Conservation of Momentum
We learned about the
momentum of a baseball that
results from the force of a bat.
What happens to the
momentum of the bat?
The bat, the batter, and the
ground are all part of a system
of interaction, so the bat can’t
be considered a single object.
Two-Particle Collisions
On the other hand, when two balls collide (like in pool), each one exerts an equal
and opposite force on the other (F1 = -F2)
The same is true for the impulse imparted on both
FΔt1 = -FΔt2
The forces and impulses exerted are
equal and opposite, regardless of the
ball’s masses - size doesn’t matter in
terms of impulse
Two-Particle Collisions
In terms of momentum, however, mass is a factor (p=mv)
p1f - p1i = -(p2f - p2i) or
p1f + p2f = p1i + p2i
The sum of the momentums of the balls is the
same before and after the collision, so the
momentum gained by one ball is lost by the other
Momentum is conserved in the system
Two-Particle Collision Practice
Two freight cars, each with a mass of 3.0 x 105 kg collide and stick together. One
was initially moving at 2.2 m/s, and the other was at rest. What is their final
speed?
Momentum In A Closed, Isolated System
In order to conserve momentum, motion must happen in a closed, isolated system
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●
A system in which in which no mass is loss or gained is a closed system
An isolated system is one in which the net external force exerted on a closed
system is zero
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No purely isolated systems exist on Earth…why?
The law of conservation of momentum states that
the momentum of any closed, isolated system does
not change
Recoil
Remember the baseball being hit by the bat…
The bat was an external force acting on the ball, so it was not an isolated system
The pool balls colliding was an isolated system since all of the forces were
between the objects in the system
●
Recoil is a change in momentum of an object due to a collision or the
emission of a particle from the object (think of a gun recoil)
Recoil
To find the velocities of each skateboarder
after they collide, we use the law of
conservation of momentum
pAf + pBf = pAi + pBi
pAf + pBf = 0
(initial velocity is zero)
pAf = -pBf
mAvAf = -mBvBf
vAf = (-mB/mA) vBf
Propulsion In Space
A rocket and the chemicals used in space propulsion
form a closed system
The forces that expel the gases are internal, so the
system is also isolated
Objects in space
accelerate by using the law
of conservation of
momentum and Newton’s
third law of motion
Practice
An astronaut at rest in space fires a thruster pistol that expels a quick burst of 35 g
of hot gas at 875 m/s. The combined mass of the astronaut and pistol is 84 kg.
How fast and in what direction is the astronaut moving after firing the pistol?
Practice
An astronaut at rest in space fires a thruster pistol that expels a quick burst of 35 g
of hot gas at 875 m/s. The combined mass of the astronaut and pistol is 84 kg.
How fast and in what direction is the astronaut moving after firing the pistol?
Known:
Unknown:
mC = 84 kg
vCf = ?
mG = 35 g = 0.035 kg
vCi = vGi = 0.0 m/s
vGf = -875 m/s
vCf = (-mG/mC) vGf
Assignment
Practice Problem #23 (page 249)