Download momentum is conserved

• Momentum
 Impulse
 Conservation of Momentum
 Collisions
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Momentum
• Momentum is the product of mass times velocity of an
object P = m v
• Momentum is a vector quantity (same direction as v)
Units = kg m/s
NEWTON’S LAWS OF
MOTION
Second LAW:
The force on an object is equal to the product of
that object’s mass times its acceleration. The
acceleration is in the same direction as the force.
F=m.a
a = Dv/Dt
F = m . Dv/Dt
F . Dt = m . Dv
Impulse =F . Dt
Dp = m . Dv
Change in “momentum”
A baseball of mass 0.14 kg is moving at 35 m/s.
a. find the momentum of the baseball
b. find the velocity at which a bowling ball, mass 7.26 kg,
would have the same momentum as the baseball
Given:
mass = 0.14 kg
velocity = 35 m/s
unknown = p
NEWTON’S LAWS OF MOTION
Third LAW:
For every force that one object exerts on a
second object, there is an equal but oppositely
directed force that the second object exerts on
the first object.
(For every action there is an equal but opposite reaction)
F . Dt = m . Dv
If the external force acting on a system of
objects is zero, the total momentum is
conserved.
CONSERVATION OF MOMENTUM
During a collision, there are no external forces, so
momentum is conserved.
This means: total momentum before collision = total
momentum after collision
The Conservation of Momentum
The law of conservation of
momentum states:
The momentum of any closed, isolated system does not
change.
This means that the momentum before a collision is equal
to the momentum after a collision.
p before
Collision
=
p after
Example
Glider “A” of mass 0.355 kg moves along a frictionless air track
with a velocity of 0.095 m/s. It collides with glider “B” of mass
0.710 kg moving in the same direction at a speed of 0.045 m/s.
After the collision, glider “A” continues in the same direction
with a velocity of 0.035 m/s. What is the velocity of glider “B”
after the collision?
Types of Collisions
• Elastic
- no kinetic energy is lost during collisions
(things bounce off each other)
• Partially
Inelastic
- some kinetic energy is lost during
collisions
• Perfectly
Inelastic
- objects stick together
Example Collision:
Total momentum before collision = Total momentum after collision
v = 10 m/s
v = 0 m/s
Before:
V’ = 5 m/s
After:
(m  10 m/s)before = (2m  V’)after
This is an example of an inelastic collision
Test your understanding:
A 1-kg cart and a 2-kg cart roll toward the center of a straight
track from opposite ends of the track, each with a speed of 1 m/s.
They collide and stick. The combined mass moves at a speed of
(A) 0 m/s.
(B) 1/2 m/s.
(C) 1/3 m/s.
(D) 1/6 m/s.
(E) 1.5 m/s.
1 m/s
1 m/s
Before:
1 m/s
1 m/s
V=?
After:
(2 kg  1 m/s - 1 kg  1 m/s)before = (3 kg  V)after
V = 1/3 m/s
Before the collision, the ball has momentum and the
person does not. The collision causes the ball to lose
momentum and the person to gain momentum. After
the collision, the ball and the person travel with the
same velocity ("v") across the ice.
Before Collision After Collision
Person
Medicine ball
Total
0
300
300
60 * v
15 * v
300
60*v + 15*v = 300
75*v = 300
v = 4 km/hr
Truck
Before Collision
3000 * 10 = 30 000
After Collision
3000 * v
Car
Total
0
30 000
1000 * 15 = 15 000
30 000
3000*v + 15 000 = 30 000
3000*v = 15 000
v = 5.0 m/s
Conservation of
Momentum in Two
Dimensions
A 2.0 kg ball, A, is moving at a velocity of 5.0 m/s. It collides with a
stationary ball, B, also of mass 2.0 kg. After the collision, ball A
moves off in a direction 300 to the left of its original direction. Ball B
moves off in a direction 900 to the right of ball A’s final direction.
a. Draw a vector diagram to find the momentum of ball A and
of ball B after the collision
b. Find the velocities of the balls after the collision
a. pA = 8.66 kg m/s pB = 5 kg m/s
b. vA’ = 4.33 m/s
vB’ = 2.5 m/s
a. pA = 8.66 kg m/s pB = 5 kg m/s
b. vA’ = 4.33 m/s
vB’ = 2.5 m/s
Example of Elastic Collisions
Behavior: Number of balls in always equals the number of balls out.
What accounts for the behavior of this system of swinging balls?
How high up will the struck ball go?
h
Behavior of balls is consistent with conservation of momentum
Total momentum before collision: mv = 0+0+0+0+mv
Total momentum after collision: mv = mv+0+0+0+0
Other possibilities also conserve momentum
2 balls in, one ball out
Momemtum before collision: 2mv = 0+0+0+(2m)v
Momentum after collision: 2mv = m(2v)+0+0+0+0
momentum is conserved
Energy Conservation
Elastic collision
KE is conserved
Case: two balls in, one ball out with twice the speed
Energy is not conserved! There is only one case where
BOTH energy and momentum are conserved