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COLLISIONSLimitations of the Conservation of
Momentum
External forces - forces caused by agents external to the "system“. The “system” is only mass 1 and mass 2.
Examples1) ‘external’ friction (the felt of a pool
table)2) air resistance3) gravity
COLLISIONS
Internal forces - forces that only act BETWEEN the objects in the system; such as the 'push' given by one skater to the other, the explosive force between the cannon and a cannon ball.
These forces are actually necessary for the exchange of momentum.
COLLISIONS
Significance?
Internal forces occur between the masses; they act on both masses. They provide the impulse that changes the momentum.
External forces occur between the individual mass and its surroundings. So the object loses its momentum to the surroundings and not to the other object.
COLLISIONS
Two Types of Collisions:
1. Elastic (ideal case) 2. Inelastic
No Energy Is Lost Energy Is LostObjects rebound: a) objects pass
through one another b) objects stick
togetherc) objects may
rebound but too much Energy is lost
(see next page)
m1
m1
m2
m2
Nearly all ordinary collisions are inelastic
COLLISIONS1. Objects pass through 2. Objects that stick
“Perfect Inelastic”Friction on block of wood from bullet
Friction on bullet from block of wood
The friction that occurs between BOTH objects is an “internal” force. Internal forces are absolutely needed to exchange momentum, but energy is still lost.
The friction that occurs between BOTH objects is an “internal” force. Internal forces are absolutely needed to exchange momentum, but energy is still lost.
INELASTIC COLLISIONS
COLLISIONS
Inelastic Analysis CASE 1:
The objects STICK TOGETHER
PERFECT inelastic collision
Maximum loss of KE.
If the two objects are stuck together at the end, what can we say about their final velocities?
COLLISIONS
fii
ffii
ffii
vmmvmvm
vmvmvmvm
vmvmvmvm
)( 212211
212211
22112211
Conservation of Momentum
Note that the final velocities are now the same
The above equation is the PERFECT INELASTIC form of the Cons. Of Momen.
We can alter the Conservation of Momentum Equation to account for that:
COLLISIONS
Example:
A 0.053 kg piece of clay is thrown at 21 m/s at a 1.3 kg wood cube sitting motionless on ice (frictionless). It hits the cube and sticks to it and they both slide on the ice together. Find their final velocity.
COLLISIONS
Example:
A 0.053 kg piece of clay is thrown at 21 m/s at a 1.3 kg wood cube sitting motionless on ice (frictionless). It hits the cube and sticks to it and they both slide on the ice together. Find their final velocity.
COLLISIONS
fii vmmvmvm )( 212211
Example:
A 0.053 kg piece of clay is thrown at 21 m/s at a 1.3 kg wood cube sitting motionless on ice (frictionless). It hits the cube and sticks to it and they both slide on the ice together. Find their final velocity.
fv)3.1053.0()0)(3.1()21)(053.0(
COLLISIONS
fii vmmvmvm )( 212211
Example:
A 0.053 kg piece of clay is thrown at 21 m/s at a 1.3 kg wood cube sitting motionless on ice (frictionless). It hits the cube and sticks to it and they both slide on the ice together. Find their final velocity.
fv)3.1053.0()0)(3.1()21)(053.0(
m/s 82.0
353.1113.1
f
f
v
v
COLLISIONS
Inelastic Analysis CASE 2:
The objects DON’T stick together
Use the regular Conservation of Momentum Law.
COLLISIONSExample:
A 0.123 kg arrow is moving at 42 m/s. It passes through a 5.2 kg piece of balsa wood sitting motionless on a frictionless surface and the arrow emerges moving at 33 m/s. How fast is the piece of balsa wood moving?
COLLISIONS
ffffiiii vmvmvmvm 22112211
Example:
A 0.123 kg arrow is moving at 42 m/s. It passes through a 5.2 kg piece of balsa wood sitting motionless on a frictionless surface and the arrow emerges moving at 33 m/s. How fast is the piece of balsa wood moving?
COLLISIONSExample:
A 0.123 kg arrow is moving at 42 m/s. It passes through a 5.2 kg piece of balsa wood sitting motionless on a frictionless surface and the arrow emerges moving at 33 m/s. How fast is the piece of balsa wood moving?
m/s 214.0
2.5113.1
2.5059.4166.5
)2.5()33)(123.0()0)(2.5()42)(123.0(
2
2
2
2
22112211
f
f
f
f
ffffiiii
v
v
v
v
vmvmvmvm
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