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1D Collisions

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```									1D Collisions

Unit A Momentum
Objectives
• You will be able to state and apply the Law of
Conservation of Momentum to linear
collisions.
• You will be able to define isolated system, and
be able to determine if a system is or is not
isolated.
Collisions and systems
• A collision is an interaction between two
objects where a force acts on each object for a
period of time.
• A group of two or more objects that interact is
known as a system.
• A system where the system’s mass is constant,
and no external net force acts on the system is
an isolated system.
Momentum of a system…
• … is defined as the sum of the momenta of all
objects in the system.

psys  p A  pB  pC  . . .
The belief in the fact that momentum is conserved in all collisions
has led to the Law of Conservation of Momentum.

                          
total p before collision  total p after collision
                           
1)    mAv A  mBvB  mAv A        mBvB  

Use when objects do not stick together.
       
2)    mAv A  mBvB  mA  mB  v

Use when objects stick together.
3)   mAv A  mBvB
Use for explosions (momentum total is zero before).
Note: These formulas are not on your formula sheets and you
can use the first formula exclusively if you like.
*
Example:
• Fred sits in a stationary, frictionless wheelchair
and throws a 3.0 kg ball outward at 8.0 m/s. If
the mass of Fred and his chair is 75 kg, what
will be the velocity of Fred and the chair
immediately after the ball is thrown?
Solution
• Before:                           • After

mB  3.0kg                         mB  3.0kg
vB  zero                           vB f  8.0m / s
mF  75kg                          mF  75kg
vF  zero                           vFf  ??
psys  zero
Because both velocities are zero.
Solution
psysi  psys f
mB vB f
psys f  0            vF f 
mF
0  pF f  pB f              3.0kg  8.0m / s
vF f 
 pF f  pB f                    75m / s
mF vFf  mBvB f            0.32m / s [ R ]
Example
• A 50 g bullet is fired into a 650 g block of
wood, which sits on a frictionless surface.
After impact the bullet and block move right
at 30 m/s. Find the bullet’s velocity just before
impact.
Solution
• Before:           • After
mB  0.050kg     mBW  mB  mW  0.700kg
vBi  ?          vBW f  30m / s
mW  0.650kg     Because wood and
vWi  zero       bullet move as a single
object.
 pWi  zero
Solution
mBW vBW f
psysi  psys f         vBi 
mB
pBi  pWi  pBW f
0.700kg  30m / s
mvBi  0  mBW vBW f   vBi 
0.050kg
 420m / s [ R ]
 0.42km / s [ R ]
Using “Conservation of Momentum”
Colliding Objects Stick Together

Example : A 1.50 g pellet is fired into a 12.3 g wood block. The
block and imbedded pellet fly off at 2.78 m/s E. What
was the pellet’s velocity before impact?
       
mAv A  mBvB  mA  mB  v

0.00150 kg  v A 


0  0.00150 kg  0.0123 kg  2.78 m
s

0.00150 kg  v A 

0  0.038364 kg  m
s

v p  25.6 m E
s

“+”

*
Example 2: A 980 kg Toyota going at 52.8 km/h N collides with and
becomes entangled with a 738 kg Honda going
79.3 km/h S. What is the velocity of the wreckage
immediately after impact?

Note: It does not matter what units of mass or velocity are used -
just be consistent!
       
mAv A  mBvB  mA  mB  v

980 kg     52.8 km 738 kg  79.3 km  980 kg  738 kg v'
h                     h
 51744   58523    1718 v'


v '  3.95 km S
h

*
Examples of “Explosion” Conservation of Momentum Problems

Example : When a 960 g plate is dropped, the first 370 g piece
flies off at 2.63 m/s S. What is the velocity of the
second piece?
      
mv  mv

370 g  2.63 m   590 g  v
s

v  1.65 m N
s

Note: In order for the total final momentum to be “0”, if one
piece flies north, the other must fly south.

*
Example 2: What is the ratio of the velocities of the 3.46 g piece
of an exploded firecracker to the other 5.96 g piece?
    
mv  mv
              
3.46 g  v1  5.96 g  v2

v1 5.96
 
v2 3.46

v1  1.72 x

Note: The smaller piece has a velocity 1.72 times the velocity of
the larger piece!

*

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