PHYS16 – Lecture 19
Ch. 9 Momentum and Collisions
Announcements
• Meet in parking lot behind Merrill on
Wednesday!
• We will do a demo then come back to class…
Energy Post-question
• Two balls have the same mass. Ball 1 is thrown
upward at 3 m/s and Ball 2 is thrown
downward with 3 m/s. Which Ball reaches the
ground with more kinetic energy?
A)
B)
C)
D)
Ball 1
Ball 2
Both balls have the same kinetic energy
There is not enough information
Energy Post-question
• If a car engine for a 1400 kg car outputs 1000 kW
of average power, how much time does it take to
accelerate from 0 to 25 m/s?
A)
B)
C)
D)
E)
0.4 s
1s
0.2 s
0.8 s
10 s
Energy Post-question
• The potential energy, U (x), is shown as a
function of position, x, in the figure. In which
region is the magnitude of the force the
highest?
A)
B)
C)
D)
Energy Post-question
• Clyde, the dinosaur, is sick of his doll-sized roller coaster
and decides to ride the 20-m tall roller coaster at Ohio’s
Cedar Point. Since Clyde is a little scared he decides to start
from a location on the track that is 10 m lower than the
top. How does Clyde’s speed at the bottom compare to a
rider that started from the top of the hill?
A) It is slower by a factor of 4.
B) It is slower by a factor of 2√2.
C) It is slower by a factor of 2.
D) It is slower by a factor of √10
E) None of the above
Ch. 9 Momentum & Collisions
• Linear Momentum
– Related to Newton’s second law
– Rocket Propulsion
• Momentum Conservation
• Collisions
– Elastic vs. Inelastic
– 1D and 2D
• Impulse
Momentum
• Momentum = mass times velocity


p  mv
– ↑ mass , then ↑ momentum
– ↑ velocity, then ↑ momentum
• Vector quantity
• Units are (kg∙m/s)
Discussion Question
• If two objects have the same inertia, do they
have the same momentum?
• Two cars of equal mass are traveling around a
round-a-bout. If object 1 has twice the
momentum of object 2, what is the ratio of
the centripetal force acting on each? What
about the ratio of their kinetic energies?
• If we have inertia and kinetic energy, why do
we need momentum?
1. Momentum and Newton’s Second Law
• In Newton’s second law F≠ ma!
 dp d

F
 mv 
dt dt

 dm 
dv
v   m 
F
dt
dt
 dm 

v   ma 
F
dt
Rockets…
http://exploration.grc.nasa.gov/education/rocket/gallery/delta/DeltaII.jpg
http://www.youtube.com/watch?v=CAAhQ6xcAnw
2. Momentum Conservation
• According to Newton’s third law momentum is
conserved in an isolated system


Faction   Freaction


Faction  Freaction  0


paction preaction

0
t
t


paction  preaction  0


pobject1  pobject2  0
Medicine Ball and Skateboard…
University of Maryland Physics Demo Facility
Elastic and Inelastic Collisions
• Perfectly Elastic – no losses due to the interaction
– Objects bounce perfectly off one another
– Ex. pool balls, gliders on air track
• Inelastic – there are losses
– Objects don’t perfectly bounce
– Ex. basketball hitting ground
• Perfectly Inelastic – objects adhere
– Ex. clay ball with floor
Conservation Laws
• Perfectly Elastic – both momentum and
energy conserved
• Inelastic – only momentum conserved
• Perfectly Inelastic – only momentum
conserved
Conclusions
• Momentum


p  mv
• Momentum Conservation

p  0
• Elastic vs. Inelastic Collisions