This document provides an overview of linear momentum and impulse. It defines momentum as the product of an object's mass and velocity (p=mv) and describes how momentum is a vector quantity. Impulse is defined as the change in momentum over time due to an external force (Impulse=Force x Time). The document explains how momentum is conserved in collisions and how the impulse-momentum theorem can be used to analyze collisions. It also distinguishes between perfectly elastic, perfectly inelastic, and inelastic collisions in terms of the objects' motions and changes to their kinetic energy before and after the collision.

1. Lesson 6-1
Momentum and Impulse

2. Linear Momentum
 Think of a batter hitting a baseball
 When the batter swings and makes contact, the
ball changes velocity very quickly
 We could use kinematics to study the motion of the ball
 We could use Newton’s Laws to explain why the ball
changes direction
 We are now concerned with the force and
duration of the collision

3. Momentum
 Momentum describes an object’s motion
 To describe force and duration of a collision, we
must first start with a new concept
 Momentum
 This word is used in everyday conversation, and
means about the same thing in physics

4. Momentum
 We might say a semi-truck has a large
amount of momentum
 Compared to the semi-truck, a person would
have a small amount of momentum
 Linear momentum directly relates an object’s
velocity to the object’s mass
 Momentum (P)
 P=mv

5. Momentum
 Momentum is a vector quantity, with the
vector matching the direction of the velocity
 The SI unit is kg∙m/s

6. Bowling
 If you bowl with a light ball, you have to throw
the ball pretty fast to make the pins react
 A heavier ball will allow a good pin reaction
with a lower velocity
 Because of the added mass
 Example 209
 Practice 209

7. Change in Momentum
 Recall: change in velocity takes an
acceleration and time
 If there is an acceleration, there exists a net
force
 Since P depends on velocity, ΔP requires
 Force
 Time

8. Change in Momentum
 Say there is a ball rolling on the ground
 You must use a large force to stop a fast rolling
ball
 You could use a smaller force to stop a slower
rolling ball
 Imagine catching a basketball
 A faster pass stings the hands a bit
 A softer pass causes almost no feeling

9. Newton’s Second Law
 Imagine a toy fire truck and a real fire truck sitting at
the top of a hill
 If they both begin to roll down the hill, which will have the
greater velocity?
 Recall: all objects fall due to gravity at the same rate
 But which would require the greater force to stop
 Examples like this show us that P is closely related
to force

10. Newton’s Second Law
 When Newton first wrote his second law
(F=ma), he wrote it as
F p
= D
D
t
F p
= D
D
t
F mv
t
mv
t
= = = ma

11. Impulse – Momentum Theorem
FDt = Dp F t p mv mv f i D = D = -
 This states a net external force, F, applied for a
certain time interval, Δt, will cause a change in the
object’s momentum equal to the product of the force
and time interval
 In simpler terms, a large constant force will cause a
rapid change in P
 A small constant force would take a much longer
time to cause a change in P

12. Impulse – Momentum Theorem
 The Impulse – Momentum theorem explains why
“follow through” is so important in many sports such
as baseball, basketball, and boxing
 When a baseball player hits a baseball and “follows
through” the ball is in contact much longer and the
force is applied over a greater period of time
 If the player does some sort of check swing, the
force is applied over a smaller period of time

13.  Sample 211
 Practice 211
 Sample 212
 Practice 213

14. Impulse – Momentum Theorem
 Change in momentum over a longer time
requires less force
 Engineers use the impulse – momentum theorem
to design safety equipment
 Safety gear aims to reduce the force exerted on
the body during a collision

15. Impulse – Momentum Theorem
 Think of jumping on a trampoline
 Do you think you could jump that high and land on
the ground and not get hurt?
 The impact with the ground is sudden and occurs
over a short period of time
 The impact with the trampoline is the same, but
occurs over a longer period of time
 Longer time interval = less force

16. Lesson 6-2
Conservation of Momentum

17. Billiards
 In a game of pool:
 The object ball is stationary
 The cue ball is moving
 During the collision, the object ball gains
momentum and the cue ball loses the same
amount of momentum
 The momentum of each ball changes during the
collision but total momentum remains constant

18. Conservation of Momentum
 Since the momentum of the two billiard balls
remains constant after the collision we say
momentum is conserved
P P P P Ai Bi Af Bf + = +
m1v1i m2v2i m1v1 f m2v2 f + = +

19. Conservation of Momentum
 As we just discussed, momentum is
conserved during collisions
 Momentum is also conserved when objects
push away from each other

