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Impulse and Momentum
UCVTS AIT Physics
Impulse and Momentum
•
Momentum
– There are two kinds of momentum, linear and angular. A spinning object has
angular momentum; an object traveling with a velocity has linear momentum.
For now, and throughout chapter 7, we'll deal with linear momentum, and
just refer to it as momentum, without the “linear”.
– Things to know about momentum.
• how momentum is defined, as the product of mass times velocity:
–
momentum :
p
mv
– momentum is a vector, momentum has the same direction as the velocity.
– Linear momentum p of an object is the product of the object’s mass m
and its velocity v (p=mv)….P and v are vector quantities, so linear
momentum is a vector that points in the same direction as the objects
velocity.
– Newton’s 2nd Law was originally written in terms of
F
m
v
t
mv f
mv0
t
ma
– logical extension of this is as the impulse-momentum theorem
described by: automotive airbags reduce the force on your body
during a collision by way of increasing in the impulse-momentum
relationship (unfortunately mass cannot be changed! at least quickly)
UCVTS AIT Physics
Impulse and Momentum
• Impulse
– relationship between momentum and force
• there is a strong connection between force and
momentum. In fact, Newton's second law was first
written in terms of momentum, rather than acceleration.
A force acting for a certain time (this is known as an
impulse) produces a change in momentum.
F
m
(
F) t
J
F t
v
t
mv f
mv f
mv0
mv0
t
J
ma
p
– Again, this is a vector equation, so the change in
momentum is in the same direction as the force.
UCVTS AIT Physics
Impulse and Momentum
• Impulse – Momentum Theorem
– When a net force acts on an object, the impulse
of the net force is equal to the change in
momentum of the object
– Automobile airbags are examples of the impulse
momentum theorem at work in real life, why?
Which variable/s in the impulse-momentum
equation below does an airbag change?
J
F t
mv f
UCVTS AIT Physics
mv0
Momentum
• Increasing Momentum Examples
– Apply the greatest force for as long as possible
• Large Impulse
– Impulse=Force X Time
» Sling shot, bow and arrow, driving a golf ball,
» Other examples??
• Decreasing Momentum Examples
– Decrease force over as long of time as possible
• Low Impulse
– Impulse = Force X Time
» Hitting a concrete wall or a wall of tires?
» Dashboard or airbag?
UCVTS AIT Physics
Momentum-Impulse
• "It's not the fall that hurts you, it's the sudden stop at the end.“
•
Seatbelts and airbags works because they increase the time it takes for our bodies to slow
down in a car accident, thus reducing the maximum force exerted on the body.
–
As far as safety equipment goes, the idea is to maximize time to minimize the force experienced by the body. Air bags and
seatbelts take longer to slow you down then say a windshield or a dashboard, so the injuries tend to be bruises rather than
broken bones.
•
This is the same reason why some of the most lethal accidents are sudden and relatively
mild looking. If a car going 200 mph flips over and rolls three times before finally coming to a
stop, the maximum force on it isn't nearly as large as a car that slams into a wall at 200 mph
and suddenly stops.
•
Skydivers are taught to tumble as they land. This is because tumbling spreads out the force
of impact over time.
•
Water is great at slowing people down slowly. That's why we can dive into a deep pool from
as high as 15 ft without any fear.
•
Much of the martial arts depends on the idea of minimizing the time used to deliver
maximum force.
UCVTS AIT Physics
Impulse and Momentum
•
Conservation of Linear Momentum
– Important point about momentum is that momentum
is conserved
• the total momentum of an isolated system is constant.
Note that "isolated" means that no external force acts
on the system, which is a set of interacting objects.
• If a system does have a net force acting, then the
momentum changes according to the impulse equation.
– Momentum conservation applies to a single object,
but it's a lot more interesting to look at a situation
with at least two interacting objects. If two objects
(a car and a truck, for example) collide, momentum
will always be conserved.
Hard steel
ball
rebounds to
its original
height
Partially
deflated
basketball
has very
little bounce
• Types of collisions: (momentum is conserved in each
case)
–
–
–
elastic - kinetic energy is conserved
inelastic - kinetic energy is not conserved
completely inelastic - kinetic energy is not conserved, and
the colliding objects stick together after the collision.
– The total energy is always conserved, but the kinetic
energy does not have to be; kinetic energy is often
transformed to heat or sound during a collision.
UCVTS AIT Physics
Deflated
basketball
has no
bounce at
all
Momentum
• Conservation of Momentum
– Conservation? What does that mean?
• Momentum= m X v
pf
p0
– M1 X V1 = M2 X V2
• Elastic and Inelastic Collisions (momentum
conservation in both cases)
– Elastic collisions
• Objects collide without being permanently deformed and
without generating heat
– The objects bounce perfectly (totally elastic collision)
– Inelastic collisions
• Objects collide and become distorted and generate heat
during a collision
– The objects collide and become entangled and attached after
the collision (totally inelastic collision)
UCVTS AIT Physics
Impulse and Momentum
•
Conservation of Linear Momentum
– Example 7
M1=0.25kg
V01=5.00m/s
M1=0.80kg
V02=0
M1=0.25kg
Vf1=?
M1=0.80kg
Vf2=?
m1v f 1 m2v f 2
m1v01 m2v02
UCVTS AIT Physics