Impulse; Conservation of
Momentum
Intro: Which Train has more
momentum?
a) While stopped?
b) When moving at the same velocity?
• Momentum (ρ)- (inertia in motion) the product
of mass and velocity of an object
• Momentum equation
ρ = mv
Momentum = mass x velocity
• The SI unit for momentum is kg·m/s
• Change in momentum equation
Δρ = mΔv or Δρ = m(vf – vo)
• Ex A: An airplane is launched from an aircraft
carrier. The plane is going from south to north.
If the airplanes launch velocity is 7.0 x 101 m/s in
the direction the ship was sailing and its mass is
2.5 x 104 kg, what is its momentum immediately
after the launch (include direction since
momentum is a vector).
• Ex A: An airplane is launched from an aircraft
carrier. The plane is going from south to north.
If the airplanes launch velocity is 7.0 x 101 m/s in
the direction the ship was sailing and its mass is
2.5 x 104 kg, what is its momentum immediately
after the launch (include direction since
momentum is a vector).
Ex. B: A 0.060kg tennis ball traveling at
10.0 m/s is returned in the opposite
direction with a speed of 36.0 m/s. What
is the change in momentum of the ball?
Ex. B: A 0.060kg tennis ball traveling at
10.0 m/s is returned in the opposite
direction with a speed of 36.0 m/s. What
is the change in momentum of the ball?
• A moving object can have a large
momentum if it has a large mass, a
lot of speed, or both.
A truck traveling the same
velocity of a truck would have
less velocity
• Impulse (J) is a force applied over a
period of time
• The SI unit for impulse is N·s
Impulse = FΔt
The man is applying
an impulse to the car
Ex. C: What is the impulse when a force of
35N is applied for 1.2 seconds?
Ex. C: What is the impulse when a force of
35N is applied for 1.2 seconds?
• An impulse causes a change in momentum
FΔt = mΔv
Impulse = change in momentum
• The unit for impulse and momentum are
equivalent
• N·s = kg·m/s
The man in the picture is
causing an impulse and
changing the cars momentum
• To increase the momentum of an object
the most you want the greatest force
possible over the longest time possible
FΔt = mΔv
• Two cars of equal mass are traveling the
same speed. What do we know about
their momentum?
10 m/s
A
B
500kg
500kg
10 m/s
• Which car is going to take less time to stop
10 m/s
A
B
500kg
500kg
10 m/s
• Which car is going to take less time to stop
• Look at the equation and determine what
this means:
FΔt = mΔv
A
B
• Which car is going to take less time to stop
FΔt = mΔv
F
Δt
= mΔv
A
B
F
Δt = mΔv
Back to Newtons 2nd Law
F=ma
• If there is a greater force on the same
object you will get a greater acceleration,
or deceleration.
• Force causes acceleration
Ex. D: A 0.060kg tennis ball traveling at
10.0 m/s is returned in the opposite
direction with a speed of 36.0 m/s. If the
ball is in contact with the racket for 0.020s,
with what average force is the ball hit?
Ex. D: A 0.060kg tennis ball traveling at
10.0 m/s is returned in the opposite
direction with a speed of 36.0 m/s. If the
ball is in contact with the racket for 0.020s,
with what average force is the ball hit?
Ex. E: Two identical cars, each traveling 20 m/s,
are brought to a stop. Car a stops by applying
its breaks the normal way. Car B stops as a
result of running into an unmovable concrete
wall. Which of the following statements is
TRUE? (explain why the incorrect statements
are false)
a.
b.
c.
d.
Car A has the greatest change in momentum.
Car B experiences the greatest impulse.
Car B has the greatest change in momentum.
Car B has the greatest force applied to it.
Ex. E: Two identical cars, each traveling 20 m/s, are brought to a stop.
Car a stops by applying its breaks the normal way. Car B stops
as a result of running into an unmovable concrete wall. Which of
the following statements is TRUE? (explain why the incorrect
statements are false)
a.
Car A has the greatest change in momentum.
b.
Car B experiences the greatest impulse.
c.
Car B has the greatest change in momentum.
d.
Car B has the greatest force applied to it.
Bouncing
• The impulse needed to bring an
object to a stop and “throw it back
again” is greater than the impulse
required to just bring an object to a
stop.
