Momentum and Impulse
Momentum (p)
◼ All
moving objects have
momentum.
◼ The momentum of a moving
object can be determined by
multiplying the object’s mass
and velocity.
◼ Momentum = Mass x Velocity
Momentum
◼ Momentum:
motion”
◼ Variable:
“the quantity of
p
momentum = mass x velocity
p = mv
◼ Units:
kg.m/s
Momentum
◼ Like
velocity, acceleration, and
force, momentum is described
by its direction as well as its
quantity (vector).
◼ The momentum of an object is
in the same direction as its
velocity.
Momentum
The more momentum a moving
object has, the harder it is to stop.
◼ The mass of an object affects the
amount of momentum the object
has.
◼ For example, you can catch a
baseball moving at 20 m/s, but you
cannot stop a moving car at the
same speed.
◼
Momentum
The car has more momentum
because it has a greater mass.
◼ The velocity of an object also affects
the amount of momentum an object
has.
◼ For example, an arrow shot from a
bow has a large momentum because,
although it has a small mass, it
travels at a high velocity
◼
Momentum
Objects which aren’t moving have no
velocity, and therefore no
momentum.
◼ The faster a body moves, the larger
its momentum. A heavy object
moving with a certain velocity has
more momentum than a light object
moving with the same velocity.
◼
Sample Momentum Problems
◼ Which
has more momentum:
a 3kg hammer swings at
1.5m/s, or a 4kg hammer
swings at 0.9m/s?
Sample Momentum Problems
◼ Which
is harder to stop: an
80-kg man running at m/s, or
a 1000-kg truck moving at
1m/s?
Impulse (J)
◼ Impulse:
The change in
momentum of an object due
to a force that is applied
during a period of time
impulse = force x time
J = Ft
◼ Units:
N.s (kgm/s)
Impact
◼
◼
Impact- The time duration in which a
change in momentum is occurring.
Units- seconds
When does change in
momentum happen?
◼ When
the mass changes.
◼ When the speed changes.
(slow down, speed up,
stopped)
◼ When the direction of motion
changes.
Impulse-Momentum
Relationship
◼ Impulse
is equal to a change
in momentum
J = Dp or
Dp = 𝑝𝑓 - 𝑝𝑖 = 𝑚𝑣𝑓 - 𝑚𝑣𝑖
or Dp = m(𝑣𝑓 - 𝑣𝑖 )
Sample Problems
1.
A.
B.
A 56.6 – g tennis ball is initially moving
with a velocity of 22.2 m/s to the right
toward the racket. After bring hit by the
racket, the ball rebounds and begins to
move to the left at 27.8 m/s. If the ball
and the racket are in contact for 0.005
second, calculate
the change in momentum of the ball
The force that the racket exerts on the
ball
A. What is impulse (change in momentum)?
B. How much force did the racket exert on the
ball to change its momentum?
Vf
27.8 m/s
22.2 m/s Vi
ball’s mass =56.6 – g (0.0566kg)
time of impact 0.005 s
Sample Problems
2. A net force of 25 newtons is applied to a
20 – kg cart for 2 seconds.
A.
B.
What is impulse (J)?
What is the change in momentum (Dp)?
Sample Problems
2. A net force of 25 newtons is applied to a
20 – kg cart for 2 seconds.
A.
B.
What is impulse (J)?
What is the change in momentum (Dp)?
Sample Problems
3. A 50 – kg object is sitting on a frictionless
surface. An unknown constant force pushes
the object for 2 seconds until it reaches a
velocity of 3 m/s.
A. What is the initial momentum of the object?
B. What is the final momentum of the object?
C. What was the force acting on the object?
D. What was the impulse acting on the object?
Forces of Impact
•Forces of impact are reduced
when time of impact increases
Forces of Impact
◼ Forces
of impact are also
reduced when:
◼ the
velocity of impact is reduced
◼ the mass of the object is
reduced
Time of Impact
◼ The
time of Impact affects the
amount of force in the
collision.
Do this!
In 2011, Ivo Karlovic of Croatia served a
tennis ball at a speed of 251 kph. If the
mass of the ball was 57 grams, and
assuming that the ball had zero initial
velocity along the horizontal and that its
final velocity was along the horizontal,
calculate how much impulse was needed to
achieve this serve.
Getting the Total
Momentum of a System
◼
Alex and Russell are riding their
bicycles side by side on the sidewalk.
The total mass of Alex and his bike is
80kg; the total mass of Russell and
his bike is 90kg. If they are both
moving at a speed of 5.5m/s, what
is their total momentum?
