelastic collisions:
objects stick together after the collision
Inelastic collisions:
objects stick together after the collision
Inelastic collisions:
objects stick together after the collision
Car A
Car B
MOMENTUM IS CONSERVED
Before the collision:
After the collision:
Total momentum = mAvA + mBvB
Total momentum = mAvA’ + mBvB’
So . . .
mAvA + mBvB = mAvA’ + mBvB’
Making sense of alphabet soup . . .
m = mass
v = velocity
p = momentum
v
1
Which
object?
y
If there’s a ‘
here, this is
the m, v, or
p after the
interaction
For 2-D
interactions,
this shows the
direction of m,
v, or p
This would be read as “the velocity of [object] 1 in the ydirection before the interaction.”
After collision
Mass of A
Before
collision
mA= 1000 kg
Velocity of A
vA = 0 m/s
vA’ = ?
Mass of B
mB= 900 kg
mB = 900 kg
Velocity of B
vB = 20 m/s
vB’ = 5 m/s
mA = 1000 kg
(1000 kg)(0 m/s)
(1000 kg)(vA’)
+(900 kg)(20 m/s)
+(900 kg)(5 m/s)
(Algebra I goes here)
vA’ = 13.5 m/s
Two identical trains are
traveling toward each
other on the same track.
Train A is traveling 10 m/s
westward, while Train B is
traveling 20 m/s eastward.
If they stick together in a
crumpled mass of torn
flesh and steel, what is the
motion of the mass after
the collision?
vf = 5 m/s, eastward
Inelastic Collisions in Reverse
A 10 kg. meatball
is sitting on a plate.
Suddenly it
explodes, breaking
up into two pieces.
One piece has a
mass of 4.0 kg and
went toward the
right with a
velocity of 21 m/s.
What was the
velocity of the
other piece?
14 m/s, to
the left
A 1784-kg launcher fires a 34-kg pumpkin a horizontal
distance of 1.2 km in 5.8 s. Assuming the launcher was
located on frictionless ice, determine the recoil velocity
of the launcher.
vL = 3.9 m/s
Elastic collisions:
objects are separate after the collision
Elastic Collision example:
Two billiard balls of equal
mass undergo a perfectly
elastic collision. The
speed of the yellow ball
was initially 2.00 m/s,
and the green ball was at
rest. After the collision,
the yellow ball is at rest.
What is the final velocity
of the green ball?
Elastic Collision example:
Two billiard balls of
equal mass undergo a
perfectly elastic
collision. The speed
of the yellow ball was
initially 2.00 m/s, and
the green ball was at
rest. After the
collision, the yellow
ball is at rest. What is
the final velocity of
the green ball?
2.00 m/s
0.00 m/s
C
9
Before collision
?
?
C
9
After collision
2 m/s, in the same direction the
yellow ball was traveling.
Elastic Collision example:
A 120.0-g rubber bullet travels at a
velocity of 150.0 m/s, hits a
stationary 8.500-kg concrete
block resting on a frictionless
surface, and ricochets in the
opposite direction with a velocity
of –100.0 m/s. How fast will the
concrete block be moving?
3.5 m/s
In a ballistics test, a 6.00-g bullet is fired into
a 3.000-kg block of clay. The block of clay
moves at 0.500 m/s after the impact, which
embeds the bullet in the clay. What was the
velocity of the bullet before it struck the clay?
251 m/s
Momentum in Two Dimensions
m1 = 1.0 kg
v1= 30.0 m/s
a=60o
q = 30o
v1y
q
v1x
m2 = 1.0 kg
v2 = 0 m/s
v1y’ a
v1x’
v2y’ b
v2x’
b=45o
Momentum must be conserved in both directions:
vertical and horizontal
Spy = 0 so
m1v1y = m1v1y’ + m2v2y’
0 = m1v1y’ + m2v2y’
0 = m1v1’cos60o + m2v2’cos45o
Solve for v1’
From summing the momenta in both directions, we
now have two equations with two unknowns.
v1’ = 8.0 m/s; v2’ = 27.0 m/s
Collision between main sequence stars
Stable nuclei are spherical or only slightly
deformed, and their protons and neutrons
are uniformly distributed. In contrast,
unstable nuclei adopt many different forms,
including clusters. These boron isotopes
show that the clustering of nucleons or
alpha particles in the nucleus changes
dramatically as the number of neutrons
increases.
physicsweb.org/article/ world/12/12/4
An unstable nucleus with a mass of 17.0 x 10-27kg initially at
rest disintegrates into three particles.
One of the particles, of mass 5.0 x 10-27kg, moves along the
positive y-axis with a speed of 6.0 x 106m/s.
Another particle, of mass 8.4 x 10-27kg, moves along the
positive x-axis with a speed of 4.0 x 106m/s.
Determine the third particle’s speed and direction of motion.
(These speeds are well under the speed of light, so we can
assume mass is conserved.)
1.8 x 107m/s, 223o or –137o
Example 2
A 900-kg car traveling east at 15 m/s collides
with a 750-kg car traveling north at 20 m/s.
The cars stick together. With what velocity
does the wreckage move just after the
collision?
A 730-N student stands in the middle of a frozen pond
having a radius of 5.0 m. He is unable to get to the other
side because of a lack of friction between his shoes and
the ice. To overcome this difficulty, he throws his 2.6-kg
physics textbook horizontally toward the north shore at a
speed of 5.0 m/s. How long does it take him to reach the
south shore?
29 s