• To produce a stop you reduce momentum
to 0 since v=0
• To bounce you need a negative momentum
since the direction of velocity changed
Problem Set #1
ρ=mv
J= FΔt
FΔt = mΔv
1. Bernie, whose mass is 70.0 kg, leaves a ski
jump with the velocity of 21.0 m/s. What is
Bernie’s momentum as he leaves the ski
jump?
2. Mark squishes a spider by applying a 20N
force for 0.1s. What is the impulse of this
action?
3. Ethel hits a 0.20 kg ball at rest causing it to go
20 m/s. What average force is applied if the
ball is in contact for 0.4s?
Problem Set #1
ρ=mv
J= FΔt
FΔt = mΔv
1. Bernie, whose mass is 70.0 kg, leaves a
ski jump with the velocity of 21.0 m/s.
What is Bernie’s momentum as he
leaves the ski jump?
Problem Set #1
ρ=mv
J= FΔt
FΔt = mΔv
2. Mark squishes a spider by applying a 20N
force for 0.1s. What is the impulse of
this action?
Problem Set #1
ρ=mv
J= FΔt
FΔt = mΔv
3. Ethel hits a 0.20 kg ball at rest causing it
to go 20 m/s. What average force is
applied if the ball is in contact for 0.4s?
0.2
(0.2
Law of Conservation of Momentum
• Momentum is neither gained nor lost in the
absence of an external force
• All momentum before = all momentum after
• p1before + p2before = p1after + p2after
expanded as
• m1v1o + m2v2o = m1v1f + m2v2f
• Net momentum before firing is 0 and
net momentum after is still 0
• The cannon and the cannonball cancel each
other out
pcannon before + pcannonball before = 0
before
after
pcannon after + pcannonball after = 0
Collisions
• Collisions follow the conservation of momentum
– When two objects collide the net momentum
before the collision equals the net momentum
of both objects after the collision
Net momentumbefore collision = Net momentumafter collision
Elastic Collisions
• Elastic collision- When objects collide
without being permanently deformed and
without generating heat.
• Net momentumbefore collision = Net momentumafter collision
Elastic Collision Equation
m1v1o + m2v2o = m1v1f + m2v2f
Elastic Collision Example
• Objects do not stick together
Inelastic Collisions
• Inelastic collision- collision where
the objects become distorted or
generate heat.
m1v1o + m2v2o = (m1+m2)(vf)
• If the two objects stick together there is
one final velocity:
Inelastic collision equation
m1v1o + m2v2o = (m1+m2)(vf)
If the objects sticking together after the collision will have
the same combined velocity.
Inelastic Collision
• Both have the same final velocity since they
stick together
Types of collisions/conservation of
momentum problems
1. Both objects start at rest (conservation of momentum)
2. One object moving other at rest (elastic collision)
3. Both objects moving same direction (elastic collision)
4. Both objects moving opposite directions (elastic collision)
5. One object moving other at rest (inelastic collision)
6. Both objects moving same direction (inelastic collision)
7. Both objects moving opposite directions (inelastic
collision)
Conservation of momentum
1. Both objects start at rest (conservation of momentum)
Vo = 0 for both objects
Ex. F: A baseball player standing on a frictionless surface
with a mass of 50 kg throws a 0.25 kg ball forward at a
velocity of 25 m/s. What is his final velocity and in
what direction?
Conservation of momentum
Ex. F: A baseball player standing on a frictionless surface
with a mass of 50 kg throws a 0.25 kg ball forward at a
velocity of 25 m/s. What is his final velocity and in
what direction?
Types of collisions
2. One object moving other at rest (elastic
collision)
Ex. G: A 1000 kg car traveling at 20.0 m/s hits a 3000 kg truck at
rest. If the truck is traveling 10 m/s forward after the elastic
collision, what is the cars final velocity?
Ex. G: A 1000 kg car traveling at 20.0 m/s hits a 3000 kg truck at
rest. If the truck is traveling 10 m/s forward after the elastic
collision, what is the cars final velocity?
Types of collisions
3. Both objects moving same direction (elastic
collision)
Ex. H: A 1000 kg car traveling at 20.0 m/s forward
hits a 3000 kg truck at 10 m/s in the same
direction. If the truck is traveling 15 m/s forward
after the elastic collision, what Is the cars final
velocity?
