ilm lesson on conservation of momentum

1. 1. Explain how momentum is conserved.
2. Show how momentum before and after collision is
equal.

2. Arrange the letters to form
a comprehensible word.

3. IMPULSE

4. MOMENTUM

5. VELOCITY

6. MASS

7. FORCE

8. IMPULSE is a measurement of mass
in motion
MOMENTUM is a term that quantifies
the overall effect of a force
acting over time

9. IMPULSE is a term that quantifies
the overall effect of a force
acting over time
MOMENTUM is a measurement of mass
in motion

26. If the balloon has
momentum in one direction,
the air must have an equal
and opposite momentum for
the total momentum to
remain zero.

27. Change in momentum = 0
Total Initial Momentum = Total Final Momentum
0 = pballoon+ pair
-pballoon = pair
-(mv)balloon = -(mv)air
Since the mass of the balloon is
greater than the mass of air, the velocity
of the air must be greater in magnitude
than the velocity of the balloon, and
must be opposite in direction.

28.  Suppose the entire world
population gathers in
one spot and at the
sounding of a
prearranged signal,
everyone jumps up.
While all the people are
in the air, does Earth
gain momentum in the
opposite direction?

29.  Take note that we should consider
Earth and the people on it to be
part of system for the total
momentum to be conserved.
 The Earth also moves in the
opposite direction.
 The change in momentum of the
Earth is equal to that of the people
but opposite in direction.
 Because of Earth’s large inertial
mass, however, there is no
perceptible change in motion.

30.  Two ice skaters stand
together. They “push off” and
travel directly away from
each other, the boy with a
velocity of 1.50 m/s. If the
boy weighs 735 N and the
girl, 490 N, what is the girl’s
velocity after they push off?
(Consider the ice to be
frictionless.)

31. Solution:
Remember that W = mg, thus,
m = W/g.
MASS VELOCITY
Boy 75 kg 1.50 m/s
Girl 50 kg ?

32. 0 = pboy+ pgirl
-pboy = pgirl
-(mv)boy = (mv)girl
-37.5 kg m/s = 50 kg (vgirl)
-0.75 m/s = vgirl

33.  Momentum is a vector quantity. It must
have both magnitude (numerical value)
and direction. The direction of the
momentum vector is always in the same
direction as the velocity vector. Like all
vector quantities, momentum vectors
can be added. For situations in which
the two vectors are in opposite
directions, one vector is considered
negative and the other positive.

34.  Two ice skaters stand
together. They “push off” and
travel directly away from
each other, the boy with a
speed of 0.50 m/s and the
girl with a speed of 0.65 m/s.
If the mass of the boy is 60
kg, what is the girl’s mass?
(Consider the ice to be
frictionless.)

35. Total Initial Momentum = Total Final Momentum
0 = pboy+ pgirl
-pboy = pgirl
-(mv)boy = (mv)girl
30.0 kg m/s = (mgirl) 0.65 m/s
46kg = mgirl

36. Two adjacent students stand on
stationary skateboards, face
each other, and push apart. The
skateboarder on the left weighs
65 kg, the one on the right is 85
kg. If the lighter skateboarder
moves at 3.2 m/s, determine the
speed and direction of the
heavier skateboarder.

37. As an assignment, list 3 ways by
which knowledge of
conservation of momentum can
benefit you.

38. A collision is an encounter between two
objects resulting in exchange of impulse and
momentum. Because the time of impact is
usually small, the impulse provided by
external forces like friction during this time
is negligible. If we take the colliding bodies
as one system, the momentum of the system
is therefore approximately conserved.

39. The total momentum of the system
before the collision is equal to the total
momentum of the system after the
collision.
total momentum before collision = total momentum after collision

40. The total momentum of the system
before the collision is equal to the total
momentum of the system after the
collision.
total momentum before collision = total momentum after collision

41. Collisions are categorized according to whether
the total kinetic energy of the system changes.
Kinetic energy may be lost during collisions
when
(1) it is converted to heat or other forms like
binding energy, sound, light (if there is
spark), etc. and
(2) it is spent in producing deformation or
damage, such as when two cars collide.

42. The two types of collision are:
1. Elastic collision – one in which the total
kinetic energy of the system does not change
and colliding objects bounce off after collision.
2. Inelastic collision – one in which the total
kinetic energy of the system changes (i.e.,
converted to some other form of energy).
Objects that stick together after collision is said
to be perfectly inelastic.

47. In the Figure, a moving steel ball
pendulum collides head-on with another
steel ball. The collision is elastic, that is,
the total kinetic energy of the system (2
steel balls) is the same before and after
the collision.

48. The total momentum of the system
before the collision is equal to the
product of the first ball’s mass and
velocity. The total momentum of the
system after the collision must be equal to
the total momentum before the collision.

49. The first ball comes to rest while the second ball
moves away with a velocity equal to the velocity of
the first ball. This is the case when the two balls
have equal masses. The momentum of the first
ball is transferred to the second ball. The first ball
loses its momentum while the second ball gains
momentum equal to that of the first ball’s
momentum

50. What do you think would happen if you
pull two balls away and release them at
the same time?
Why is it so?

51. Mass
Velocity
(before collision)
Cart 1 0.30 kg 1.2 m/s
Cart 2 0.50 kg 0

52. Mass
Velocity
(before collision)
Cart 1 0.30 kg 1.2 m/s
Cart 2 0.50 kg 0

53. Mass
Velocity
(before collision)
Cart 1 0.30 kg 1.2 m/s
Cart 2 0.50 kg 0

54. Since the two carts stuck together
after collision, they have the same
velocity after collision. The combined
carts move at 0.45 m/s after the
collision.