MOMENTUM!

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MOMENTUM!
Momentum Impulse
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Momentum Defined

p momentum vector m mass v velocity vector
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Momentum Facts

• p m v
• -
• Velocity and momentum vectors point in the same
  direction.
• SI unit for momentum - (no special name).
• Momentum is a conserved quantity (this will be
  proven later).
• -
• Momentum is directly proportional to both mass
  and speed.
• Something big and slow could have the same
  momentum as something small and fast.

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Momentum Examples
3 m /s
30 kg m /s
10 kg
10 kg
Note The momentum vector does not have to be
drawn 10 times longer than the velocity vector,
since only vectors of the same quantity can be
compared in this way.
9 km /s
26º
p 45 kg m /s at 26º N of E
5 g
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Equivalent Momenta
Car m -- kg v -- m /s p 1.44
105 kg m /s
Bus m -- kg v -- m /s p 1.44
105 kg m /s
Train m 3.6 104 kg v 4 m /s
p 1.44 105 kg m /s
continued on next slide
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Equivalent Momenta (cont.)
The train, bus, and car all have different masses
and speeds, but their momenta are the same in
magnitude. The massive train has a slow speed
the low-mass car has a great speed and the bus
has moderate mass and speed. Note We can only
say that the magnitudes of their momenta are
equal since theyre arent moving in the same
direction. --
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Impulse Defined
Impulse is defined as the product force acting on
an object and the time during which the force
acts. The symbol for impulse is J. So, by
definition Example A 50 N force is applied
to a 100 kg boulder for 3 s. The impulse of this
force is J (50 N) (3 s) 150 N s.
Note that we didnt need to know the mass of the
object in the above example.
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Impulse Units
J F t shows why the SI unit for impulse is the
Newton second. There is no special name for
this unit, but it is equivalent to a kg m /s.
proof 1 N s 1 (kg m /s2) (s) 1
kg m /s

Fnet m a shows this is equivalent to a newton.
--
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Impulse - Momentum Theorem
The impulse due to all forces acting on an object
(the net force) is equal to the change in
momentum of the object
net t ?
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Stopping Time
F t F t
Imagine a car hitting a wall and coming to rest.
The force on the car due to the wall is large
(big F ), but that force only acts for a small
amount of time (little t ). Now imagine the
same car moving at the same speed but this time
hitting a giant haystack and coming to rest. The
force on the car is much smaller now (little F
), but it acts for a much longer time (big t ).
In each case the impulse involved is the same
since the change in momentum of the car is the
same. Any net force, no matter how small, can
bring an object to rest if it has enough time. A
pole vaulter can fall from a great height without
getting hurt because the mat applies a smaller
force over a longer period of time than the
ground alone would.