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Phys.
121:
Thursday,
16
Oct.
Reading: Finish ch. 12.
Written HW 8: due Tuesday.
Mastering Phys.: Sixth assign. due by midnight.
Assign. 7 now up and due in one week.
Extra credit problems now available.
Exam 1: I will add 1 pt. (curve) to score shown.
Written problems (9 and 10) may be re-worked for
half the credit back if you missed more than 0.1 on
them; go to an OSL tutor by next Monday, then
bring the corrected problems AND exam back to me.
Exam 2: will cover chapters 7, 8, 10, and 11, and
will most likely be the week after next.
Reading Question 9.4
Clickers: The total momentum of a system is
conserved...
A.
B.
C.
D.
Always.
If the system is isolated.
If the forces are conservative.
Never; it’s just an approximation.
Law of Conservation of Momentum
 An isolated system is a system for
which the net external force is zero:
 For an isolated system:
 Or, written mathematically:
Clickers:
The two boxes are on a frictionless surface. They had
been sitting together at rest, but an explosion between
them has
just pushed them apart. How
fast is the 2 kg box going?
A. 1 m/s.
B. 2 m/s.
C. 4 m/s.
D. 8 m/s.
E. There’s not enough information to tell.
Clickers: 9.3
A 2.0 kg object moving to the
right with speed 0.50 m/s
experiences the force shown. What
are the object’s speed and direction
after the force ends?
A.
0.50 m/s left.
B. At rest.
C.
0.50 m/s right.
D. 1.0 m/s right.
E.
2.0 m/s right.
Clickers:
A force pushes the cart for 1 s, starting from rest. To achieve the
same speed with a force half as big, the force would need to
push for
A.
B.
1
4
1
2
s.
s.
C. 1 s.
D. 2 s.
E. 4 s.
Clickers: Which of the following statements
is true for an inelastic collision?
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a) Total momentum is not conserved.
b) Total energy is not conserved.
c) Kinetic energy is gained.
d) Kinetic energy is lost.
e) The Socorro Warm Springs are famous for
having a unique species of trilobite living in them.
Collisions: Elastic vs. Inelastic
• Energy is always conserved in collisions! But sometimes
it takes other forms (heat, sound) besides kinetic or
potential energy.
• In an Elastic Collision, the kinetic energy of the objects
is conserved also. (Example: drop a ball onto the floor
which bounces ALL the way back up.)
• In a Totally Inelastic Collision, the objects stick together
after colliding. (Example: drop a lump of clay onto the
floor which sticks without bouncing at all.)
• Most collisions are neither perfectly elastic nor inelastic
(most dropped balls will bounce back to only part of their
original height).
Strategy for collision problems:
• Always conserve total momentum of colliding objects!
Special case: if one object is VERY much more massive
than the other (a brick wall or the Earth versus a pingpong ball, for example), then treat the massive object as
fixed in place instead.
• If perfectly elastic, use conservation of kinetic energy to
solve for the final velocities. If perfectly inelastic,
assume that the objects stick together and only use
momentum conservation to solve for final velocities (or
masses or other unknowns).
Let's work this out again, CAREFULLY...
Example: find the final velocity of
each block after all (elastic) collisions are
over.
m
2m
m
Example: find the final velocity of
each block after all (elastic) collisions are
over.
m
2m
m
[Clickers: While moving inventory at the gym,
you drop several balls toward the floor. Can any
of these ever bounce back to higher than their
original height, if they were dropped from rest?]
a) Yes; physics will allow it.
 b) No: that's magic and only works
for Harry Potter.
 c) Ask again when it's not 49ers
week, and maybe I will care then.

Example (Astro-Blaster): Two balls are dropped
from a height h, and bounce elastically off each
other and the floor. Find the maximum height
that the top ball rebounds to if it has much less
mass than the bottom ball.
(Chapter 12:) Definition of the center of mass:
The center of mass is used a lot in physics! For
instance, the weight of an object acts like it points
downward from the center of mass (for instance,
remember the front-wheel-drive problem: 70 percent
of the normal force was on the front tires, because the
center of mass was close to the front tires).
The center of mass is where you can balance an
extended object. In force diagrams, it's as if the
entire object's weight acts “at” the center of mass.
P
total
=
p=
i
m v=M
v
i i
total CM
Total momentum P is total mass times velocity
of the center of mass... this gives:
Only external forces, which come from things
you're not keeping track of in the total momentum,
can change the total momentum.
Example with no external force: Ptotal = 0!
But things can still happen anyway...
External force (gravity): CM moves in a parabola