20. Conservation of Momentum
 Imagine you stand on the ground and jump up
 It seems as if momentum is not conserved because you
leave the ground with a velocity
 Recall, the Earth does move away when you jump (a very
small distance), so total momentum is conserved in reality
 You exert a downward force on the Earth and the Earth
exerts an upward force on you
 Total momentum is ZERO

21. Conservation of Momentum
 The reason total momentum is zero when two
objects push apart is based on sign
 The objects have the same amount of
momentum
 But in opposite directions
 So when the two momentums are summed, the
result is zero

22.  Sample 218
 Practice 219

23. Relation to Newton’s Third Law
 Consider two bumper cars of mand m1 2
 FDt = Dp
describes the change in
momentum is one of the cars
 and
F t m v 1 1 1i D = F t m v 2 2 2i D =
 F1 is the force that m1 exerts on m2
 F2 is the force that m2 exerts on m1

24. Relation to Newton’s Third Law
 Since the only forces are from the two bumper cars,
Newton’s third law tells us the forces must be equal
and opposite
 Additionally, the impulse (time of collision) is equal
and opposite for both cars
 This means EVERY interaction between the two
cars is equal and opposite and can be expressed
by:
m1v1i m1v1 f m2v2i m2v2 f - = -d - i

25. Relation to Newton’s Third Law
 The equation says ‘if the momentum of one object
decreases during a collision, the momentum of
another object will increase by the same amount’
 At all times during a collision the forces are equal
and opposite
 The magnitudes and directions are constantly changing
 The value we use for force is equal to average force

26. Lesson 6-3
Elastic and Inelastic
Collisions

27. Everyday Collisions
 You see collisions everyday
 In some collisions, the objects stick together and travel as
one mass
 In another type of collision, the objects hit and bounce
apart
 In either case, total momentum is conserved
 KE is usually not conserved because some energy
is lost to heat and sound energies

28. Perfectly Inelastic Collisions
 When two objects collide and move together
as one mass, the collision is called perfectly
inelastic
 A good example of this type of collision is a
meteor hitting the Earth
 Perfectly inelastic collisions are easy to
analyze in terms of momentum because the
two objects essentially become one after the
collision

29. Perfectly Inelastic Collisions
 The final mass is equal to the combined
mass of the two objects
 The two objects travel together with one final
velocity after the collision
 Studied with the following equation:
m1v1i m2v2i m1 m2 v f + = ( + )

30. Perfectly Inelastic Collisions
 KE does not remain constant in an inelastic
collision
 KE is lost due to sound, internal energy, and
heat of fusion

31. Elastic vs Inelastic
 The phenomena of fusion helps us to
understand the difference between elastic
and inelastic collisions
 When we think of something that is elastic (a
rubber band, a bungee cord, a spring) we
think of something that returns to its original
shape
 During an elastic collision, the objects
maintain their original shapes

32. Elastic vs Inelastic
 Objects in inelastic collisions do not maintain
their original shapes as they form a new
mass after the collision
 We can calculate the loss of KE with the
conservation of KE formula
 KEnet = KEf – Kei
 Sample 225
 Practice 226

33. Elastic Collisions
 When a soccer player kicks a soccer ball, the
ball and the player’s foot remain separate
 Since there are no shape changes or
deformities, the is no change in KE
 As with any collision, total momentum is
conserved

34. In the Real World
 It should be mentioned that there is no such
thing as a perfectly inelastic or perfectly
elastic collision in the real world
 Objects do not hit into each other and fuse
together and move as one object
 Objects do not bounce off of each other
without loss of KE
 KE lost to heat, sound, deformation

35. In the Real World
 So that means that most collisions fall into a third
category called inelastic collisions (note: not
perfectly inelastic)
 This is where objects collide, make noise, give off heat, do
not stick together, and travel in another direction with
separate velocities
 These are impossible to study to complete exactness
 To study these types of collisions, we simplify things

36. Elastic Collisions
 KE is conserved in elastic collisions
 There are instances that are very, very close to
perfectly elastic collisions
 Bowling ball into bowling pins
 Golf club hitting a golf ball
 In these instances, we assume total KE and
total momentum remain constant throughout
the collision

37. Elastic Collisions
 We can study elastic collisions with the following
formulas:
m1v1i m2v2i m1v1 f m2v2 f + = +
1
2
m v m v m v m v 2 i i f f + = +
 Sample 228
 Practice 229
1
2
1
2
1
2
1 1 2 2
2
2
1 1
2
2 2