Download Conservation of Momentum Notes

Conservation of Momentum
Law of Conservation of
Momentum
• The sum of the momenta before
a collision equal the sum of the
momenta after the collision in an
isolated system (=no external
forces acting… i.e. no friction to
slow down the ice skaters).
Law of Conservation of Momentum:
• The total momentum of an isolated system of bodies remains
constant.
• (Isolated system: meaning that all forces acting on the bodies are
included… and the sum of the external forces applied to the system is
zero. External forces like Ff or Fg.)
• Momentum before = Momentum after
•m1v1 + m2v2 = m1v'1 + m2v'2 (Elastic Collision)
•m1v1 + m2v2 = (m1 + m2)v‘ (Inelastic Collision)
•v = velocity before collision
•v' = velocity after collision
Elastic Collisions!
Elastic Collision
• Elastic Collisions: Two or more objects collide, bounce (don’t stick
together), and kinetic energy is conserved.
• An ideal situation that is often never quite reached… billiard ball
collisions are often used as an example of elastic collisions.
• Kinetic (motion) energy is conserved:
• KE1 + KE2 = KE'1 + KE'2
• ½m1v12 + ½m2v22 = ½m1v'12 + ½m2v'22
•Momentum is conserved:
•m1v1 + m2v2 = m1v'1 + m2v'2
Forces During a Collision
Inelastic Collision
• Inelastic Collision: two or more objects collide and do not bounce off
each other, but stick together. Or, an explosion where one object
starts w/one momentum and then separates into two or more objects
w/separate final momenta.
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Kinetic energy is not conserved.
KEbefore = KEafter + heat + sound + etc.
The kinetic energy “lost” is transformed into other types of energy, but…
Total energy is always conserved!
•Momentum is conserved:
•m1v1 + m2v2 = (m1 + m2)v'
Inelastic Collisions: For now, we’ll consider perfectly
inelastic collisions:
A perfectly inelastic collision results whenever the two
objects move off at a common final velocity.
Elastic vs. Inelastic Collisions
• (a) A hard steel ball would
rebound to its original height
after striking a hard marble
surface if the collision were
elastic.
• (b) A partially deflated
basketball has little bounce on a
soft asphalt surface.
• (c) A deflated basketball has no
bounce at all.
• Show “happy balls”
• A ball of mass 0.250 kg and velocity +5.00 m/s collides head on with
a second ball of mass 0.800 kg that is initially at rest. No external
forces act on the balls. If the balls collide and bounce off one
another, and the second ball moves with a velocity of +2.38 m/s,
determine the velocity of the first ball after the collision, including
direction.
Did you get…?
• vf1 = -2.62 m/s (ball 1 rebounds)
Question: The total momentum of a
system is conserved…
A. always.
B. if no external forces act on the
system.
C. if no internal forces act on the
system.
D. never; momentum is only
approximately conserved.
Answer:
The total momentum of a system is
conserved…
A. always.
B. if no external forces act on
the system.
C. if no internal forces act on the
system.
D. never; momentum is only
approximately conserved.
Question: In an inelastic collision,
A. impulse is conserved.
B. momentum is conserved.
C. force is conserved.
D. Kinetic energy is conserved.
E. elasticity is conserved.
Answer:
In an inelastic collision,
A. impulse is conserved.
B. momentum is conserved.
C. force is conserved.
D. Kinetic energy is conserved.
E. elasticity is conserved.
The Law of Conservation of Momentum
In terms of the initial and final total momenta:
In terms of components:
Example Problem
A curling stone, with a mass of 20.0 kg,
slides across the ice at 1.50 m/s. It
collides head on with a stationary 0.160kg hockey puck. After the collision, the
puck’s speed is 2.50 m/s. What is the
stone’s final velocity?
•Answer: 1.48 m/s
Rocket propulsion is an example of conservation of momentum:
The rocket doesn’t push on the environment. The rocket pushes the exhaust
gas in one direction (backward), and the exhaust gas pushes the rocket in the
opposite direction (forward).
Newton’s third law, the force and time acting on the rocket and the gas (as a
whole) are equal and opposite. The momentum is conserved. The momentum
before is zero and the momentum after is a total of zero. Positive momentum of
the rocket = Negative momentum of the gas.
Example Problem
Jack stands at rest on a skateboard.
The mass of Jack and the skateboard
together is 75 kg. Ryan throws a 3.0
kg ball horizontally to the right at 4.0
m/s to Jack, who catches it. What is
the final speed of Jack and the
skateboard?
•Answer: 0.154 m/s