Conserving momentum

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Conserving momentum
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1 You release a ball from rest to let it fall to
the ground. It gives a sound upon hitting the
ground. Which of the following cases is possible?
A It rises to the original height when it
rebounds. B It rises to a greater height. C It
rises to a smaller height.
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2 You are going ashore after travelling in a
small boat. What happens to the boat when you
step onto the bank (?)?
A It moves towards the bank. B It moves away from
the bank. C It remains stationary.
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1 Types of collisions

• If the total KE of a system

remains unchanged before and after collision
? collision is elastic
otherwise collision is inelastic
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1 Types of collisions

• The ball bounces back to the same height h

? NO energy loss during collision
? completely elastic collision
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1 Types of collisions
plasticine

• Plasticine sticks to the ground

(not bounces back)
? KE of plasticine is lost during collision
? completely inelastic collision
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Experiment 8b
Completely inelastic collisions
Set up the following apparatus.
velcro attachment
friction-compensated runway
give A a sharp push to collide with stationary
trolley B
A
B
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Experiment 8b
Completely inelastic collisions
Note and save the v-t graph displayed on the
computer screen.
Repeat the experiment by adding masses to double
and then triple the mass of trolley A.
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Experiment 8b
Completely inelastic collisions
Video
Simulation
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a Completely inelastic collisions
v-t graph of completely inelastic collision
collision of A with B which is initially at rest
vA
vA B
trolley A pushed to move from rest
v before collision (vA) 0.35 m s1 v after
collision (vA B ) 0.17 m s1
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a Completely inelastic collisions
Typical result
(mA mB)v 1.0 ? 0.17
0.17
mAu 0.5 ? 0.35 0.18
(mA mB)v 1.5 ? 0.55
0.83
mAu 1.0 ? 0.82 0.82
mass of each trolley 0.5 kg
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a Completely inelastic collisions
Typical result
(mA mB)v 2.0 ? 0.38
0.76
mAu 1.5 ? 0.51 0.77

• Total ? of trolleys before collision

total ? of trolleys after collision
total momentum is conserved in completely
inelastic collision
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Experiment 8c
Elastic collisions
Set up the following apparatus.
friction-compensated runway
A
spring-loaded plunger (released)
B
A 'll collide with stationary B, ? move off
separately
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Experiment 8c
Elastic collisions
Note and save the v-t graph displayed on the
computer screen.
Repeat the experiment by adding masses to double
and then triple the mass of trolley A.
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Experiment 8c
Elastic collisions
Video
Simulation
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b Elastic collisions
v-t graph of elastic collision
vA
trolley A pushed to move from rest
vA after collision
collision
B stationary before collision
vB after collision
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b Elastic collisions
Typical result
mAvA mBvB 0.27
mAuA mBuB 0.30
mAvA mBvB 1.05
mAuA mBuB 1.05
mass of each trolley 0.5 kg
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b Elastic collisions
mAvA mBvB 1.03
mAuA mBuB 1.05

• Total ? of trolleys before collision

total ? of trolleys after collision
total momentum is conserved in elastic collision
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Experiment 8d
'Explosion' of trolleys
Set up the following apparatus.
Place trolleys A B in contact end-on in the
middle of a level runway.
Release plunger ? 2 trolleys 'explode'
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Experiment 8d
'Explosion' of trolleys
Note and save the v-t graph displayed on the
computer screen.
Repeat the experiment by adding masses to double
and then triple the mass of trolley A.
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Experiment 8d
'Explosion' of trolleys
Video
Simulation
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c 'Explosion' of trolleys
v-t graph of 'explosion' of trolleys
explosion
vA
Graphs of both trolleys are ?ve,
since each moves towards its motion sensor.
vB
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c 'Explosion' of trolleys
Typical result
?0.58 m s?1
0.56 m s?1
spring-loaded plunger
mBvB ?0.29
mAvA 0.28
? final total ? ?0.01
0.32 m s?1
?0.68 m s?1
mBvB ?0.34
mAvA 0.32
? final total ? ?0.02
mass of each trolley 0.5 kg
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c 'Explosion' of trolleys
0.22 m s?1
?0.68 m s?1
mBvB ?0.34
mAvA 0.33
? final total ? ?0.01

