MOMENTUM AND
IMPULSE
Chapter 9
Standards
• SP3. Students will evaluate the forms and
transformations of energy.
• c. Measure and calculate the vector nature of momentum.
• d. Compare and contrast elastic and inelastic collisions.
• e. Demonstrate the factors required to produce a change in
momentum.
Momentum
• Momentum is a commonly used term in sports.
Momentum
• 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 that is on the move has the momentum. If
an object is in motion (on the move) then it has
momentum.
What is momentum?
• Momentum is a property of moving matter.
• Momentum describes the tendency of objects to keep
going in the same direction with the same speed.
• A force is required to change momentum.
Momentum Equation
p = mv
•
p = momentum vector
• m = mass
•
v = velocity vector
How do I find momentum?
• The momentum of a ball depends on its mass and
velocity.
• Ball B has more momentum than ball A.
When could the truck and rollercoaster
have equal momentum vectors?
Equivalent Momenta
Car: m = 1800 kg; v = 80 m /s
p = 1.44 ·105 kg · m /s
Bus: m = 9000 kg; v = 16 m /s
p = 1.44 ·105 kg · m /s
Train: m = 3.6·104 kg; v = 4 m /s
p = 1.44 ·105 kg · m /s
Objects at Rest
• Momentum can be thought of as
mass in motion
• An object at rest has NO
momentum at all
Difference Between Momentum and Inertia
• Inertia is another property of mass that resists
changes in velocity; however, inertia depends
only on mass.
• Inertia is a scalar quantity.
• Momentum is a property of moving mass that
resists changes in a moving object’s velocity.
• So momentum is a vector quantity.
Units
• The SI unit of momentum is kg * m/s
• Mass times velocity
• Anything that is a measure of mass times a
measure of velocity is acceptable though
• Grams * Miles/hour
• Cg * cm/s
Path of an Object
• Ball A is 1 kg moving 1m/sec, ball B is 1kg at 3 m/sec.
• A 1 N force is applied to deflect the motion of each ball.
• What happens?
• Does the force deflect both balls equally?
 Ball B deflects much
less than ball A when
the same force is
applied because ball B
had a greater initial
momentum.
Kinetic Energy and Momentum
• Kinetic energy and momentum are different quantities,
even though both depend on mass and speed.
• Kinetic energy is a scalar quantity.
• Momentum is a vector, so it always depends on direction.
Two balls with the same mass and speed have the same kinetic energy
but opposite momentum.
A Force is Required to Change Momentum
The relationship between force and motion
follows directly from Newton's second law.
Force (N)
Change in time (sec)
F=Dp
Dt
Change in momentum
(kg m/sec)
Impulse
• The product of a force
and the time the force
acts is called the
impulse.
• Impulse is a way to
measure a change in
momentum because it is
not always possible to
calculate force and time
individually since
collisions happen so fast.
Impulse Changes Momentum
• A force sustained for a long time produces more change
in momentum than does the same force applied briefly.
• Both force and time are important in changing an object’s
momentum.
• When you push with the same force for twice the time,
you impart twice the impulse and produce twice the
change in momentum.
Impulse is Equal to Change in Momentum
• The quantity force × time interval is called
impulse.
• impulse = F × t
• The greater the impulse exerted on something,
the greater will be the change in momentum.
• impulse = change in momentum
• Ft = ∆(mv)
• This is called the Impulse - Momentum
Theorem!
Impulse Changes Momentum
• If the change in momentum occurs over a long time, the
force of impact is small.
Impulse Changes Momentum
• If the change in momentum occurs over a short time, the
force of impact is large.
Impulse Changes Momentum
When you jump down to the ground,
bend your knees when your feet
make contact with the ground to
extend the time during which your
momentum decreases.
A wrestler thrown to the floor extends
his time of hitting the mat, spreading
the impulse into a series of smaller
ones as his foot, knee, hip, ribs, and
shoulder successively hit the mat.
Impulse Changes Momentum
The impulse provided by a boxer’s jaw counteracts the
momentum of the punch.
a. The boxer moves away from the punch.
