momentum & collisions - edl · conservation of linear momentum the net force acting on an...
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Chapter 9 – Momentum & Collisions
Impulse
Elastic & Inelastic Collisions
HW Assignment Due on 12/16/12
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Linear Momentum
Momentum is a vector; its direction is the same as the
direction of the velocity.
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Linear Momentum
Change in momentum:
(a) mv
(b) 2mv
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Forces and Motion - Questions
• A constant force acts on an object.
• How does the speed of the object change with
time?
• Now have a force opposing the first force. How
does the time needed to change the direction of
motion relate to the magnitude of a force
opposing that motion?
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Momentum and Newton’s Second Law
Newton’s second law, as we wrote it before:
is only valid for objects that have constant mass. Here is a
more general form, also useful when the mass is changing:
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Impulse
Shows effect of time interval that a force acts over. Impulse is a
vector, in the same direction as the average force.
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Impulse
We can rewrite
as
So we see that
The impulse is equal to the change in momentum.
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Impulse
Therefore, the same change in
momentum may be produced
by a large force acting for a
short time, or by a smaller
force acting for a longer time.
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Example 9-2 : Jumping for Joy
• Pg. 261
• 72 kg person jumps
• Impulse?
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Conservation of Linear Momentum
The net force acting on an object is the rate of change of its
momentum:
If the net force is zero, the momentum does not change:
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Conservation of Linear Momentum
Internal Versus External Forces:
Internal forces act between objects within the system.
As with all forces, they occur in action-reaction pairs. As all pairs act
between objects in the system, the internal forces always sum to zero:
Therefore, the net force acting on a system is the sum of the external forces acting on it.
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Conservation of Linear Momentum
Furthermore, internal forces cannot change the momentum of a
system.
However, the momenta of components of the system may change.
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Conservation of Linear Momentum
An example ( EXAMPLE 9-3 ) of internal forces moving components of a system:
• Pg. 264
• Mass 1 = 130 kg
• Mass 2 = 250 kg
• Momentum after 1.2 sec
of pushing
• Find a, v, then p
• Other ways to answer?
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Different Methods
• Honors-side � use IMPULSE concept
– Answer?
• AP-side � use acceleration, velocity
– Answer?
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Inelastic Collisions
Collision: two objects striking one another
Time of collision is short enough that external forces may
be ignored
Inelastic collision: momentum is conserved but kinetic
energy is not
Completely inelastic collision: objects stick together
afterwards
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Inelastic Collisions
Solving for the final momentum in terms of the initial momenta
and masses:
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Inelastic Collisions
Ballistic pendulum: the height h can be found using conservation
of mechanical energy after the object is embedded in the block.
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Elastic Collisions
In elastic collisions, both kinetic energy and momentum are
conserved.
One-dimensional elastic collision:
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Elastic Collisions
We have two equations (conservation of momentum and
conservation of kinetic energy) and two unknowns (the final
speeds). Solving for the final speeds:
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Elastic Collisions
Two-dimensional collisions can only be solved if some of the final
information is known, such as the final velocity of one object:
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3rd Six-Weeks Test• Tuesday, December 11
• Covers Chapters 5-9
• Study Quizzes!!
• Simple momentum/impulse question but with conceptual questions on collisions
– Definitions
– Setting a problem up ( given enough info? ) / True-False