Download Momentum and Collisions

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What is momentum?
Momentum is a property of objects
with mass and velocity.
It is a vector quantity with the same
direction as the velocity of the object.
What is the equation for momentum?
momentum = mass × velocity
p = mv
If mass is measured in kg and velocity in
m s–1, what are the units of momentum?
The units are kg m s–1. (This can also be expressed as N s).
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Momentum as a vector
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Force and momentum
In order to change the momentum of an object, a force must
be applied (from Newton’s first law).
The rate of change of momentum of an object is
proportional to the resultant force acting on the object.
This is an alternative way of stating Newton’s second law
in terms of momentum.
In a tennis match, when a player
exerts a force on the ball, it
changes momentum. This means
the ball can change speed,
direction, shape or size, etc.
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Rate of change of momentum
Stated mathematically, Newton’s second law is:
For constant masses this becomes
Δ(mv)
F=
Δt
m Δv
F=
= ma
Δt
It can therefore be seen that the familiar equation F = m a is a
special case of the more general equation for Newton’s
second law in terms of momentum.
The more general form of the equation is
necessary when mass is not constant, for
example for a space shuttle taking off.
The mass decreases as fuel is burned.
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True or false?
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Using the momentum equations
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Conservation of linear momentum
The principle of conservation of linear momentum states:
The total linear momentum of a system of interacting
bodies is constant, providing no external forces act.
This applies to collisions, where objects move together and
hit one other, and to explosions, where objects fly apart from
one another after initially being at rest.
collision
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explosion
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Collisions
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Explosions
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Calculations: conservation of momentum
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Elastic and inelastic collisions
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Momentum and energy
When one ball is swung on
Newton’s cradle, one ball moves
out at the other end. If two balls
are swung, two balls move out.
Two balls have double the mass, and
double the momentum. In each
collision, momentum is conserved.
Total energy is also conserved in each collision because
energy cannot be created or destroyed.
Therefore, why do the balls eventually come to rest?
Because kinetic energy is not always conserved, but is
converted to other forms, in this case sound and heat. The
collisions are therefore inelastic.
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Equation for kinetic energy
An equation for kinetic energy, Ek, in terms of momentum
can be derived for a non-relativistic particle.
m v2
Ek =
2
p = mv
therefore
p
v=
m
Substituting in for v in the equation for Ek:
p
m m
Ek =
2
2
( )
Ek =
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=
m p2
2 m2
p2
2m
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Fill in the missing words
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What is impulse?
The impulse of a force is defined as:
impulse = F Δt
Impulse is a vector quantity with the same direction as the
force. It is measured in newton seconds (N s).
Newton’s second law in the form F = Δ(mv) / Δt can be
rearranged to give: F Δt = Δ(mv)
The quantity F Δt is the impulse of the force, so it can be
seen that
impulse = change in momentum
Note that N s are the same as kg m s–1 as expected since
impulse = Δ(mv), but N s are usually used for impulse.
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Force–time graphs
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Impulse and collisions
F Δt = Δ(mv)
Look at the equation for impulse. What determines how much
damage is done in a collision, and how can it be reduced?
The size of force controls
how much damage there is.
Momentum is conserved in
a collision, so impulse is
constant.
To reduce the force, the time
over which the collision takes
place should be increased.
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Applications
In a car crash, force and therefore damage is reduced by
increasing the amount of time over which a collision occurs.
Measures such as seat belts
can help with this. The seat belt
stretches slightly to prolong the
passenger’s impact with it.
Crumple zones also
increase the time over
which the collision takes
place, due to the time it
takes them to crumple.
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How much do you know about impulse?
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Impulse and force–time graphs
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Glossary
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What’s the keyword?
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Multiple-choice quiz
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