Download Principles and Problems Chapter 9 Linear

Lecture Outlines
Chapter 9
Physics: Principles and
Problems
Chapter 9
Linear Momentum and
Collisions
Units of Chapter 9
Linear Momentum
Impulse
Conservation of Linear Momentum
Elastic and Inelastic Collisions
Center of Mass
Jet Propulsion and Rockets
6.1 Linear Momentum
Definition of linear momentum:
The linear momentum of an object is the product of
its mass and velocity.
Note that momentum is a vector—it has both
a magnitude and a direction.
SI unit of momentum: kg • m/s. This unit has
no special name.
6.1 Linear Momentum
For a system of objects, the total momentum
is the vector sum of each.
6.1 Linear Momentum
The change in momentum is the difference
between the momentum vectors.
6.1 Linear Momentum
If an object’s momentum changes, a force
must have acted on it.
The net force is equal to the rate of change of
the momentum.
6.2 Impulse
Impulse is the change in momentum:
Typically, the force
varies during the
collision.
6.2 Impulse
Actual contact times may be very short.
6.2 Impulse
When a moving object stops, its impulse
depends only on its change in momentum. This
can be accomplished by a large force acting for
a short time, or a smaller force acting for a
longer time.
6.2 Impulse
We understand this instinctively—we bend
our knees when landing a jump; a “soft”
catch (moving hands) is less painful than a
“hard” one (fixed hands).
This is how airbags work—they slow down
collisions considerably—and why cars are
built with crumple zones.
6.3 Conservation of Linear
Momentum
If there is no net force acting on a system, its
total momentum cannot change.
This is the law of conservation of momentum.
If there are internal forces, the momenta of
individual parts of the system can change, but
the overall momentum stays the same.
6.3 Conservation of Linear
Momentum
In this example, there is no external force, but
the individual components of the system do
change their momenta:
6.3 Conservation of Linear
Momentum
Collisions happen quickly enough that any
external forces can be ignored during the
collision. Therefore, momentum is conserved
during a collision.
6.4 Elastic and Inelastic Collisions
In an elastic
collision, the total
kinetic energy is
conserved.
Total kinetic energy
is not conserved in
an inelastic
collision.
6.4 Elastic and Inelastic Collisions
A completely inelastic
collision is one where the
objects stick together
afterwards.
6.4 Elastic and Inelastic Collisions
The fraction of the total kinetic energy that is
left after a completely inelastic collision can
be shown to be:
6.4 Elastic and Inelastic Collisions
For an elastic collision, both the kinetic
energy and the momentum are conserved:
6.4 Elastic and Inelastic Collisions
Collisions may take
place with the two
objects approaching
each other, or with
one overtaking the
other.
6.5 Center of Mass
Definition of the center of mass:
The center of mass is the point at which all of the
mass of an object or system may be considered to be
concentrated, for the purposes of linear or
translational motion only.
We can then use Newton’s second law for the
motion of the center of mass:
6.5 Center of Mass
The momentum of the center of mass does
not change if there are no external forces on
the system.
The location of the center of mass can be
found:
This calculation is straightforward for a
system of point particles, but for an
extended object calculus is necessary.
6.5 Center of Mass
The center of mass of a flat object can be
found by suspension.
6.5 Center of Mass
The center of mass may be located outside a
solid object.
6.6 Jet Propulsion and Rockets
If you blow up a balloon and then let it go,
it zigzags away from you as the air shoots
out. This is an example of jet propulsion.
The escaping air exerts a force on the
balloon that pushes the balloon in the
opposite direction.
Jet propulsion is another example of
conservation of momentum.
6.6 Jet Propulsion and Rockets
This same phenomenon explains the
recoil of a gun:
6.6 Jet Propulsion and Rockets
The thrust of a rocket works
the same way.
6.6 Jet Propulsion and Rockets
Jet propulsion can be used to slow a rocket
down as well as to speed it up; this involves
the use of thrust reversers. This is done by
commercial jetliners.
Summary of Chapter 6
Momentum of a point particle is defined as
its mass multiplied by its velocity.
The momentum of a system of particles is
the vector sum of the momenta of its
components.
Newton’s second law:
Summary of Chapter 6
Impulse–momentum theorem:
In the absence of external forces,
momentum is conserved.
Momentum is conserved during a collision.
Kinetic energy is also conserved in an
elastic collision.
Summary of Chapter 6
The center of mass of an object is the point
where all the mass may be considered to be
concentrated.
Coordinates of the center of mass: