Transcript Momentum

Momentum
the quantity of motion
§ 8.1–8.2
What’s the point?
• Nature keeps careful account of
momentum.
Think Question
Which process will require more time?
A.
B.
C.
Pulling as hard as you can to accelerate a little red
wagon from rest to a speed of 1 m/s.
Pulling as hard as you can to accelerate a horse trailer
from rest to a speed of 1 m/s.
The two take the same amount of time.
Think Question
Which process will require more force?
A.
B.
C.
Accelerating a little red wagon from rest to a speed of
1 m/s in ten seconds
Accelerating a horse trailer from rest to a speed of
1 m/s in ten seconds.
The two take the same force.
Impulse
Effect of a force over time
Impulse = FDt
where
F Is net force
Dt is duration
Impulse is a vector.
Think Question
Two objects of different masses move at the
same velocity. Which one is harder to stop?
A. The light object.
B. The massive object.
Think Question
Two objects with the same mass move
different speeds. Which one is harder to
stop?
A. The fast object.
B. The slow object.
Momentum
Formula
p = mv
momentum is a vector.
Whiteboard Work
Prove that when a net force F is applied to
an object of mass m for a time Dt, its change
in momentum is
Dp = FDt
Impulse–Momentum Theorem
• Impulse = FDt.
• FDt = maDt = mDv
• So FDt = D(mv) = change in momentum
Newton’s second law
As Newton had it:
dp
F=
dt
Poll Question
Which changes its momentum the most?
A. A moving object that stops when it hits a
barrier.
B. A moving object that bounces back from
a barrier.
Hints: Momentum is a vector.
Which receives the greater impulse?
Rebound and Momentum
final p – initial p
initial p
final p
Dp
final p – initial p
initial p
final p = 0
Dp
Poll Question
Which changes its kinetic energy the most?
A. A moving object that stops when it hits a
barrier.
B. A moving object that bounces back from
a barrier.
Hints: Kinetic energy is a scalar.
Which has the greater net work done?
Conservation of Momentum
Here today, somewhere tomorrow
§ 8.2
Poll Question
If a 0.25-g insect collides with a 1250-kg
compact car, which experiences the greatest
impulse in the collision?
A.
B.
C.
D.
The insect.
The car.
It’s a tie.
Insufficient information to answer.
Hint: Remember Newton’s third law.
Poll Question
If a 0.25-g insect collides with a 1250-kg
compact car, which experiences the greatest
momentum change in the collision?
A.
B.
C.
D.
The insect.
The car.
It’s a tie.
Insufficient information to answer.
Hint: Remember the impulse-momentum theorem.
Conservation of Momentum
• Newton’s first law:
– no outside force
– no change in v
– thus no change in p
• So an isolated object’s momentum never
changes.
Conservation of Momentum
• Newton’s third law:
– interacting objects apply equal and opposite
impulses to each other
– they experience equal and opposite
momentum changes
• So the sum of their momenta remains the
same.
• ∑pi = ∑pf
Conservation of Momentum
The total momentum of an isolated
system never changes.