Physics 1A
Lecture 6B
"The sun rises. In that short phrase, in a single
fact, is enough information to keep biology,
physics, and philosophy busy for the rest of time.”
--Lyall Watson
Momentum
The impulse-momentum theorem basically states
that your momentum will change if you apply a
net force over any time period.
If the force is not constant, then use the average
force applied.
The impulse imparted by a force
during Δt is equal to the area
under the force-time graph.
OR the impulse is equal to the
average force multiplied by the
time interval:
Δp = (Favg)Δt
Momentum
Example
A soccer player kicks a ball (initially at rest)
with a velocity of 20m/s. The mass of the ball
is 0.45kg. The duration of the impact of her
foot with the ball is 0.05s.
a) What is the change in momentum of the
ball?
b) What is the average force applied to the
ball by her foot?
Answer
First, you must define a coordinate system.
Let’s choose the direction of motion of the soccer
ball as the positive x-direction.
Momentum
Answer
Look at the change in momentum:
Since the ball is initially at rest: vi = 0. Such that:
From the Impulse-momentum theorem:
In class question
A 1kg ball is thrown horizontally towards a wall with a
speed of 10m/s. The initial velocity is chosen to be the
positive x-direction for this question. The ball
horizontally rebounds back from the wall with a speed
of 10m/s in the negative x-direction. What is the
change in momentum, Δp, of the ball?
A) 0 kg(m/s).
B) 10 kg(m/s).
+x
ball
v
C) –10 kg(m/s).
D) 20 kg(m/s).
E) –20 kg(m/s).
v ball
wall
In class question
Impulse is:
A) a force that is applied at a random time.
B) a force that is applied very suddenly.
C) the area under the force curve in a force-versustime graph.
D) the time interval that a force lasts.
E) a scalar.
Momentum
Newton’s 2nd Law is actually written in the
following way:
<- as written by Newton
If the mass of the object is constant, then:
<- as written before in class
So we wrote Newton’s 2nd Law correctly before as
long as the mass of the object remains constant.
Momentum
Looking at this new form of Newton’s 2nd Law:
ΣF is the net external force on an object (the sum
of forces due to outside systems).
If the net external force is zero, then:
Momentum
So, in a closed, isolated system (i.e. no net external
forces) momentum is constant.
This is the law of conservation of momentum.
Mechanical energy and momentum do not both have
to be conserved at the same time.
In fact many times one is conserved and the other is
not.
Momentum
Example
Two cars (A and B) have the same mass and
velocity but are headed in opposite directions.
They collide and come to rest.
a) Is mechanical energy conserved?
b) Is momentum conserved?
A
v
v
B
Answer
First, you must define a coordinate system.
Let’s choose the direction of car A as the positive
x-direction.
Answer
Momentum
Let’s also define A and B as a single system. Every
force between them is now internal.
Initially, the mechanical energy of the system is:
Emec = KEA + PEA + KEB + PEB
Emec = KEA + 0 + KEB + 0 = (1/2)mv2 + (1/2)mv2
Emec = mv2
Finally, the mechanical energy of the system is:
Emec = KEA + PEA + KEB + PEB
Emec = 0 + 0 + 0 + 0 = 0
Here, Emec initial ≠ Emec final
Momentum
Answer
Next, calculate momentum.
Initially, the momentum of the system is:
Finally, the momentum of the system is:
Thus, momentum is conserved, since:
Collisions
If I throw a ball up into the air, I can fully
describe the motion until it hits the ground.
There is a collision, it adds a force; how much we
are not sure.
Conservation of linear momentum can help us to
describe the resulting motion.
There are two types of collisions: elastic and
inelastic.
Elastic collisions are collisions in which kinetic
energy is conserved.
Collisions
Inelastic collisions are collisions in which kinetic
energy is not conserved.
For Next Time (FNT)
Start the Homework for Chapter 6.
Finish Reading Chapter 6.