Impulse Changes Momentum
The impulse provided by a boxer’s jaw counteracts the
momentum of the punch.
a. The boxer moves away from the punch.
b. The boxer moves toward the punch. Ouch!
Padded gloves are worn to reduce the effect of the impulses. The padding
increases the time over which the force is experienced. This reduces the force
(and thus the hurt on the hand.
Boxers often ride the punch when they know they are going to be hit. They
allow their head to continue backwards with the gloved fist in order to increase
the time over which the fist is brought to a stop. This in turn decreases the
force.
Impulse Changes Momentum
A glass dish is more likely to survive if it is
dropped on a carpet rather than a sidewalk.
The carpet has more “give.”
Since time is longer hitting the carpet than
hitting the sidewalk, a smaller force results.
The shorter time hitting the sidewalk results
in a greater stopping force.
Safety net for acrobats is a good example.
Cassy imparts a
large impulse to the
bricks in a short
time and produces
considerable force.
Her hand bounces
back, yielding as
much as twice the
impulse to the
bricks.
Bouncing
The impulse required to bring an object to a
stop and then to “throw it back again” is
greater than the impulse required merely to
bring the object to a stop.
Bouncing
Suppose you catch a falling pot with
your hands.
• You provide an impulse to reduce
its momentum to zero.
• If you throw the pot upward again,
you have to provide additional
impulse.
Bouncing
If the flower pot falls from
a shelf onto your head,
you may be in trouble.
If it bounces from your
head, you may be in more
serious trouble because
impulses are greater when
an object bounces. The
increased impulse is
supplied by your head if
the pot bounces.
Try this
• In a physics demonstration, two identical balloons (A and B)
are propelled across the room on guide wires. The motion
diagrams (depicting the relative position of the balloons at
time intervals of 0.05 seconds) are shown below.
• Which balloon (A or B) has the greatest acceleration?
• Which balloon (A or B) has the greatest final velocity?
• Which balloon (A or B) has the greatest momentum
change?
• Which balloon (A or B) experiences the greatest impulse?
Momentum is Conserved
• The law of conservation of momentum states when a
system of interacting objects is not influenced by outside
forces (like friction), the total momentum of the system
cannot change.
• Initial Momentum = Final Momentum
Conservation of Momentum
The momentum before firing is zero. After firing, the net momentum is still
zero because the momentum of the cannon is equal and opposite to the
momentum of the cannonball.
Conservation of Momentum
Momentum has both direction and magnitude. It is a vector
quantity.
• The cannonball gains momentum and the recoiling
cannon gains momentum in the opposite direction.
• The cannon-cannonball system gains none.
• The momenta of the cannonball and the cannon are
equal in magnitude and opposite in direction.
• No net force acts on the system so there is no net
impulse on the system and there is no net change in the
momentum.
Conservation of Momentum
• Equation:
Cart and Brick
• In the collision between the cart and the dropped brick, total
system momentum is conserved.
• Before the collision, the momentum of the cart is 60 kg*cm/s
and the momentum of the dropped brick is 0 kg*cm/s; the total
system momentum is 60 kg*cm/s.
• After the collision, the momentum of the cart is 20.0 kg*cm/s
and the momentum of the dropped brick is 40.0 kg*cm/s; the
total system momentum is 60 kg*cm/s. The momentum of the
cart-dropped brick system is conserved.
• The momentum lost by the cart (40 kg*cm/s) is gained by the
dropped brick.
Collisions in One Dimension
• A collision occurs when two or more objects hit
each other.
• During a collision, momentum is transferred from
one object to another.
• Collisions can be elastic or inelastic.
Collisions
When objects collide without being permanently deformed
and without generating heat, the collision is an elastic
collision.
Colliding objects bounce perfectly in perfect elastic collisions.
The sum of the momentum vectors is the same before and
after each collision.
Collisions
a. A moving ball strikes a ball at rest.
Collisions
a. A moving ball strikes a ball at rest.
b. Two moving balls collide head-on.
Collisions
a. A moving ball strikes a ball at rest.
b. Two moving balls collide head-on.
c. Two balls moving in the same direction collide.