Ex. H: A 1000 kg car traveling at 20.0 m/s forward
hits a 3000 kg truck at 10 m/s in the same
direction. If the truck is traveling 15 m/s forward
after the elastic collision, what Is the cars final
velocity?
Types of collisions
4. Both objects moving opposite directions (elastic
collision)
Ex. I: What is the initial velocity of a 1000 kg car
traveling to the right that hits a 3000 kg truck
traveling at 20 m/s to the left. After the elastic
collision, the truck is traveling 10 m/s and the car
is traveling 15 m/s both to the left?
Ex. I: What is the initial velocity of a 1000 kg car
traveling to the right that hits a 3000 kg truck
traveling at 20 m/s to the left. After the elastic
collision, the truck is traveling 10 m/s and the car
is traveling 15 m/s both to the left?
Types of collisions
5. One object moving other at rest (inelastic
collision)
Ex. J: In an experiment, a toy wooden car with a
mass of 300g, initially at rest, is struck in the rear
by a 30g dart traveling at 15 m/s as shown. With
what speed does the car with the dart stuck in it
move after the collision?
V= 15 m/s
30g
V= 0 m/s
300g
V= ?
30g
300g
Ex. J: In an experiment, a toy wooden car with a mass of
300g, initially at rest, is struck in the rear by a 30g dart
traveling at 15 m/s as shown. With what speed does the
car with the dart stuck in it move after the collision?
V= 15 m/s
30g
V= 0 m/s
300g
V= ?
30g
300g
Types of collisions
6. Both objects moving same direction (inelastic
collision)
Ex. K: A 50 kg astronaut traveling at 8 m/s to the
left catches a 10 kg meteor traveling at 20 m/s to
the left. What is the final velocity of the
astronaut holding the meteor?
Ex. K: A 50 kg astronaut traveling at 8 m/s to the
left catches a 10 kg meteor traveling at 20 m/s to
the left. What is the final velocity of the
astronaut holding the meteor?
Types of collisions
7. Both objects moving opposite directions
(inelastic collision)
Ex. L: A 50 kg astronaut traveling at 8 m/s to the
right catches a 10 kg meteor traveling at 20 m/s
to the left. What is the final velocity of the
astronaut holding the meteor?
Ex. L: A 50 kg astronaut traveling at 8 m/s
to the right catches a 10 kg meteor
traveling at 20 m/s to the left. What is the
final velocity of the astronaut holding the
meteor?
Problem Set #2
1.
A 35 kg child runs across a store at 4.0 m/s and jumps onto a 35
kg shopping cart initially at rest. At what speed will the shopping
cart and the child move together across the store assuming
negligible friction?
2.
Bruno throws a 0.20kg football and knocks over a 0.88kg vase at
rest. After the collision the football bounces straight back with a
speed of 3.9 m/s while the vase is moving at 2.6 m/s in the
opposite direction. How fast did Bruno throw the football?
3.
Martha tosses a 1.5kg ball at a 0.8kg milk jug initially at rest. The
ball is thrown to the right at 7.8 m/s and continues to move to the
right at 3.0 m/s after the collision. What is the velocity of the jug
after the collision?
4.
Sam, who is 85kg, jumps into a 300 kg rowboat initially at rest.
His initial velocity was 5 m/s forward. What is the velocity of Sam
in the boat after he lands?
Problem Set #2
1. A 35 kg child runs across a store at 4.0 m/s
and jumps onto a 35 kg shopping cart initially
at rest. At what speed will the shopping cart
and the child move together across the store
assuming negligible friction?
Problem Set #2
2. Bruno throws a 0.20kg football and knocks over a
0.88kg vase at rest. After the collision the football
bounces straight back with a speed of 3.9 m/s while
the vase is moving at 2.6 m/s in the opposite direction.
How fast did Bruno throw the football?
Problem Set #2
3. Martha tosses a 1.5kg ball at a 0.8kg milk jug initially at
rest. The ball is thrown to the right at 7.8 m/s and
continues to move to the right at 3.0 m/s after the
collision. What is the velocity of the jug after the
collision?
Problem Set #2
4. Sam, who is 85kg, jumps into a 300 kg
rowboat initially at rest. His initial
velocity was 5 m/s forward. What is the
velocity of Sam in the boat after he
lands?