1. +
Momentum and Collisions
Chapter 8

2. +
Momentum and Impulse

3. +
What do you think?
 Imagine an automobile collision in which an
older model car from the 1960s collides with
a car at rest while traveling at 15 mph. Now
imagine the same collision with a 2007
model car. In both cases, the car and
passengers are stopped abruptly.
 List the features in the newer car that are
designed to protect the passenger and the
features designed to minimize damage to the
car.
 How are these features similar?

4. +
What do you think?
 What
are some common uses of the term
momentum?
 Write
a sentence or two using the term
momentum.
 Do any of the examples provided
reference the velocity of an object?
 Do
any of the examples reference the
mass of an object?

5. +
Momentum
 Momentum (p) is proportional to both mass and
velocity.
 A vectorquantity, so direction matters!!
 Things moving right are positive
 Tings moving left are negative
 SI Units: kg • m/s

6. +
Example
 A 2250kg pick-up truck has a velocity of
25m/s to the east. What is the momentum
of the truck?
 m= 2250kg v=25m/s east (+)
 P= mv
 P= (2250)(25)
 P= 56,250 kg • m/s

7. +
Momentum and Newton’s 2nd Law
 Provethat the two equations shown below are
equivalent.
F = ma and F = p/t
 Newton actually wrote his 2nd Law as F = p/t.
 Force
depends on how rapidly the momentum
changes.

8. +
Impulse and Momentum
The quantity F t is called impulse.
 SI units: N•m or kg•m/s
Impulse equals change in momentum.
 Another version of Newton’s 2nd Law
 Changes in momentum depend on both the
force and the amount of time over which the
force is applied.

9. +
Changing momentum
 Greater changes in
momentum (p) require
more force (F) or more
time (t) .
 A loadedtruck requires
more time to stop.
 Greater p for truck with more
mass
 Same stopping force

10. +
Movie
 file:///Volumes/Physics_mac/inquiry_ppts/f
iles/ch06/70598.html
 Put Advanced CD in to work

11. +
Example
 A 1400kg car moving westward with a velocity
of 15m/s collides with a utility pole and is
brought to rest in 0.3sec. Find the force
exerted on the car during collision.
 Given:
m=1400kg t= 0.30sec F=??
vi= 15m/s west (-) vf= 0m/s

12. +
Example
 Ft= mvf- mvi
mv f mvi
F
t
(1400)(0) (1400)( 15)
F
0.30
 F=70,000N to the east

13. +
Example
 A 2240kg car traveling west slows down
uniformly from 20m/s to 5m/s. how long
does it take the car to slow down if the
force on the car is 8410N to the east?
How far does the car travel during the
time it slows down?

14. +
Example
mv f mvi
 Given: t
F
 m= 2240kg
(2240)( 5) (2240)( 20)
 v i= 20m/s west (-) t
8410
 vf= 5m/s west (-)
 F= 8410N east (+)  t= 4 sec
 t= ?? d=??

15. +
Example
 d= ½ (vi + vf)t
 d= ½ (-20-5) 4
 d= -50 m/s or 50 m/s west

16. +
Stopping Time
 Ft = p = mv
 When stopping, p is the same for rapid or gradual
stops.
 Increasing the time (t) decreases the force (F).
 What examples demonstrate this relationship?
 Air bags, padded dashboards, trampolines, etc
 Decreasing the time (t) increases the force (F).
 What examples demonstrate this relationship?
 Hammers and baseball bats are made of hard
material to reduce the time of impact.

17. +
Conservation of Momentum

18. +
What do you think?
• Two skaters have equal mass and are at rest.
They are pushing away from each other as
shown.
• Compare the forces on the two girls.
• Compare their velocities after the push.
• How would your answers change if the girl on
the right had a greater mass than her friend?
• How would your answers change if the girl on
the right was moving toward her friend before
they started pushing apart?

