Download Notes with Impulse

MOMENTUM AND IMPULSE
•  Momentum is a vector.
•  An object with momentum is MOVING.
•  Impulse is a change is momentum.
•  When two (or more) objects collide, the momentum of the objects
before the collision is the same as the momentum after the collision
I. Definition of LINEAR MOMENTUM


p = mv
Units: kg m/s
•  Momentum, p, is a vector. It is the product of an object’s mass and velocity.
•  An object at rest has a momentum of 0.
•  This helps distinguish momentum from inertia. An object must be in MOTION
to have momentum.
•  An object with a SMALL mass can have a LARGE momentum if it has a LARGE v.
•  An object with a LARGE mass can have a SMALL momentum if it is at rest or
moving slowly.
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II. IMPULSE
A. Definition of IMPUSLE
IMPULSE is a CHANGE in MOMENTUM.
Well, you won’t likely change an object’s momentum by changing its mass.
Momentum changes when an unbalanced force causes a CHANGE IN ACCELRATION.
In other words, a change in velocity is accompanied by a change in momentum.
If the word “impulse” makes you think about time, your intuition is correct.
Impulse has to do with changing momentum with a force applied over a given time.
Here’s the math:


F = ma


Δv
F=m
t


Ft = mΔv
Impulse = force x time
force x time equals a change in
momentum
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B. Examining the IMPULSE equation


Ft = mΔv
Let’s set the right hand side of the equation, change in momentum,
equal to a constant. It doesn’t change.
Now, what happens if we change force and time on the left hand side?
for a given value of momentum change…
A LARGE FORCE is required for a SMALL (short) contact time of the force.
A SMALL FORCE is required for a LARGE (long) contact time of the force.
Basically, the shorter the contact time, the larger the force for a given momentum.
If you run into a brick wall with momentum x, the contact time is short and the force large (ouch!)
If you run into a wall of pillows with momentum x, the contact time is long and force small
(pain is minimized)
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III. CONSERVATION OF MOMENTUM
For a collision occurring between
object 1 and object 2 in an ISOLATED
system, the total momentum of the
two objects before the collision is
equal to the total momentum of the
two objects after the collision. That
is, the momentum lost by object 1 is
equal to the momentum gained by
object 2.
The cue ball, when it strikes
the yellow motionless ball,
transfers its momentum
to the yellow ball. The cue
ball has a final momentum
of 0.
The word ISOLATED means that external forces do not act on the colliding objects
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conservation of momentum, continued
By Newton’s 3rd law, we know that during a collision, the force exerted
by each object is equal in magnitude and opposite in direction

F2


F 1 = −F 2
m1
m2

F1
If m1 > m2 but their
velocities are the same
when they collide,
in which direction will
the balls move?
since the contact time is the same, the impulse is the same (but in opposite directions)


F 1t = −F 2t
m1Δv1 = −m2 Δv2
all the - signs are doing is
indicating DIRECTION
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conservation of momentum, continued
For momentum to be conserved, the sum of the momentum of each colliding body
before and after the collision must equal 0.
(m1v1 + m2 v2 )before + (m1v1 + m2 v2 )after = 0
Newton’s cradle. This toy shows how the momentum of one sphere is
transferred to a sphere on the other end of the row.
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