Transcript momentum is conserved

PHYSICS 103: Lecture 14
Agenda for Today:
• Momentum and Energy
Conservation
 Newton’s cradle demo
Momentum
• Momentum is the product of mass times velocity of an
object P = m v
• Momentum is a vector quantity (same direction as v)
Units = kg m/s
NEWTON’S LAWS OF MOTION
Second LAW:
The force on an object is equal to the product of
that object’s mass times its acceleration. The
acceleration is in the same direction as the force.
F=m.a
a = Dv/Dt
F = m . Dv/Dt
F . Dt = m . Dv
Impulse =F . Dt
Dp = m . Dv
Change in “momentum”
NEWTON’S LAWS OF MOTION
Third LAW:
For every force that one object exerts on a
second object, there is an equal but oppositely
directed force that the second object exerts on
the first object.
(For every action there is an equal but opposite reaction)
F . Dt = m . Dv
If the external force acting on a system of objects is zero, the
total momentum is conserved.
CONSERVATION OF MOMENTUM
During a collision, there are no external forces, so
momentum is conserved.
This means: total momentum before collision = total
momentum after collision
Types of Collisions
• Elastic
- no kinetic energy is lost during collisions
(things bounce off each other)
• Partially
Inelastic
- some kinetic energy is lost during
collisions
• Perfectly
Inelastic
- objects stick together
Class Demo: Example of Elastic Collisions
Behavior: Number of balls in always equals the number of balls out.
What accounts for the behavior of this system of swinging balls?
How high up will the struck ball go?
h
Behavior of balls is consistent with conservation of momentum
Total momentum before collision: mv = 0+0+0+0+mv
Total momentum after collision: mv = mv+0+0+0+0
Other possibilities also conserve momentum
2 balls in, one ball out
Momemtum before collision: 2mv = 0+0+0+(2m)v
Momentum after collision: 2mv = m(2v)+0+0+0+0
momentum is conserved
Other possibilities also conserve momentum
2 balls in, 4 balls out
Momentum before collision: 2mv = 0+0+0+(2m)v
Momentum after collision 2mv = (4m)(0.5v)+0
momentum is conserved
What Physics are we missing?
Energy Conservation
Elastic collision
KE is conserved
Case: two balls in, one ball out with twic the speed
Energy is not conserved! There is only one case where
BOTH energy and momentum are conserved
Main Points from Today’s Lecture
• Momentum
You should understand impulse, momentum,
conservation of momentum in different kinds of
collisions. You should review the example problems in
this lecture.
Read Ch. 7
HW
CH7:
Q2,Q6,Q8,Q9,Q17,E2,E9,E10,CP5 (for
next week)