Elastic Collision
8 Momentum
Collisions
Inelastic Collisions
A collision in which the colliding objects become distorted and
generate heat during the collision is an inelastic collision.
Momentum conservation holds true even in inelastic collisions.
Whenever colliding objects become tangled or couple
together, a totally inelastic collision occurs.
8 Momentum
Collisions
In an inelastic collision between two freight cars, the
momentum of the freight car on the left is shared with the
freight car on the right.
8 Momentum
Collisions
The freight cars are of equal mass m, and one car moves at 4
m/s toward the other car that is at rest.
net momentum before collision = net momentum after collision
(net mv)before = (net mv)after
(m)(4 m/s) + (m)(0 m/s) = (2m)(vafter)
Twice as much mass is moving after the collision, so the
velocity, vafter, must be one half of 4 m/s.
vafter = 2 m/s in the same direction as the velocity before the
collision, vbefore.
8 Momentum
Collisions
The initial momentum is
shared by both cars without
loss or gain.
Momentum is conserved.
External forces are usually
negligible during the collision,
so the net momentum does not
change during collision.
8 Momentum
8.5 Collisions
do the math!
Consider a 6-kg fish that swims toward and swallows a
2-kg fish that is at rest. If the larger fish swims at 1 m/s,
what is its velocity immediately after lunch?
8 Momentum
8.5 Collisions
do the math!
Consider a 6-kg fish that swims toward and swallows a
2-kg fish that is at rest. If the larger fish swims at 1 m/s,
what is its velocity immediately after lunch?
Momentum is conserved from the instant before lunch until the
instant after (in so brief an interval, water resistance does not
have time to change the momentum).
8 Momentum
8.5 Collisions
do the math!
8 Momentum
8.5 Collisions
do the math!
Suppose the small fish is not at rest but is swimming
toward the large fish at 2 m/s.
8 Momentum
8.5 Collisions
do the math!
Suppose the small fish is not at rest but is swimming
toward the large fish at 2 m/s.
If we consider the direction of the large fish as positive, then
the velocity of the small fish is –2 m/s.
8 Momentum
8.5 Collisions
do the math!
The negative momentum of the small fish slows the large fish.
8 Momentum
8.5 Collisions
do the math!
If the small fish were swimming at –3 m/s, then both fish
would have equal and opposite momenta.
Zero momentum before lunch would equal zero momentum
after lunch, and both fish would come to a halt.
8 Momentum
8.5 Collisions
do the math!
Suppose the small fish swims at –4 m/s.
The minus sign tells us that after lunch the two-fish system
moves in a direction opposite to the large fish’s direction
before lunch.
Elastic collisions
Two 0.165 kg billiard balls roll toward
each other and collide head-on.
Initially, the 5-ball has a velocity of 0.5
m/s.
The 10-ball has an initial velocity of -0.7
m/s.
The collision is elastic and the 10-ball
rebounds with a velocity of 0.4 m/s,
reversing its direction.
What is the velocity of the 5-ball after
the collision?
Elastic
collisions
1.
2.
3.
4.
5.
You are asked for 10-ball’s velocity after collision.
You are given mass, initial velocities, 5-ball’s final velocity.
Diagram the motion, use m1v1 + m2v2 = m1v3 + m2v4
Solve for V3 : (0.165 kg)(0.5 m/s) + (0.165 kg) (-0.7 kg)=
(0.165 kg) v3 + (0.165 kg) (0.4 m/s)
V3 = -0.6 m/s
Inelastic collisions
A train car moving to the right at 10 m/s
collides with a parked train car.
They stick together and roll along the
track.
If the moving car has a mass of 8,000 kg
and the parked car has a mass of 2,000
kg, what is their combined velocity after
the collision?
1.
2.
You are asked for the final velocity.
You are given masses, and initial velocity of moving
train car.
Inelastic collisions
3.
4.
Diagram the problem, use m1v1 + m2v2 = (m1v1 +m2v2)
v3
Solve for v3= (8,000 kg)(10 m/s) + (2,000 kg)(0 m/s)
(8,000 + 2,000 kg)
v3= 8 m/s
The train cars moving together to right at 8 m/s.
Collisions Summarized