Professor Dave here, let's talk about
impulse and momentum.
In chemistry we learned about the
conservation of matter. Here in physics
we learned about the conservation of
energy. These concepts can be extended to
formulate another law, and that is the
law of conservation of momentum. momentum
is a term we may be familiar with, but
once again we must learn the rigorous
definitions of these words, and linear
momentum is defined as mass times
velocity, which will be represented by
the letter p. Momentum is a vector
quantity as it involves a velocity
vector being multiplied by the scalar
value of the object's mass. This means
momentum will be expressed with SI units
of kilograms meters per second. In this
case our everyday use of the word is
fairly accurate, and we might say that as
a ball rolls downhill
it will gather momentum. This is true
because its velocity will increase as
the force of gravity accelerates it
towards the ground. The more momentum the
ball gathers the more difficult it will
be to bring it to a stop, and an object
in motion can therefore have a larger
momentum by virtue of being more massive
like a huge boulder, or also by moving at
high velocity, like a tiny hailstone or
meteorite falling from the sky. If we
consider a car in motion, it too will
have a momentum equal to mass times
velocity, and if you slam on the brakes
to avoid a collision, the car will skid a
certain distance, because force must
be applied over some duration of time to
bring a moving object to rest. The
heavier the car and the faster it was
moving, the greater this factor will be.
A small force acting over a long time will
do it, like if you take your foot off the
gas and let the friction from the road
slowly stop the car, or a large force
acting over a short time could do it
like firmly applying the brakes to the
tires. The force that is applied times the
duration of time that it is applied is
called the impulse, which will be
measured in Newton seconds. The
relationship between impulse and
momentum is summarized in the
impulse-momentum theorem.
It states that the impulse, f delta t, is
equal to the change in momentum, or delta p
which can also be expressed as mv final
minus mv initial. So if you apply
some force to push an object for some
duration of time that object will gain a
proportional amount of momentum. If an
object loses momentum it must be
imparting some force to something else
over some time period. Just as the
work-energy theorem describes
conservation of mechanical energy, the
impulse-momentum theorem describes
conservation of linear momentum. Another
ramification of this theorem is that the
force imparted on a moving object when
it strikes some surface will be very
large if the impact is instantaneous, and
much less if the impact involves some
time duration. If you fall off your roof
onto the ground it will hurt, but if you
fall onto a trampoline it won't be as
bad because the change in momentum
imparted on your body, instead of
happening instantly, will be delivered
over the entire duration of your contact
with the trampoline's surface, as it
stretches from the force of your fall.
This is also why baseball players are
taught to swing through the ball rather
than stopping the swing upon impact.
Because if contact is maintained between
the bat and the ball for as long as
possible, the maximum possible force will
be imparted upon the ball. In the case of
an object striking another object, total
momentum will be conserved through the
collision and the sum of the momenta of
the two objects will be the same before
and after the collision. The easiest
example of this concept involves balls
on a pool table. We will often observe
that one ball has momentum while the
other does not,
and after the collision, the first ball
has stopped and all of its momentum has
been imparted onto the other ball. This
type of scenario illustrates
conservation of momentum. There is much
more to discuss regarding collisions
which we will go over in the next
tutorial, but first let's check
comprehension.
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