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MOMENTUM
Forces – “Time of Action”
Forces in physics cover a wide range of timescales:
“Steady Forces”
“Impact Forces”
“Periodic Forces”
F
F
F
t
Examples:
t
Examples:
t
Examples:
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Earth-Moon gravity
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Sound waves
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Collisions
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Lift force on a plane
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Elastic forces (springs)
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Explosions
Forces and Time – “The Big Picture”
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What determines the overall effect of forces on a
physical system?
The strength and direction of Fnet
F net
a=
m
–
Newton's Second Law:
–
We can calculate instantaneous acceleration
Also, the amount of time Fnet acts for
–
–
A weak force acting for a short time has little effect
A strong force acting for a long time has large effect
Impulse
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To emphasize the importance of “time of action”,
physicists invented the concept of “impulse”
–
Describes the overall effect of the force
F avg =average force exerted
Impulse = F avg t
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Example: Impact Force
t =time of action
F
Favg
t
Impact Forces and Damage
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Consider two different impact forces:
F
F
Fpeak
Fpeak
t
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These two forces produce the same impulse
–
●
t
But the peak force is different in the two cases!
The peak force determines the damage to objects
–
Strong, quick forces are more damaging than weak, slow ones
Impact Forces – Examples
Water Balloon Toss
Golf club hits ball
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Large force acting for short time
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Amount of force at any time can
be estimated by deformation of
ball
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Balloon breaks if force gets too
large
To stop balloon without breaking
it, must exert weak force for long
time
Impulse and Mass
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For a given impulse:
–
–
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A system with small mass will feel a large effect
A system with large mass will feel a small effect
Example: Swinging a baseball bat
Has a large effect
on a baseball
Has a small effect on a dump truck
Momentum
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An impulse produces a change in velocity ( Δv )
–
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The size of Δv depends on the mass of the system
To emphasize the importance of mass, physicists
invented the concept of “momentum”
Momentum = m v
●
m = mass
v = velocity
An impulse changes the momentum of a system
F t =  m v 
Momentum vs. Impulse in Physical Systems
What Systems “Have”
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Mass ( m )
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Position ( x )
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Velocity ( v )
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Acceleration ( a )
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Momentum ( mv )
x
m
v
a
What Systems “Exchange”
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Force ( F )
●
Impulse ( F t )
F
The “Force-Momentum Chain”
Force
Impulse
Change in Momentum
Time
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Newton's Third Law: The force exerted by the system is
equal in strength to the force exerted on the system
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If a system's momentum is changing in a certain direction:
–
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Another system's momentum changes in the opposite direction
Systems can exchange momentum, but never create it
Conservation of Momentum
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If the external Fnet on a system is zero:
–
–
The momentum of that system will stay constant
Internal forces do not change the system's momentum
The total momentum of the
Earth-Moon system is constant
(The Earth and Moon exchange
momentum)
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If the external Fnet on a system is not zero:
–
–
The system exchanges momentum with another system
One gets more positive, the other gets more negative
Collisions
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Consider a two-object collision
–
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Let the system be made up of both objects
The impact force is an internal force to the system
–
–
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The external force is zero
The total momentum stays constant
Rightward momentum is transferred to second object
Collisions of Unequal Mass
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General rule
–
The larger the mass, the smaller the Δv
The truck has a small
change in speed, but the
car takes off
The truck picks up a
small speed, but the
car has a large change
in velocity
Elastic vs. Inelastic Collisions
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Elastic collisions
–
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The objects bounce off each other with little deformation
Inelastic collisions
–
–
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As a result of the collision, the objects:
Change shape
Stick together
Impulse and “Bounce-Backs”
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Consider a small object colliding with a very large one
–
–
The large object gets a very small Δv (ignore it)
Let's focus on the small object
“Perfectly Inelastic” Collision
“Perfectly Elastic” Collision
The small object sticks to the big one
Small object bounces off big one
The impulse is just enough to stop the
small object
The impulse stops the small object
AND pushes it back ( 2x as much )
Explosions
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System includes an exploding object
–
–
Any forces exerted by the explosion will be internal
The total momentum of the system will be conserved
m1v1
●
m2v2
Total momentum is zero before and after explosion!
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After explosion: left momentum + right momentum = 0
Summary
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When an external force acts for a certain amount of
time, it delivers an impulse to the system ( F t )
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The impulse changes the momentum of the system
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If we choose our system so there is no external force:
–
–
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The total momentum of the system remains constant
This is true even if there are internal forces acting
We can use this “conservation of momentum” to
predict the effects of collisions and explosions