2. Chapter 6: Momentum and Collisions
6.1 Linear Momentum
6.2 Impulse
6.3 The Conservation of Linear Momentum
6.4 Elastic and Inelastic Collisions
6.5 Center of Mass
5. Loosen Up! II
Impulse is found by multiplying the force acting on an object by the amount of time
the force acts. The amount of impulse that an object experiences is equal to the
amount that its momentum changes. This means that the same change in
momentum can be accomplished by exerting a large force for a short amount of
time or a small force for a longer amount of time.
Seat belts are designed to give a little when they are properly fastened. If not, they
would not work as well at keeping you from injury in an accident or sudden stop.
Use the concept of impulse equaling the change in momentum to explain why they
need to give.
Physics Daily WarmUps # 91
Solution: The time to bring a person to stop is
increased, thereby decreasing the force exerted
on the person by the belt.
6.
7. 6.1 Linear Momentum
• The SI unit of momentum is the kg∙m/s.
• The total linear momentum of a system is the vector sum of the momenta of
the individual particles.
p = p1 + p2 + p3 + … = ∑ pi
i
8. 6.1 Linear Momentum
Example 6.1: Which has more linear momentum:
a) a 1500 kg car moving at 25.0 m/s or
b) a 40,000 kg truck moving at 1.00 m/s?
9. 6.1 Linear Momentum
Example 6.2: Two identical 1500 kg cars are moving perpendicular to each
other. One moves with a speed of 25.0 m/s due north and the other moves at
15.0 m/s due east. What is the total linear momentum of the system?
15. 6.2 Impulse
● In fact, Newton used the momentum form of his second law when he first started
formatting the law.
● For a system in which mass is not a constant, such as rocket propulsion, the
momentum form should be used.
16. 6.2 Impulse
Example 6.3: A 0.10 kg ball is dropped onto a table top. The speeds of the ball
right before hitting the table top and right after hitting the table top are 5.0 m/s and
4.0 m/s respectively. If the collision between the ball and the tabletop lasts 0.15 s,
what is the average force exerted on the ball by the table top?
25. Collision Conservation
Momentum is always conserved in any collision, as is energy. However, energy
usually transformed into several different types as a result of the collision. In most
collisions, a significant amount of the kinetic energy is converted into other forms,
and the colliding objects’ movements are greatly affected. These are called inelastic
collisions. There are some collisions, like the colliding steel balls suspended by strings
in a Newton’s Cradle, in which kinetic energy is almost conserved. Since so little
energy is lost in each collision, they seem to just go on bouncing. These collisions
represent elastic collisions.
Elastic collisions always seem to catch our attention. Because they are so rare, they
seem unusual to us. Write down a personal experience where you witnessed an
elastic collision.
Physics Daily WarmUps # 97
28. Momentum is conserved in an isolated system. The motion in two
dimensions may be analyzed in terms of the components of momentum,
which is also conserved.
If m1 and m2 are equal, they will split apart at a
90 degree angle.
29. Conservation of Momentum
a) Before the rifle is fired, the total momentum of the rifle and the bullet is zero.
b) During firing, there are equal and opposite internal forces, and the
instantaneous total momentum of the rifle-bullet system remains zero.
c) When the bullet leaves the barrel, the total momentum of the system is still
zero.
30. 6.3 The Conservation of Linear Momentum
Example 6.4: A 50 kg pitching machine (excluding the baseball) is placed on a
frozen pond. The machine fires a 0.40 kg baseball with a speed of 35 m/s in the
horizontal direction. What is the recoil velocity of the pitching machine? (Assume
negligible friction.)
31. 6.3 The Conservation of Linear Momentum
Example 6.5: A 10 gram bullet moving at 300 m/s is fired into a 1.0 kg block. The
bullet emerges (does not stay embedded in the block) with half of its original
speed. What is the velocity of the block right after the collision?
40. Inelastic collisions
• In inelastic collisions, momentum is conserved but kinetic energy is not.
• Collisions like the ones shown here, in which the objects stick together , are
called completely inelastic collisions.
• The maximum amount of kinetic energy lost is consistent with the conservation
of momentum.
6.4 Elastic and Inelastic Collisions
41. 6.4 Elastic and Inelastic Collisions
Example 6.6: While standing on skates on a frozen pond, a student of mass 70.0 kg
catches a 2.00 kg ball travelling horizontally at 15.0 m/s toward him.
a) What is the speed of the student and the ball immediately after he catches it?
b) How much kinetic energy is lost in the process?
42. 6.4 Elastic and Inelastic Collisions
Example 6.7: A rubber ball with a speed of 5.0 m/s collides head on elastically with
an identical ball at rest. Find the velocity of each object after the collision.
43. 6.4 Elastic and Inelastic Collisions: Check for Understanding
44. 6.4 Elastic and Inelastic Collisions: Check for Understanding
45. 6.4 Elastic and Inelastic Collisions: Check for Understanding
46. 6.4 Elastic and Inelastic Collisions: Check for Understanding
47. 6.4 Elastic and Inelastic Collisions: Check for Understanding
48. 6.4 Elastic and Inelastic Collisions: Check for Understanding
49. 6.4 Elastic and Inelastic Collisions: Check for Understanding
50. 6.4 Elastic and Inelastic Collisions: Check for Understanding
51. 6.4 Elastic and Inelastic Collisions: Check for Understanding
55. 6.5 Center of Mass
• The center of mass of a system is the point at which all the mass of the
system may be considered to be concentrated.
• If the acceleration due to gravity, g, is a constant, then the center of
gravity, or the point at which al the weight of the system may be concentrated,
is at the center of mass.
• The conservation of momentum allows us to analyze a system of particles;
the system can be replaced by an equivalent single particle at the center of
mass.
• The motion of the center of mass also obeys Newton’s second law,
Fnet = ma.
• If the net external force on a system is zero, the total linear momentum of
the center of the mass stays constant (or zero).
56. 6.5 Center of Mass
How can you find the center of mass (or center of gravity) of an object?
1) Symmetry (the center of the object)
2) Mathematically (beyond the scope of this course)
3) Experimentally (by suspension)
