Transcript Ch 8.3 - 8.5 chap 8.3

Chap 8.3 and 8.4
Conservation of Momentum
•Conservation of Linear Momentum
• Inelastic Collisions
• Elastic Collisions
Conservation of Linear Momentum
Conservation of Momentum
If the net force acting on an object is zero,
its momentum is conserved
Collisions
Collisions are governed by Newton's laws.
Newton’s Third Law tells us that the
force exerted by body A on body B in a
collision is equal and opposite to the force
exerted on body B by body A.
Conservation of Linear Momentum
An example of internal forces moving components of
a system:
Collisions
Collision: two objects striking one another
The collision between
two billiard balls on
a frictionless surface in
isolated system.
Collisions
 During a collision, external forces are
ignored.
 The time frame of the collision is very
short.
 The forces are impulsive forces (high
force, short duration).
Collision Types
Elastic (hard, no deformation)
momentum is conserved, KE is conserved
Inelastic (soft; deformation)
momentum is conserved, KE is NOT conserved
Perfectly Inelastic (stick together)
momentum is conserved, KE is NOT conserved
Inelastic Collisions
A completely inelastic collision:
Inelastic Collisions
Ballistic pendulum: the height h can be found using
conservation of mechanical energy after the object
is embedded in the block.
Elastic Collisions
One-dimensional elastic collision:
Conservation of Momentum
Newton’s 2nd law becomes difficult or impossible to
solve collisions.
Let’s see Elastic head-on collision:
A
B
before collision
Forces during the
collision are an
action/reaction pair.
during collision
According to Newton’s III law,
=-
Elastic Head-on Collision
After collision
Change in momentum of A = - (Change in momentum of B)
m11'  m11  (m22'  m22 )
Conservation law of momentum – total momentum of a system remain constant
m11  m22  m11'  m22'
before
after
Conservation Law of
Momentum
If the resultant external force on a system
is zero, then the vector sum of the
momenta of the objects will remain
constant.
ΔpB = ΔpA
 Chubby, Tubby and Flubby are astronauts on a spaceship. They each
have the same mass and the same strength. Chubby and Tubby
decide to play catch with Flubby, intending to throw her back and
forth between them. Chubby throws Flubby to Tubby and the game
begins. Describe the motion of Chubby, Tubby and Flubby as the
game continues. If we assume that each throw involves the same
amount of push, then how many throws will the game last?
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Head-on Elastic Collisions
The coefficient of elasticity
 is a measure of the "restitution" of a
collision between two objects.
 The coefficient, e is defined as the ratio of
relative speeds after and before an impact
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E is usually positive, between 0-1
e=0, the perfect inelastic collision.
e=1 the perfect elastic collision.
0<e<1, real world inelastic
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Answer: Truck Collision
Comparison of the collision variables for the two
trucks:
A greater change in
velocity implies a greater
change in kinetic energy
and therefore more work
done on the driver.
Ride in the bigger truck! There are good physical reasons!
Perfectly Inelastic Collision #1
An 80 kg roller skating grandma collides
inelastically with a 40 kg kid as shown.
What is their velocity after the collision?
Perfectly Inelastic Collisions #3
A fish moving at 2
m/s swallows a
stationary fish
which is 1/3 its
mass. What is the
velocity of the big
fish and after
dinner?
Perfectly Inelastic Collisions #2
A train of mass
4m moving 5
km/hr couples
with a flatcar of
mass m at rest.
What is the
velocity of the
cars after they
couple?
Explosion
When an object separates suddenly, this
is the reverse of a perfectly inelastic
collision.
Mathematically, it is handled just like an
ordinary inelastic collision.
Momentum is conserved, kinetic energy is
not.
Examples:
Cannons, Guns, Explosions, Radioactive
decay.
Recoil Problem #1
A gun recoils when it is fired. The
recoil is the result of action-reaction
force pairs. As the gases from the
gunpowder explosion expand, the
gun pushes the bullet forwards and
the bullet pushes the gun backwards.