Download File - IBT LUMHS

Lecture no 17&18
Conservation of Momentum
Prepared by
Engr.Sarfaraz Khan Turk
Lecturer at IBT LUMHS Jamshoro
Momentum
• In classical mechanics, linear momentum or
translational momentum (pl. momenta; SI unit
kg m/s, or equivalently, N s) is the product of the
mass and velocity of an object. For example, a
heavy truck moving fast has a large momentum—it
takes a large and prolonged force to get the truck up
to this speed, and it takes a large and prolonged
force to bring it to a stop afterwards. If the truck were
lighter, or moving more slowly, then it would have
less momentum.
• Like velocity, linear momentum is a vector quantity,
possessing a direction as well as a magnitude:p=mv
Momentum
• Linear momentum is also a conserved quantity, meaning
that if a closed system is not affected by external forces,
its total linear momentum cannot change. In classical
mechanics, conservation of linear momentum is implied
by Newton's laws; but it also holds in special relativity
(with a modified formula) and, with appropriate
definitions, a (generalized) linear momentum
conservation law holds in electrodynamics, quantum
mechanics, quantum field theory, and general relativity.
Conservation of Momentum
Conservation on Momentum
• In the absence of an external force the
momentum of a closed system is
conserved.
Law of Conservation of Momentum
In a closed system, the vector
sum of the momenta before and
after an impact must be equal.
Before
After
m1v1 +m2v2 = m1v1’ + m2v2’
Closed System:
• A system that has no gain nor loss of mass.
Isolated System:
• A closed system with no net external force
acting on it.
Internal and External Forces
• Internal Forces: act between objects
within a system.
• External Forces: are exerted by objects
outside the system.
• A stationary firecracker
explodes. What Question
is the
total momentum of the
pieces that it breaks
into?
Coyle ,4th of July 2009, Hudson River
Example: Recoiling Cannon
Example 1: Recoiling Cannon
A cannon of mass 750kg shoots a cannon
ball of mass 30kg with a velocity of 20m/s.
Find the recoil velocity of the cannon.
m1v1 +m2v2
Answer: -0.8m/s
=
m1v1’ + m2v2’
Collisions
• Elastic (Kinetic Energy is conserved)
• Inelastic (Kinetic Energy is not
conserved)
• Deformed objects
• Objects stick together
• Note: Momentum is conserved in both
types of collisions.
Example 2: Inelastic Collision
• A bullet of mass 0.010kg is shot at a
speed of 30m/s towards a 5kg stationary
block. The bullet becomes embedded in
the block an the two fly off together.
• Find the speed with which they fly off.
Answer: 0.06m/s
Problem 3
• A 45 kg student is riding on a 7kg
scateboard with a velocity of +4m/s. The
student jumps of the cart with a velocity of
-1m/s. Find the velocity of the scateboard
after the student jumped off.
• Answer: +36m/s