19. +
Momentum During Collisions
 Thechange in momentum for one object is equal and
opposite to the change in momentum for the other object.
 Total momentum is neither gained not lost during
collisions.

20. +
Conservation of Momentum
 Total momentum remains constant during collisions.
 The
momentum lost by one object equals the
momentum gained by the other object.
 Conservation of momentum simplifies problem
solving.

21. +
Example
 A 76kg boater, initially at rest, in a
stationary 45kg boat steps out of the boat
onto the dock. If the boater moves out of
the boat with a velocity of 2.5m/s to the
right, what is the final velocity of the boat?

22. + Given
 m 1= 76kg  m 2= 45kg
 v1i= 0m/s  v2i= 0m/s
 v1f= 2.5 m/s  v2f= ??
 m1v1i + m2v2i= m1v1f + m2v2f
 (76)(0)+(45)(0)=(76)(2.5)+(45)(v2f)
 0= 190 + 45v2f
 -190 = 45v2f
 v2f= -4.2 m/s to the right but notice the negative
 v2f= 4.2 m/s to the left

23. +
Now what do you think?
• Two skaters have equal mass and are at
rest. They are pushing away from each
other as shown.
• Compare the forces on the two girls.
• Compare their velocities after the push.
• How would your answers change if the girl
on the right had a greater mass than her
friend?
• How would your answers change if the girl
on the right was moving toward her friend
before they started pushing apart?

24. +
Elastic and Inelastic Collisions

25. +
What do you think?
• Collisions are 1. A baseball and a bat
sometimes described 2. A baseball and a glove
as elastic or inelastic.
To the right is a list of 3. Two football players
colliding objects. Rank 4. Two billiard balls
them from most elastic
5. Two balls of modeling clay
to most inelastic.
6. Two hard rubber toy balls
• What factors did you
consider when ranking 7. An automobile collision
these collisions?

26. +
Collisions
 Perfectly inelastic collisions
 A collision where 2 objects stick together
after colliding
 Perfectlyinelastic collisions are analyzed
in terms of momentum
 Dueto the fact that the objects become one
object after the collision

27. +
Perfectly Inelastic Collisions
 Two objects collide and stick together.
 Two football players
 A meteorite striking the earth
 Momentum is conserved.
 Masses combine.

28. +
Perfectly Inelastic Collisions
 v1i is + (m1 is moving to the right)
 V2i is – (m2 is moving to the left)

29. +
Example
 A 1850kg luxury sedan stopped at a traffic
light is struck from the rear by a compact
car with a mass of 975kg. Te 2 cars
become entangled as a result of the
collision. If the compact car was moving at
a velocity of 22m/s to the north before the
collision, what is the velocity of the mass
after the accident?

30. +
Example
 m 2= 975kg
 m 1= 1850kg
 v2i= 22m/s north (+)
 v1i= 0m/s
 vf= ??
 m1v1i + m2v2i= (m1+ m2) vf
(1850)(0) (975)(22)
vf
1850 975
 vf= 7.59 m/s north

31. +
Classroom Practice Problem
 Gerard is a quarterback and Tyler is a
defensive lineman. Gerard’s mass is 75.0
kg and he is at rest. Tyler has a mass of
112 kg, and he is moving at 8.25 m/s
when he tackles Gerard by holding on
while they fly through the air. With what
speed will the two players move together
after the collision?
 Answer: 4.94 m/s

32. +
Classroom Practice Problems
 An 2.0 x 105 kg train car moving east at 21 m/s
collides with a 4.0 x 105 kg fully-loaded train car
initially at rest. The two cars stick together. Find
the velocity of the two cars after the collision.
 Answer: 7.0 m/s to the east

33. +
Inelastic Collisions
 Kinetic energy is less after the collision.
 It is converted into other forms of energy.
 Internal energy - the temperature is
increased.
 Sound energy - the air is forced to vibrate.
 Some kinetic energy may remain after the
collision, or it may all be lost.

