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MomentumMomentum – Key Ideas– Key Ideas
Review – If a force Fx is applied to abody over a displacement x, theproduct Fx x = (Fcos)x = Work
Review – If a force Fx is applied to abody over a displacement x, theproduct Fx x = (Fcos)x = Work
If the friction force is less than Fx, the work increases the object’s Kinetic Energy
2 2o
1 12 2netW KE m m
NOW ask: What is the effect of applyinga force over a time interval?
Vocabulary: events in which objects apply forces to each other are called
INTERACTIONS
NOW ask: What is the effect of applyinga force over a time interval?
Vocabulary: events in which objects apply forces to each other are called
INTERACTIONS
You predicted the outcomes of someinteractions..
How did you do?
You predicted the outcomes of someinteractions..
How did you do?
A general rule about interaction forces:
A general rule about interaction forces:
Forces come in
12 21F F
A general rule about interaction forces:
Forces come in
12 21F F
This is Newton’s 3rd Law.
The product of mass and velocity
(a quantity) is called
(symbol: )
ve
Definition
t
c or
:
moment p
m
um
p
Newton's second law (one force):
Rearrange:
F ma mt
F t m
Impulse = Change of momentum
Newton's second law (one force):
Rearrange:
F ma mt
F t m
Impulse = Change of momentum
Newton meter (N mUni ) = kg m st:
The impulse is the area under the force vs. time curve. The average force gives the same impulse to the object in the time interval Δt as the real time-varying force.
Conservation of Momentum
The principle of conservation of momentum states when no external forces act on a system consisting of two objects that collide with each other, the total momentum of the system remains constant in time.
Specifically, the total momentum before the collision will equal the total momentum after the collision.
Conservation of Momentum
Mathematically: 1 2 2 1 2 2f fm m m m
Momentum is conserved for the system of objects.The system includes all the objects interacting with each other.Assumes only internal forces are acting during the collision.Can be generalized to any number of objects.
Force as a function of time for the two colliding particles.
In all collisions, total momentum is conserved.
We consider two types of collisions in one dimension:
1. Totally elastic
2. Totally inelastic
Perfectly Inelastic Collisions
When two objects stick together after the collision, they have undergone a perfectly inelastic collision.
Conservation of momentum becomes
1 2 22
1 2 1 2
1 2 12
1 2 2 1 2 2
1 2
1
2 1 2 2
2 1 2
Final vel
1 1 1 1
2 2 2 2
2
2
ocities:
f f
f f
f i
f i
m m m m
m m m
m m m m
m m m
m m
m m m m
m m
1 2 2 1 2i i fm m m m
Elastic Collisions
Both momentum and kinetic energy are conserved.
1 2 22
1 2 1 2
1 2 12
1 2 2 1 2 2
1 2
1
2 1 2 2
2 1 2
Final vel
1 1 1 1
2 2 2 2
2
2
ocities:
f f
f f
f i
f i
m m m m
m m m
m m m m
m m m
m m
m m m m
m m