Linear Momentum and Impulse

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Lecture 18

• Linear Momentum and Impulse

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Momentum and Newtons Second Law
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Impulse
The change in linear momentum for a certain time
interval is called the impulse J (something like
how much of an effect did the force have by
being applied during a given time interval ).
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Short-duration collision, large maximum
force. eg. Hitting a hard ball with a bat
F
Same impulse
Long-duration collision, small maximum force. eg.
Hitting a soft ball with a bat
t
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Units of Momentum and Impulse
SI units
Its the same!
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ACT Egg tossing

• In an egg-tossing contest, two people toss a
  raw egg back and forth. After each successful
  toss, each person takes a step back. Catching the
  egg without breaking it becomes harder and
  harder. Usually the trick is moving your hand
  down with the egg when you receive it. This works
  better because

A. It decreases the change in momentum. B. It
decreases the impulse. C. It decreases the force
on the egg.
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If the flying egg has speed v, the change in
momentum is ?p 0 mv - mv
(independent of how you catch it)
The impulse is just the same! J ?p - mv
By the way Catching the egg is harder and
harder because its speed becomes larger (and the
required change in momentum, too), so exerting a
small force becomes harder as well.
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Sure!
Do you git much work nowadays, Jerry?
LOOK OUT!
Example
Impulse
I know, but it wuz only on your head a second.
Ooooh! Did you see the size of that brick?
Tush tush! Dont make so much noise!
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Jiggs is completely missing the point If the
brick has m 1 kg and has been dropped from 10
m, what is the average force on Jerrys head
during the 10 ms it is in contact with his head?
Right before hitting Jerrys head, the speed of
the brick is
If the brick is completely stopped by his head,
the change in momentum is
Therefore, the average force is
Equivalent to 315 lb. Ouch!!
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EXAMPLE System of three particles

• Consider a system of 3 particles that are
  exerting forces (of whatever nature) on one
  another, and theres also an external force on A
  (done by some external agent)

A
C
B
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Define total linear momentum for the system
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Conservation of momentum
The really important case
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EXAMPLE Tug of war on ice

• Two guys of masses m1 75 kg and m2 90 kg
  pull on both ends of a rope on an ice rink. After
  a couple of seconds, the thin one is moving at
  0.2 m/s. What is the speed of the big one?

Grrr
Grrr
m1
m2
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Two guys of masses m1 75 kg and m290 kg pull
on both ends of a rope on an ice rink. After a
couple of seconds, the thin one is moving at 0.2
m/s. What is the speed of the big one?
No friction No net vertical force
The force produced a momentum tranfer.
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Conservation of momentum in a
2-particle system
The interaction results in an exchange of linear
momentum between two objects.
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This is general for any isolated system (a system
which is not subject to a net external force).
Each interaction within the system represents
momentum exchange between the particles but the
total momentum of the system remains constant.
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Example Rain
Rain falls vertically into a 10-kg open cart
rolling at 2.0 m/s along a straight horizontal
track with negligible friction. The cart fills at
a rate of 0.1 liters per minute. What is the
speed of the cart after 10 minutes?
External horizontal force 0
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Rain falls vertically into a 10-kg open cart
rolling at 2.0 m/s along a straight horizontal
track with negligible friction. The cart fills at
a rate of 0.1 liters per minute. What is the
speed of the cart after 10 minutes?
How much water is inside the cart after 10
minutes?
Linear momentum is conserved.
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Collisions, explosions
These are situations where
Or The momentum transfer due to the internal
forces is much larger than that due to external
forces.
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What happens to the total kinetic energy?
Special case Perfectly inelastic collisions,
when the objects stick together. Example Pin and
putty
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ACT Big block, small block
Consider the following two collisions between two
blocks of masses m and M (gt m). In both cases,
one of the blocks is initially moving with speed
v and the other is at rest. After the collision,
they move together. The final speed of the two
objects is larger when
A. The big block is initially at rest. B. The
small block is initially at rest. C. The speed is
the same in both cases.
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Use conservation of linear momentum
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Or use energy considerations (faster!)
More energy available in this case.
DEMO Sticky gliders