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Momentum and Impulse
- the Physics of Collisions
Sports teams are often said to have momentum. As they win more
consecutive games, their morale increases, their excitement increases,
and they become harder to defeat.
Momentum is a driving force when it comes to sports. Just ask any
odds maker, “Who should win the game” and they will almost always
mention which team has more momentum behind them.
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 that is on the move has the 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 that 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 lower case
"p". Thus, the above equation can be rewritten as
p=m•v
where m is the mass and v is the velocity. The equation illustrates
that momentum is directly proportional to an object's mass and
Momentum and Impulse
- the Physics of Collisions
So, objects in motion are said to have momentum. This momentum is a vector. It
has a size and a direction. The size of the momentum is equal to the mass of the
object multiplied by the size of the object's velocity. The direction of the
momentum is the same as the direction of the object's velocity.
Momentum is a conserved quantity in physics. This means that if you have
several objects in a system, perhaps interacting with each other, but not being
influenced by forces from outside of the system, then the total momentum of the
system does not change over time. However, the separate momenta of each object
within the system may change. One object might change momentum, say losing
some momentum, as another object changes momentum in an opposite manner,
picking up the momentum that was lost by the first.
So, the Symbol for momentum is lower case p
The equation for momentum is: p = m • v
and the unit is kgm/s or kilogram meter per second
From understanding the idea 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. Which would you rather get hit by?
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.
The momentum of any object that is at rest is 0.
Objects at rest do not have momentum
- they do not have any "mass in motion."
Let's solve some basic Momentum problems:
Remember the equation for momentum . . . .
1. Determine the momentum of a ...
a. 60-kg athlete moving eastward at 9 m/s.
b. 1000-kg car moving northward at 20 m/s.
c. 40-kg student moving southward at 2 m/s.
2. A car possesses 20,000 kgm/s of momentum. What would be the
car's new momentum if ...
a. its velocity was doubled.
b. its velocity was tripled.
c. its mass was doubled (by adding more passengers and a greater
load)
d. both its velocity was doubled and its mass was doubled.
Impulse is another Physics term.
It is the amount that momentum changes.
Impulse = Change in momentum
The symbol for impulse is: I
In equation form, ,
I=Δp
OR:
I=Δm•v
OR:
I=m•Δv
If we combine this equation with Newton's Second Law of Motion
(F=ma),
we can develop this equation: F • t = m • Δ v.
Therefore, we can see that Impulse is also the force on an object
multiplied by the time the force is exerted on the object.
Impulse is the reason behind innovative designs in practical life.
When we look at Impulse = Force * time, and this is also the change
an object experiences, we can see that if we extend the time over
which a force is applied, we can change how much momentum we feel.
Take some time now and talk with your neighbor. Try to develop ideas
of when we extend the time over which we apply a force or a force
is applied on us. Write down your ideas and eventually share them
with the class.
Here are some examples of Impulse:
When a baseball player catches a pass, they allow their mitt to move backwards as the
ball enters it.
As you exit a highway, the guardrail will often have water barrels to help “soften” an
accident.
As a human, if you jump and land, your legs will bend and extend the time over which
your knees feel the impact of landing
1.
Here’s a generic Momentum / Impulse problem . . .
2.
Problem: A 100kg object travelling at 25m/s comes to a sudden stop. In 0.5second
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a. What was the object’s initial momentum?
b. What was the object’s final momentum?
c. What was the object’s impulse?
d. How much force did the object feel in coming to a stop?
e. If the stop was extended over 3 seconds, what was the object’s final momentum?
f. What was the object’s impulse
g. How much force did the object feel in coming to a stop?
Here’s another problem to try:
By putting water barrels on the highway, a car traveling at 20m/s comes to a
stop in 2.3 seconds. The car’s mass is 1100kg.
a. How much force is placed on the passengers as it collides with the barrels?
b.
If the water barrels were not there, the car would have come to a stop in
0.08 seconds. How much force would the passengers have felt then?
A 50kg jumper lands in a trampoline after jumping off a building. They are
traveling at 40m/s as their final velocity. It took 2 seconds for the jumper
to come to a stop in a trampoline.
a. What is their momentum as they were about to land?
b. How much force did the jumper experience as they came to a stop?
c. How quickly did they decelerate as they stopped?