34. +
Example
2 clay balls collide in a perfect inelastic
collision. The 1st ball has a mass of 0.500kg
and an initial velocity of 4.0m/s to the right.
The 2nd ball has a mass of 0.250 kg. and an
initial velocity of 3.0m/s to the left. What is the
decrease in kinetic energy during the collision?

35. +
Example
 m 1= 0.500 kg  KE=
 v1= 4m/s right (+)  KE= KEf – KEi
 m 2= 0.250kg  KEi= ½ m1v1i + m2v2i
 v2= 3m/s left (-)  KEf= ½ (m1+m2)vf2

36. +
Example
 m1v1i + m2v2i= (m1+ m2) vf
m1v1i m2v2i (0.5)(4) (0.25)( 3)
vf
(m1 m2 ) (0.5 0.25)
 vf= 1.67 m/s
 KEi= ½ (0.5)(42) + ½ (0.25)(-32)= 5.125J
 KEf= ½ (0.5 + 0.25) 1.672 = 1.05J
 KE= 1.05 – 5.125 = -4.08J
 Means that KE is lost

37. +
Elastic Collisions
 Objects collide and return to their original shape.
 Kinetic energy remains the same after the collision.
 Perfectly
elastic collisions satisfy both conservation
laws shown below.

38. +
Elastic Collisions
 Two billiard balls collide head on, as shown.
Which of the following possible final
velocities satisfies the law of conservation of
momentum?
 vf,A = 2.0 m/s, vf,B = 2.0 m/s m = 0.35 kg m = 0.35 kg
 vf,A = 0 m/s, vf,B = 4.0 m/s
 vf,A = 1.5 m/s, vf,B= 2.5 m/s
 Answer: all three
v = 4.0 m/sv= 0 m/s

39. +
Elastic Collisions
 Two billiard balls collide head on, as shown.
Which of the following possible final
velocities satisfies the law of conservation of
kinetic energy?
 vf,A = 2.0 m/s, vf,B = 2.0 m/s m = 0.35 kg m = 0.35 kg
 vf,A = 0 m/s, vf,B = 4.0 m/s
 vf,A = 1.5 m/s, vf,B= 2.5 m/s
 Answer: only vf,A = 0
m/s, vf,B = 4.0
m/s
v = 4.0 m/s v= 0 m/s

40. +
Example
 A 0.015 kg marble moving to the right at 0.225
m/s makes an elastic head on collision with a
0.030 kg shooter marble moving to the left at
0.180m/s. After the collision, the smaller
marble moves to the left at 0.315m/s. Assume
neither marble rotates at all and both marbles
are on a frictionless surface. What is the
velocity of the 0.030kg marble after the
collision?

41. + Example
 m 1= 0.015kg  m 2= 0.030kg
 v1i= 0.225m/s right (+)  v2i= 0.18m/s left (-)
 v1f= 0.315m/s left (-)  vf= ??
 m1v1i + m2v2i= m1v1f + m2v2f
 (0.015)(0.225) + (0.030)(-0.18) = (0.015)(-0.315) + (0.030)(vf)
 0.003375 + -0.0054 = -0.004725 + 0.030 vf
 -0.002025= - 0.004725 + 0.030 vf
 0.0027 = 0.030vf
 vf= 0.09 m/s right

42. +
Types of Collisions
Click below to watch the Visual Concept.
 file:///Volumes/Physics_mac/inquiry_ppts/f
iles/ch06/70600.html
 Put Advanced CD in to work

43. +
Types of Collisions

44. +
Now what do you think?
• To the right is a list of 1. A baseball and a bat
colliding objects. Rank 2. A baseball and a glove
them from most elastic
to most inelastic. 3. Two football players
4. Two billiard balls
• What factors did you
consider when ranking 5. Two balls of modeling clay
these collisions? 6. Two hard rubber toy balls
7. An automobile collision