Title: Impulse; Conservation of Momentum
1Impulse Conservation of Momentum
2Intro Which Train has more momentum?
- While stopped?
- When moving at the same velocity?
Both have no velocity no momentum
The larger has more mass more momentum
3- Momentum (?)- (inertia in motion) the product of
mass and velocity of an object - Momentum equation
- ? mv
- Momentum mass x velocity
- The SI unit for momentum is kgm/s
- Change in momentum equation
- ?? m?v or ?? m(vf vo)
4- 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).
5- 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).
6- 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?
7- 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?
8- 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
9- Impulse (J) is a force applied over a period of
time - The SI unit for impulse is Ns
- Impulse F?t
The man is applying an impulse to the car
10- Ex. C What is the impulse when a force of 35N
is applied for 1.2 seconds?
11- Ex. C What is the impulse when a force of 35N
is applied for 1.2 seconds?
12- An impulse causes a change in momentum
- F?t m?v
- Impulse change in momentum
- The unit for impulse and momentum are equivalent
- Ns kgm/s
The man in the picture is causing an impulse and
changing the cars momentum
13- To increase the momentum of an object the most
you want the greatest force possible over the
longest time possible
F?t m?v
14- Two cars of equal mass are traveling the same
speed. What do we know about their momentum?
They have the same momentum pmv
10 m/s
500kg
A
10 m/s
500kg
B
15- Which car is going to take less time to stop
stops in less time
10 m/s
500kg
A
10 m/s
500kg
B
16- Which car is going to take less time to stop
- Look at the equation and determine what this
means F?t m?v
stops in less time
A
B
17- Which car is going to take less time to stop
-
- F?t m?v
-
- F?t m?v
- F?t m?v
with the same momentum
less time more force
A
more time less force
B
18Back to Newtons 2nd Law
- Fma
- If there is a greater force on the same object
you will get a greater acceleration, or
deceleration. - Force causes acceleration
19- 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?
20- 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?
21- 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) - 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.
22- 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) - 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.
23Bouncing
- 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
v0 - To bounce you need a negative momentum since the
direction of velocity changed
24- Problem Set 1 ?mv J F?t F?t
m?v - Bernie, whose mass is 70.0 kg, leaves a ski jump
with the velocity of 21.0 m/s. What is Bernies
momentum as he leaves the ski jump? - Mark squishes a spider by applying a 20N force
for 0.1s. What is the impulse of this action? - 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?
25- Problem Set 1 ?mv J F?t
F?t m?v - Bernie, whose mass is 70.0 kg, leaves a ski jump
with the velocity of 21.0 m/s. What is Bernies
momentum as he leaves the ski jump?
26- Problem Set 1 ?mv J F?t
F?t m?v - 2. Mark squishes a spider by applying a 20N force
for 0.1s. What is the impulse of this action?
27- Problem Set 1 ?mv J F?t
F?t m?v - 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
.
28Law 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
29- 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
30Collisions
- 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
31Elastic Collisions
- Elastic collision- When objects collide without
being permanently deformed and without generating
heat. - Net momentumbefore collision Net momentumafter
collision
32Elastic Collision Equation
33Elastic Collision Example
- Objects do not stick together
34Inelastic Collisions
- Inelastic collision- collision where the objects
become distorted or generate heat. - m1v1o m2v2o (m1m2)(vf)
- If the two objects stick together there is one
final velocity
35Inelastic collision equation
- m1v1o m2v2o (m1m2)(vf)
- If the objects sticking together after the
collision will have the same combined velocity.
36Inelastic Collision
- Both have the same final velocity since they
stick together
37Types 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)
38Conservation of momentum
- 1. Both objects start at rest (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?
Vo 0 for both objects
39Conservation 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?
40Types 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?
41Ex. 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?
42Types 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?
43- 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?
44Types 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?
45- 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?
46Types 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
V 0 m/s
V ?
300g
30g
300g
30g
47- 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
V 0 m/s
V ?
300g
30g
300g
30g
48Types 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?
49- 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?
50Types 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?
51- 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?
52- Problem Set 2
- 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? - 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? - 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? - 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?
53- Problem Set 2
- 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?
54- 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?
55- 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?
56- 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?