• Total ? of trolleys before 'explosion'

total ? of trolleys after 'explosion'
total momentum is conserved in 'explosion'
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Q1 Which of the following...
Which of the following is an elastic collision?
A A ball hits a wall and rebounds with the same
speed. B A bowl knocks down some pins with a loud
sound. C A car crashes into a lamp-post.
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Q2 Identify the type of...
Identify the type of the following collisions.
(a)
before collision
ball A
ball B
after collision
ball A
ball B
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Q2 Identify the type of...
Total KE before collision (2 ? __2 1 ?
___2) ____ J
5 m s1
4 m s1
1
5
4
2 kg
1 kg
2
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1 m s1
4 m s1
Total KE after collision ____________________
______ ________ (All/Some/No) KE is lost in the
collision, the collision is ___________.
2 kg
1 kg
9 J
Some
inelastic
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Q2 Identify the type of...
Identify the type of the following collisions.
(b)
at rest
before collision
ball A
ball B
after collision
ball A
ball B
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Q2 Identify the type of...
Total KE before collision
2 m s1
at rest
2 kg
1 kg
4 J
2/3 m s1
8/3 m s1
Total KE after collision
2 kg
1 kg

4 J
No KE is lost in the collision,
the collision is elastic.
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2 Is momentum conserved in collisions?

• Total momentum is conserved in

Expt. 8b Completely inelastic collisions
Expt. 8c Elastic collisions
Expt. 8d 'Explosion' of trolleys
? total momentum is conserved in all cases
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2 Is momentum conserved in collisions?

• Law of conservation of momentum

In a collision, total momentum of colliding
objects before collision is equal to the total
momentum after collision,
provided that there is no external force acting
on the objects.
mAuA mBuB mAvA mBvB
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2 Is momentum conserved in collisions?
Simulation
Simulation
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Example 7
Colliding skaters

• While skating,

v ?
4 m s?1
3 m s?1
40 kg
30 kg
After collision
Before collision
If they move together after collision, what are
their velocities v after collision?
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Example 7
Colliding skaters
v ?
4 m s?1
3 m s?1
40 kg
30 kg
Applying law of conservation of momentum,

• total ? before collision total ? after collision

(40 30) ? v
40 ? 3 30 ? (?4)
? v 0 m s?1
They come to a stop after collision.
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Example 8
Exploding trolleys
compressed spring
2 kg
3 kg
B
A
plunger releases
vB
60 cm s?1

• Find the velocity of trolley B after 'explosion'.

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Example 8
Exploding trolleys
vB
60 cm s?1
2 kg
3 kg
B
A
ve
Applying law of conservation of momentum,

• total ? before 'explosion' total ? after
  'explosion'

2 ? 60 3v
0
? vB ?40 cm s?1
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3 More examples of conservation of momentum
a 'Newtons cradle'
A toy consisting of a line of 5 steel balls.
It can demonstrate the law of conservation of
momentum.
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Experiment 8e
'Newtons cradle'
Pull one ball to one side and then release.
Repeat using 2, 3 and then 4 balls.
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Experiment 8e
'Newtons cradle'
Video
Simulation
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b Velocity of an air-rifle bullet
plasticine on toy railway car
air-rifle
friction-compensated track
What is it?
How to find it?
1 m
end stop

• Bullet is fired into a lump of plasticine.

