Transcript Momentum and collisions

Momentum &
collisions
Principia Mathematica (1687)
1 Every body continues in its state of rest, or of uniform motion in a
right line, unless it is compelled to change that state by forces
impressed upon it.
2 The alteration of motion is ever proportional to the motive force
impressed; and is made in the direction of the right line in which
that force is impressed.
3 To every action there is always opposed an equal reaction; or, the
mutual actions of two bodies upon each other are always equal,
and directed to contrary parts.
Teaching challenges
• Newton’s laws of motion are mostly counter-intuitive.
Newton himself struggled for many years to produce
the consistent account given in Principia.
• Newton’s 3rd law: students have difficulty identifying
force pairs. This is not helped by popular shorthand
phrases for Newton 3 (e.g. ‘every action has an equal
and opposite reaction’) which do not make clear what
the forces are acting on.
Example: a book on a table
What forces are acting?
Let the book fall
– is Newton’s 3rd law broken?
Interaction = a forces pair
The book and the Earth interact via
the force of gravity
the Earth pulls on the book
and
the book pulls on the Earth
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Forces always come in pairs
Newton’s 3rd law
All forces arise from an interaction between 2 objects.
F  F
1 on 2
2 on1
Identify 3rd law pair of forces, which match the descriptors:
• same kind of force
• same magnitude, but opposite direction
• act on two different objects
‘Visualizing Newton’s 3rd Law’ (YouTube clip)
Newton said
“To every action there is always opposed an equal
reaction; or, the mutual actions of two bodies upon
each other are always equal, and directed to contrary
parts.”
Newton’s examples
“Whatever draws or presses another is as much drawn or pressed by
that other. If you press a stone with your finger, the finger is also
pressed by the stone. If a horse draws a stone tied to a rope, the
horse (if I may so say) will be equally drawn back towards the stone:
for the distended rope, by the same endeavour to relax or unbend
itself, will draw the horse as much towards the stone as it does the
stone towards the horse, and will obstruct the progress of the one as
much as it advances that of the other.”
Interaction pairs
In small groups:
Work out what the interaction pair is, in each of these situations:
• a book resting on a table
• a car tyre pushing back on the road
• a foot pushing back on a path
• a deflating balloon pushing back on air
• a springy toy pushing down on the table (as the toy launches itself)
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Getting going
C21activity Get a move on
C21 video Starting to move
C21 activity Getting going
Force – time graphs
It is unusual for the force to
be constant during an
interaction. But in all cases
the area under the graph
represents the impulse of
the force.
Hooke’s law
force of the mass pulling on the spring
= force of the spring pulling on the mass
Not falling through the floor
A sound floor
always exerts
exactly the
right upward
force to
support a
person (or
object).
Why?
Collisions
Elastic collisions - e.g. using Newton’s cradles
A moving mass hits a mass that is initially stationary.
• When the two masses are equal, what happens is …
the first one stops, the second one moves off with the same velocity
• When the moving mass hits a smaller mass …
they both move off going forwards
• When the moving mass hits a larger mass …
the moving mass rebounds and the bigger mass moves forwards
Think extremes – elephants and ping pong balls!
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Newton’s 2nd law
expressed in its most general form
(mv)
F
t
Ft  (mv)
delta) means ‘change in’
mv is ‘momentum’, a vector (unit is kg m s-1)
Ft is the ‘impulse of the force’, a vector (unit is N s)
Impulse = change in momentum
TASK C21 activity 4.16
Momentum is ‘conserved’
Trucks A & B collide. Newton’s 3rd law says
FBA   FAB
The time of interaction (t) is the same for both trucks, so
FBAt  FABt
change in momentum of truck A = - change in momentum of truck B
mA (v A u A )  mB (vB  u B )
In symbols,
mAv A  mAu A  mB vB  mB u B
mAu A  mB u B  mAv A  mB vB
Elastic & inelastic collisions
Momentum is conserved in ALL interactions.
A further test
2
mv
Is kinetic energy (
) also conserved?
2
Class experiments
Arrange the runway so that it is friction-compensated.
Investigate what happens when:
• 1 trolley collides with stationary trolley of equal mass
• 1 trolley collides with 2 stationary trolleys
In small groups (3 or 4). Half the groups study elastic collisions, other half
study inelastic collisions. Everyone collects ticker tapes to analyse.
Calculate the total momentum before and after the collision.
Explosion!
• single trolley, with spring plunger
• two trolleys
Making pop-corn:
What makes the pop-corn jump?
Rocket principle
A rocket pushes back on its exhaust gases. The
exhaust gases push forward on the rocket. Both
forces act for the same time.
Force x time experienced by the rocket and its
exhaust gases is the same, but in opposite
directions. This called the impulse of the force.
Force x time = mass x acceleration x time
= mass x change in velocity
This means that the change of momentum is the
same for rocket and its exhaust gases.
So the total change in momentum here is zero.
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Newton’s 2nd law, again
(mv)
F
t
Constant mass:
mv
F
 ma
t
Constant velocity (e.g. rocket):
vm
F
t
Momentum is conserved
The total momentum of a ‘closed system’ (i.e.
unaffected by any external forces) does not
change, in any interaction.
• applies at all length scales, from sub-atomic particles to galaxies
Quantitative problems
involving momentum
Unifications in physics
Mechanical theory
(Galileo & Newton)
 celestial motions
 terrestrial motions, in 3-D
 heat (kinetic theory)
Entities: particles, inertia, force that lies along a
line between interacting particles
Support, references
talkphysics.org
David Sang (ed., 2011) Teaching secondary physics ASE / Hodder
Practical Physics experiments and guidance notes, Topic Forces &
motion, Collections Newton’s third law and Collisions