The sports announcer says "Going into the
all-star break, the Chicago White Sox have the
momentum." The headlines declare "Chicago Bulls
Gaining Momentum." The coach pumps up
his team at half-time, saying "You have the
momentum; the critical need is that you use
that momentum and bury them in this third
quarter."
Momentum is a
commonly used term in sports. A team that has the
momentum is on the move and is going to take some
effort to stop. A team that has a lot of momentum is
really on the move and is going to be hard to
stop. Momentum is a physics term; it refers to the
quantity of motion that an object has. A sports team
which is "on the move" has the momentum. If an object is
in motion ("on the move") then it has momentum.
Momentum
can be defined as "mass in motion." All objects have
mass; so if an object is moving, then it has momentum -
it has its mass in motion. The amount of momentum which
an object has is dependent upon two variables: how much
stuff is moving and how fast the stuff is
moving. Momentum depends upon the variables mass
and velocity.
In terms of an equation, the momentum of an object is
equal to the mass of the object times the velocity of the
object.
Momentum = mass *
velocity
In physics, the symbol for the quantity
momentum is the small case "p"; thus, the above equation
can be rewritten as
p = m *
v
where m = mass and v=velocity. The equation
illustrates that momentum is directly proportional to an
object's mass and directly proportional to the object's
velocity.
The units for momentum would be mass
units times velocity units. The standard metric unit of
momentum is the kg*m/s. While the kg*m/s is the standard
metric unit of momentum, there are a variety of other
units which are acceptable (though not conventional)
units of momentum; examples include kg*mi/hr, kg*km/hr,
and g*cm/s. In each of these examples, a mass unit is
multiplied by a velocity unit to provide a momentum unit.
This is consistent with the equation for momentum.
Momentum is a
vector quantity. As
discussed in an earlier unit, a
vector quantity is a quantity which
is fully described by both magnitude and direction. To
fully describe the momentum of a 5-kg bowling ball moving
westward at 2 m/s, you must include information about
both the magnitude and the direction of the bowling ball.
It is not enough to say that the ball has 10
kg*m/s of momentum; the momentum of the ball is
not fully described until information about its
direction is given. The direction of the momentum vector
is the same as the direction of the velocity of the ball.
In a previous unit, it was said that the
direction of the velocity vector is the same as the
direction which an object is moving. If the bowling ball
is moving westward, then its momentum can be fully
described by saying that it is 10 kg*m/s, westward. As a
vector quantity, the momentum of an object is fully
described by both magnitude and direction.
From the definition of momentum, it
becomes obvious that an object has a large momentum if
either its mass or its velocity is large. Both variables
are of equal importance in determining the momentum of an
object. Consider a Mack truck and a roller skate moving
down the street at the same speed. The considerably
greater mass of the Mack truck gives it a considerably
greater momentum. Yet if the Mack truck were at rest,
then the momentum of the least massive roller skate would
be the greatest; for the momentum of any object which is
at rest is 0. Objects at rest do not have momentum
- they do not have any "mass in
motion." Both variables - mass and velocity - are
important in comparing the momentum of two objects.
The momentum
equation can help us to think about how a change in
one of the two variables might effect the momentum of an
object. Consider a 0.5-kg physics cart loaded with one
0.5-kg brick and moving with a speed of 2.0 m/s. The
total mass of loaded cart is 1.0 kg and its
momentum is 2.0 kg*m/s. If the cart was instead loaded
with three 0.5-kg bricks, then the total mass of the
loaded cart would be 2.0 kg and its momentum would
be 4.0 kg*m/s. A doubling of the mass results in a
doubling of the momentum.
Similarly,
if the 2.0-kg cart had a velocity of 8.0 m/s (instead of
2.0 m/s), then the cart would have a momentum of 16.0
kg*m/s (instead of 4.0 kg*m/s). A quadrupling in
velocity results in a quadrupling of the momentum.
These two examples illustrate how the equation p=m*v
serves as a "guide to thinking" and not merely a
"recipe for algebraic problem-solving."
Check
Your Understanding
Express your understanding of the concept and
mathematics of momentum by answering the following
questions. Depress the mouse on the "pop-up" menu to view
the answers.
1. Determine the momentum of a ...
60-kg halfback moving eastward at 9
m/s.
1000-kg car moving northward at 20 m/s.
40-kg freshman moving southward at 2 m/s.
2. A car possesses 20 000 units of momentum. What
would be the car's new momentum if ...
its velocity were doubled.
its velocity were tripled.
its mass were doubled (by adding more passengers
and a greater load)
both its velocity were doubled and its mass were
doubled.
3. A halfback (m = 60 kg), a tight end (m = 90 kg),
and a lineman (m = 120 kg) are running down the football
field. Consider their ticker
tape patterns below.
Compare the velocities of these three players. How
many times greater is the velocity of the halfback and
the velocity of the tight end than the velocity of the
lineman?