After impact, the car runs.
Use a stop-watch to measure the time to travel 1
m.
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Example 9
Measuring velocity of an air-rifle bullet
plasticine on toy railway car

• air-rifle

friction-compensated track
mass of bullet 0.002 kg mass of car 0.25 kg
1 m
end stop
A bullet is fired into a lump of plasticine on a
toy railway car which takes 4.0 s to move 1 m.
Find the velocity of bullet.
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Example 9
Measuring velocity of an air-rifle bullet
v
mass of bullet 0.002 kg mass of car 0.25
kg car travels 1 m in 4 s
0.25 m s?1
1 m in 4 s
v after impact
1 m / 4 s
0.25 m s?1
Applying law of conservation of momentum,

• total ? before impact total ? after impact

0.002 ? u 0
(0.25 0.002) ? 0.25
? u 31.5 m s?1
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c Recoil velocity of a rifle
When a bullet is fired, the rifle recoils.
recoil velocity
v
forward momentum
backward momentum
forward backward momentum 0

• total momentum 0

Conservation of momentum
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c Recoil velocity of a rifle
Simulation
Simulation
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Example 10
Recoil velocity of a rifle
5 kg
Before firing
5 kg
10 g
After firing
200 m s?1
v ?

• Find the recoil velocity v of the rifle.

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Example 10
Recoil velocity of a rifle
ve
5 kg
10 g
200 m s?1
v ?
Applying law of conservation of momentum,
total ? of rifle bullet after firing

• total ? of rifle bullet before firing

change to SI unit
0
5v 0.01 ? 200
(opposite direction)
? v ?0.4 m s?1
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4 Momentum not conserved?
Momentum disappeared?
v

• running

stop
NO!
mass m
momentum mv
momentum 0
? 0
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4 Momentum not conserved?

• If you step from a rowing boat onto the bank

backward force on boat
forward force on shoe
the boat moves away from you.
Your forward momentum is equal opposite to the
backward momentum of the boat.
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4 Momentum not conserved?

• When a truck runs on a road, the road (Earth)
  should move behind it!

m 1 ? 104 kg
Total ? before truck moves
Total ? after car moves
v

25 m s?1
0 1 ? 104 ? 25
6 ? 1024 v
v ?2.4 ? 10?19 m s?1
negligible!
m 6 ? 1024 kg
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5 Energy changes in collisions
In the beginning of 8.2, we said that KE is
conserved in elastic collisions,
but not in inelastic collisions.
Let's confirm this in Experiment 8f.
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Experiment 8f
Energy changes in collisions
1 Calculate the sum of KE of the trolleys before
after the completely inelastic collisions in
Experiment 8b.
2 Calculate the sum of KE of the trolleys before
after the elastic collisions in Experiment 8c.
Video
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Experiment 8f
Energy changes in collisions
The result can be summed up as
 
Momentum conserved?
Kinetic energy conserved?
Yes
Yes
Elastic collision
Inelastic collision
Yes
No
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Experiment 8f
Energy changes in collisions
Simulation
Simulation
Simulation
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5 Energy changes in collisions
Why is KE not conserved in some collisions?
Because in these collisions some of the KE is
changed to work done against friction or other
forms of energy (such as heat sound) during
impact.
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Q1 A shot is fired from...
A shot is fired from a cannon. The ball flies in
the positive direction. What is the recoil
velocity of the cannon?
A 0.0133 m s1 B ?0.0133 m s1 C 13.3 m
s1 D ?13.3 m s1
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Q2 A book is dropped from...
(a) A book is dropped from a height. Why is the
momentum of the book not conserved?
gravitational
It is because _______________ force acts on the
book. This net force accelerates the book
downwards and changes its momentum.
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Q2 A book is dropped from...
(b) How can we consider the situation so that
momentum is conserved?
Momentum is conserved if the momenta of the book
and the ___________________ is considered
together.
Earth
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Q3 Consider a system...
Consider a system without external force. In
elastic collisions, both ______________ and
________________ are conserved. In inelastic
collisions, only ______________ is conserved, but
not __________________.
momentum
kinetic energy
momentum
kinetic energy
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Q4 A jet fighter...

• A jet fighter of total mass 8000 kg fires five
  20-kg rockets in 1 s. Find the speed of it just
  after rockets are fired.

100 m s?1
v ?
500 m s?1
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Q4 A jet fighter...
v ?
100 m s?1
8000 kg
20 kg
500 m s?1
Applying law of conservation of momentum,

• total ? before firing rockets

total ? after firing rockets

8000
20 ? 5
20
500
5
? v ________
94.9 m s?1
(slowed down!)