# PHYS 2108 Lecture Notes - Lecture 6: Momentum, Headon, Lab Partners

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16 Jun 2018
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6-1
LAB 6:
Conservation of Linear Momentum
Ituitiel, hih of the folloig has oe otio, a osuito o a sei-truck travelling at the same
velocity? Which is more difficult to slow down? Which would win in a collision and which is more
destructive? I askig hih ojet otais oe otio, e see to ko the ase ee though
both are travelling with the same velocity, and this means the velocity alone appears not to be enough
to ase the uestio. Whatee this ualit of otio is, it appears also to depend upon the
ojet’s mass.
You may be tempted to say that the kinetic energy of the objects can see as a gauge of the ojet’s
otaied otio, ut consider an exploding ball. Before the explosion, there is no motion. After the
explosion, fragments may fly off in many directions. A sste’s ete of ass a ol e oed he
acted upon by an outside force, and because the eplosio is osideed a iteal foe, the
fagets’ combined center of mass is unmoved. Using kinetic energy (a scalar quantity) is
iappopiate fo desiig the otio a ojet possesses eause thee’s o a to add up
contributions from the fragments in a way that gives us zero for the combined center of mass. We need
something else that is a vector.
The quality of otio we have described is called momentum, specifically linear momentum. It is
given the symbol
, it is a vector quantity, and it is a conserved quantity in physics. If we allow to
epeset a ojet’s ass ad
to epeset its eloit, the the ojet’s oetu is
Eqn. 6-1:
Linear Momentum
The momentum vector’s direction is the same as the velocity vector’s. The oetu’s agitude is
the product of (mass · velocity), which gives us the unit of momentum, kg · m/s. Unlike Newtons (kg ·
m/s2) for force or Joules (N · m or kg · m2/s2) for energy, the unit for momentum has no special name.
In the case of the mosquito and semi-truck mentioned above, if we were to slow them both to a halt in
the same amount of time, the semi-truck would require much greater force due to its greater
momentum. Similarly, it would have a more dominant effect than the mosquito in a head-on collision.
The faster-moving or more-massive object is not always the dominant one! A speeding low-mass car
that did’t see the ed light ill do uh oe daage tha a high-mass semi-truck slowly inching
forward at an intersection. A light high-velocity spitwad will do much less damage than the heavy
slowly-lumbering bully who shot it. One must always consider the product of mass and velocity over
either one of them alone.
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6-2
The momentum of an object a ol e haged  a eteal foe. This is i fat Neto’s faous
Second Law of Motion; more specifically, the net rate of change of momentum is proportional to the
net force applied.

This defiitio of Neto’s “eod Law is more general than the version you may have first learned
because it allows for situations where the mass might not be constant while the velocity changes (e.g.,
rocket fuel consumed in flight, exotic circumstances involving Special Relativity). In cases where the
mass is constant, this equation takes a more familiar form.

  
Collisions
Momentum is a conserved quantity in the absence of an external force. That means in a collision
between two (or more objects), the total momentum before the interaction is equal to the total
momentum after the interactionthe Law of Conservation of Momentum.




Eqn. 6-2:
Momentum Conservation
The motion of two objects involved in a collision can be predicted and examined by considering the
conservation of momentum. There are two varieties of collisions.
Elastic collisions: Momentum and Kinetic Energy are conserved during the collision.
 


Eqn. 6-3:
Conservation of KE
In perfectly elastic collisions, the objects perfectly transfer kinetic energy with none of it
converted into other forms such as heat, sound and physical deformation. A nearly perfectly
elastic collision is similar to two billiard balls wherein one stops completely after colliding with a
stationary other while the other leaves the collision with the same speed as the first.
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6-3
Inelastic collisions: Momentum only is conserved. Some Kinetic Energy is lost to other forms.
   
Because the kinetic energy is not conserved before and after the collision, using it to analyze the
collision is not usually helpful. Remember that this does not violate the law of conservation of
energy to say that KE is not conserved. The total amount of energy is the same; it’s just ee
changed from KE to thermal heat, deformation of the objects, sound, or various other forms.
In a perfectly inelastic collision, there is a certain theoretial aiu of osualekieti
energy that must be lot. This osuale KE is taken mostly by the sticking together of
objects involved, a sure sign of a perfectly inelastic collision.
During any collision the objects are deformed slightly in order to generate a force on one
aothe. I a elasti ollisio the to shapes spig ak to thei oigial shape. I a
inelastic collision they do not. Two billiard balls collide almost perfectly elastically; two balls of
clay do not.
Most real-life collisions are not perfectly elastic or inelastic. “oe eeg is alas lost fo a elasti
collision, and some of the consumable kinetic energy always escapes consumption in an inelastic
collision.
Explosions
A special momentum-oseig eese ollisio situatio ioles a ojet breaking up into
fragments. For an object at rest exploding into two pieces, each piece must have equal and opposite
momenta in order to sum to zero. The same applies to an object already in motion. Any extra
oetu gaied  the foad piee ust e deduted fo the rearward piee suh that the
net momentum for the center of mass remains unchanged.
Ee though the fagets’ oeta add to zeo for an exploding object initially at rest, the fact that
they have velocities mean they have kinetic energies. Those energies must have originated from
somewhere. A stored eplosio potetial eeg is converted to kinetic energy and released to the
fragments. This potential energy can come from many sources. It can be chemical, nuclear, electrical or
as simple as the stored energy in a compressed spring.
   
A real-world explosion will not perfectly convert the stored explosion energy into KE with 100%
efficiency. Some will be lost to other forms. Consider an exploding festival ball at a fireworks show. The
eplosio does’t ol satte the fagetsit also releases heat, a concussive boom and glowing
light.
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