Transcript Momentum and Energy

Chapter 6: Momentum
and Collisions
Objectives
• Understand the concept of momentum.
• Use the impulse-momentum theorem to solve
problems.
• Understand how time and force are related in
collisions.
Momentum
momentum: inertia in motion;
the product of mass and velocity
p=m·v
How much momentum does a
2750 kg Hummer H2 moving at
31 m/s possess?
Note: momentum is a vector; units are kg·m/s
Impulse Changes Momentum
Newton actually wrote his second law in this form:
SF · Dt = m · Dv
The quantity SF·Dt is called impulse.
The quantity m·Dv represents a change in momentum.
Thus, an impulse causes
a change in momentum
SF·Dt = m·Dv = Dp
“impulse-momentum theorem”
SF
Highway Safety and Impulse
SF = (m · Dv) / Dt
Seatbelts and
airbags also
increase the
stopping time
and reduce the
force of impact.
Water-filled highway
barricades increase
the time it takes to stop
a car. Why is this safer?
They reduce the force
during impact!
Impulse Problem
A car traveling at 21 m/s hits a
concrete wall. If the 72 kg
passenger is not wearing a
seatbelt, he hits the
dashboard and stops in 0.13 s.
• What is the Dp?
• How much impulse is
applied to the passenger?
• How much force does the
dashboard apply to the
passenger?
What is the force
applied to the
passenger if he is
wearing a seatbelt
takes 0.62 s to stop?
Impulse Problem
The face of a golf club applies an average force of
5300 N to a 49 gram golf ball. The ball leaves the
clubface with a speed of 44 m/s. How much time is
the ball in contact with the clubface?
SF·Dt = m·Dv
SF
Bouncing
Which collision involves more force: a ball bouncing
off a wall or a ball sticking to a wall? Why?
The ball bouncing because there is a greater Dv.
SF · Dt = m · Dv
so
SF ~ Dv
Pelton wheel
Objectives
• Understand the concept of conservation of
momentum.
• Understand why momentum is conserved in
an interaction.
• Be able to solve problems involving collisions.
Conservation of Momentum
conservation of momentum: in any interaction (such
as a collision) the total combined momentum of the
objects remains unchanged (as long as no external
forces are present).
system: all of the objects involved in an interaction
system
Conservation
of
Momentum
ma·vai + mb·vbi = Spi
mb
ma
vai
-Dp = -SF · Dt -SF
vbi
+SF Dp = +SF · Dt
Dt
DpTOTAL = ( -SF·Dt ) + ( +SF·Dt ) = 0
ma·vaf + mb·vbf = Spf
ma
mb
vaf
vbf
S pi = S pf
Law of Conservation
ma·vai + mb·vbi = ma·vaf + mb·vbf
of Momentum:
Slingshot Manuever
The spacecraft is pulled
toward Jupiter by gravity,
but as Jupiter moves along
its orbit, the spacecraft just
misses colliding with the
planet and speeds up.
Jupiter
S pi = S pf
The spacecraft substantially
increased its momentum
(as speed) and Jupiter
lost the same amount
of momentum, but because
Jupiter is so massive,
its overall speed remained
virtually unchanged.
Conservation of Momentum Problem
A 0.85 kg bocce ball rolling at 3.4 m/s hits a stationary 0.17 kg
target ball. The bocce ball slows to 2.6 m/s. How fast does
the target ball (“pallino”) move? Assume all motion is in one
dimension.
ma·vai + mb·vbi = ma·vaf + mb·vbf
Objectives
• Understand the difference between elastic
and inelastic collisions.
• Solve problems involving conservation of
momentum during an inelastic collision.
Collisions
• elastic: objects collide and rebound,
maintaining shape
• both KE and p are conserved (DEMO—
Newton spheres)
• perfectly inelastic: objects collide, deform,
and combine into one mass
• KE is not conserved (becomes sound, heat,
etc.)
• real collisions are usually somewhere in
between
Types of Collisions
elastic
ma·vai + mb·vbi = ma·vaf + mb·vbf
perfectly inelastic
ma·vai + mb·vbi = (ma+ mb) ·vf
Conservation of Momentum Problem
Victor, who has a mass of 85 kg, is trying to make a
“get-away” in his 23-kg canoe. As he is leaving the
dock at 1.3 m/s, Dakota jumps into the canoe and sits
down. If Dakota has a mass of 64 kg and she jumps
at a speed of 2.7 m/s, what is the final speed of the
the canoe and its passengers?
Conservation of Momentum
in Two-Dimensions
Collisions in 2-D
involve vectors.
paf
ma
initial
ma
Spi
final
mb
mb
pbf
Equal Mass Collision
A cue ball (m = 0.16 kg) rolling at 4.0 m/s hits a stationary
eight ball of the same mass. If the cue ball travels 25o
above its original path and the eight ball travels 65o below
the original path, what is the speed of each ball after the
collision?
Unequal Mass Collision
A 0.85 kg bocce ball rolling at 3.4 m/s hits a stationary 0.17 kg
target ball. The bocce ball slows to 2.8 m/s and travels at a
15o angle above its original path. What is the speed of the
target ball it travels at a 75o below the original path?