Getting the Total Momentum
of a System 𝑃𝑡 = 𝑚1 𝑣1 + 𝑚2 𝑣2
5.5 m/s
Alex
80 kg
5.5 m/s
Russell
90 kg
Getting the Total
Momentum of a System
◼
Now let’s assume that Alex is riding
his bike at 5.5 m/s westward and
that Russell is riding his bike
eastward at 5.5 m/s. What is their
total momentum?
Getting the Total Momentum
of a System 𝑃𝑡 = 𝑚1 𝑣1 + 𝑚2 𝑣2
5.5 m/s
5.5 m/s
90 kg
80 kg
Russell
Alex
Getting the Total Momentum
of a System
𝑃𝑡 = 𝑚1 𝑣1 + 𝑚2 𝑣2
Calculate the total momentum of
each pair of the objects below
1 m/s
2 m/s
1 kg
2 kg
1 m/s
2 m/s
3
kg
1 kg
𝑃𝑡 = 𝑚1 𝑣1 + 𝑚2 𝑣2
Calculate the total momentum of
each pair of the objects below
1 m/s
2 m/s
2 kg
2 kg
1 m/s
3
kg
1 m/s
3
kg
COLLISIONS
◼
◼
◼
◼
◼
Billiard ball hitting another on the table
A car crashing into another car
An asteroid striking a planet
A cue stick hitting a ball
A baseball bat hitting a ball
TYPES OF COLLISION
◼ Elastic
◼ Inelastic
ELASTIC COLLISION
An elastic collision results when two
elastic bodies collide
◼ When two bodies collide then
separate afterwards
◼ Examples:
➢ Collision between billiard balls
➢ Collision between ball and bat
➢ Tennis ball and racket
➢ Collision between atoms
◼
INELASTIC COLLISION
When two bodies collide and stick
together after the collision
◼ Examples:
➢ A car crashed with another car
➢ A car crashing against the tree
➢ A gum thrown on to the wall
➢ A dropped ball of clay doesn’t
rebound
◼
COLLISION DEPENDS ON
MATERIALS
Whether the collision between two
objects is elastic or inelastic depends
on the materials that make up the
objects.
◼ Recall that an elastic material is
capable of being temporarily deformed
by forces and returning to its original
size and shape once the forces are
removed.
◼
Conservation of Momentum
In everyday language, conservation
means saving resources.
◼ The word conservation has a more
specific meaning in physical science.
◼ In physics, conservation refers to the
conditions before and after some
events.
◼ The total momentum of objects have
is conserved when they collide.
◼
Conservation of Momentum
Momentum may be transferred from
one object to another, but none is
lost. This fact is called the Law of
Conservation of Momentum.
◼ The law states that, in the absence of
outside force, the total momentum of
objects that interact does not
change.
◼
Conservation of Momentum
◼
The amount of momentum is the
same before and after they interact.
𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑃𝑎𝑓𝑡𝑒𝑟
𝑃𝑖 = 𝑃𝑓
𝑚1 𝑣1 + 𝑚2 𝑣2 = 𝑚1 𝑣1′ + 𝑚2 𝑣2′
Law of Conservation
of Momentum
In the absence of an
external force, the
momentum of a system
does not change.
Elastic Collisions
Inelastic Collisions
◼ When
colliding objects
stick together and travel
off as one object
◼ For
two objects in an
inelastic collision:
momentum1 + momentum2 = combined momentum1&2
m1v1 + m2v2 = (m1 + m2)vf
Inelastic Collisions
Bell Ringer 10/18
One pool ball traveling with a velocity of 5
m/s hits another ball of the same mass,
which is stationary. The collision is head
on, as momentum is conserved, and they
bounce off each other.
What type of collision is this?
What are the final velocities of both
bodies?
◼
A 0.150-kg baseball moving at a speed of
45.0 m/s crosses the plate and strikes
the 0.250-kg catcher's mitt (originally at
rest). The catcher's mitt immediately
recoils backwards (at the same speed as
the ball) before the catcher applies an
external force to stop its momentum.
Determine the post-collision velocity of
the mitt and ball.
Bell Ringer
◼
Two meatballs are speeding directly
toward each other. One is a 4.0-kg
meatball moving with a speed of 6.0
m/s, and the other has a mass of 2.0
kg and a speed of 4 m/s. If they
collide inelastically, what will be the
speed of the resulting 6.0 kg meatball
immediately after the collision?
Review Question
◼
A bullet with a mass of 0.020 kg collides
inelastically with a wooden block of mass
2.5 kg, initially at rest. After the collision,
the bullet + block has a speed of 1.2
m/s. What was the initial speed of the
bullet?
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