Transcript Physics 106P: Lecture 1 Notes

Physics 101: Chapter 7
Impulse and Momentum

Today’s lecture will cover Textbook Sections 7.1 - 7.5
UB, Phy101: Chapter 7, Pg 1
UB, Phy101: Chapter 7, Pg 2
UB, Phy101: Chapter 7, Pg 3
Demo: change in momentum
UB, Phy101: Chapter 7, Pg 4
Chapter 7, Preflight
Two identical balls are dropped from the same height onto the floor. In
case 1 the ball bounces back up, and in case 2 the ball sticks to the
floor without bouncing. In which case is the impulse given to the ball by
the floor the biggest? [See conceptual example 3]
1. Case 1
correct
2. Case 2
3. The same
The impulse-momentum theory says that the impulse
that acts on an object is given by the change in the
momentum of the object, and this change is
proportional change in velocity. The ball that sticks
has a velocity of downward to zero, but the velocity
of the ball that bounces goes downward then
upward. This change in momentum is greater and
therefore has a greater impulse on it.
UB, Phy101: Chapter 7, Pg 5
Chapter 7, Preflight
In both cases of the above question, the direction of the impulse given
to the ball by the floor is the same. What is this direction?
1. Upward
correct
2. Downward
time
UB, Phy101: Chapter 7, Pg 6
You drop an egg onto
1) the floor
2) a thick piece of foam rubber
In both cases, the egg does not bounce.
In which case is the impulse greater?
A) case 1
B) case 2
C) the same correct
In which case is the average force greater
A) case 1
B) case 2
C) the same
correct
Define momentum conservation
UB, Phy101: Chapter 7, Pg 7
Impulse and Momentum Summary
Favet  I = pf - pi = p

For single object….
F = 0  momentum conserved (p = 0)

For collection of objects …
 Fext = 0  total momentum conserved (Ptot = 0)
 Fext = mtotal a
UB, Phy101: Chapter 7, Pg 8
Momentum Conservation (Fext=0)
UB, Phy101: Chapter 7, Pg 9
Chapter 7, Preflight
Is it possible for a system of two objects to have zero total momentum
while having a non-zero total kinetic energy?
1. YES
2. NO
correct
the example of the ice skaters starting from
rest and pushing off of each other...the total
momentum is zero because they travel in opposite
directions but the kinetic energy is not zero
(they start with none and gain a bunch)
if the objects have the same mass and velocities
that cancel each other out, the total momentum is
zero. but they still have kinetic energy, because
they are moving, and the velocities are squared
there so direction doesn't matter.
UB, Phy101: Chapter 7, Pg 10
Chapter 7, Preflight
Movies often show someone firing a gun loaded with blanks. In a blank
cartridge the lead bullet is removed and the end of the shell casing is
crimped shut to prevent the gunpowder from spilling out. When a gun
fires a blank, is the recoil greater than, the same as, or less than when
the gun fires a standard bullet?
1. greater than
2. same as
3. less than
correct
pgun = -pbullet
If there is no bullet then pbullet = 0 so pgun = 0
As if ice skater had no one to push…
UB, Phy101: Chapter 7, Pg 11
Collisions
m2
m1
m2
m1
“before”
“after”
Procedure
• Draw “before”, “after”
• Define system so that Fext = 0
• Set up axes
• Compute Ptotal “before”
• Compute Ptotal “after”
• Set them equal to each other
Explosions
“before”
M
m1
m2
“after”
UB, Phy101: Chapter 7, Pg 12
Chapter 7, Preflight
A railroad car is coasting along a horizontal track with speed V when it
runs into and connects with a second identical railroad car, initially at
rest. Assuming there is no friction between the cars and the rails, what
is the speed of the two coupled cars after the collision?
1. V
2. V/2
3. V/4
CORRECT
4. 0
UB, Phy101: Chapter 7, Pg 13
Chapter 7, Preflight
What physical quantities are conserved in the above collision?
1. Only momentum is conserved
CORRECT
2. Only total mechanical energy is conserved
3. Both are conserved
4. Neither are conserved
Momentum is conserved because the sum of external
forces equal to zero. Total mechanical energy is not
conserved because some of the energy is lost when
the car runs into the other car.
UB, Phy101: Chapter 7, Pg 14
Chapter 7, Preflight
Is it possible for a system of two objects to have zero total momentum
and zero total kinetic energy after colliding, if both objects were
moving before the collision?
1. YES
CORRECT
2. NO
if both objects are moving in oposite directions with
the same mass and velocity they would have a
resulting velocity of zero.
i really just dont think it is possible. but if i am
wrong, i am sure you will have a great demo to make
me feel dumb for answering the wrong question.
UB, Phy101: Chapter 7, Pg 15
Some Terminology
• Elastic Collisions: collisions that conserve energy
• Inelastic Collisions: collisions that do not conserve energy
* Completely Inelastic Collisons: objects stick together
Demo: perfectly inelastic collision
UB, Phy101: Chapter 7, Pg 16
UB, Phy101: Chapter 7, Pg 17
Chapter 7, Ballistic Pendulum
L
L
L
L
m v
V=0
H
M+m
M
V
A projectile of mass m moving horizontally with speed v
strikes a stationary mass M suspended by strings of length
L. Subsequently, m + M rise to a height of H.
Given H, what is the initial speed v of the projectile?
See example 9 in textbook
UB, Phy101: Chapter 7, Pg 18
Explosions
“before”
M
v1
m1
m2
v2
“after”
• Example: m1 = M/3 m2 = 2M/3
• Which block has larger momentum?
* Each has same momentum
• Which block has larger velocity?
* mv same for each  smaller mass has larger velocity
• Which block has larger kinetic energy?
* KE = mv2/2 = m2v2/2m = p2/2m
*  smaller mass has larger KE
• Is energy conserved?
* NO!!
UB, Phy101: Chapter 7, Pg 19
Collisions or Explosions in Two Dimensions
y
x
before
after
• Ptotal,x and Ptotal,y independently conserved
Ptotal,x,before = Ptotal,x,after
Ptotal,y,before = Ptotal,y,after
UB, Phy101: Chapter 7, Pg 20
Explosions
“before”
M
A
B
Which of these is possible?
A
B
both
UB, Phy101: Chapter 7, Pg 21
Shooting Pool...
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
Assuming
Collision is elastic (KE is conserved)
Balls have the same mass
One ball starts out at rest
Then the angle between the balls after the collision is 90o
pf
pi
vcm
Pf
F
before
after
UB, Phy101: Chapter 7, Pg 22
Shooting Pool...

Tip: If you shoot a ball spotted on the “dot”, you have a
good chance of scratching !
UB, Phy101: Chapter 7, Pg 23
Center of Mass



m1r1  m2 r2
rcm 
 mi
Center of Mass = Balance point
L
Example 1:
m
m
xCM = (0 + mL)/2m = L/2
L
Example 2:
m
5m
X=0
X=L
xCM = (0 + 5mL)/6m = 5L/6
UB, Phy101: Chapter 7, Pg 24
Center of Mass (Preflight 6)
Shown is a yummy doughnut. Where
would you expect the center of mass of
this breakfast of champions to be located?
Homer: "mmmm.....donut...(slobbering)...center of mass in tummy...."
Flanders: "why no diddly-o there Homer. The center of mass would be in
the center of the hole."
Homer: "Doe!"
Normally it's the geometric center, but since the geometric center isn't
there....i'd have to guess that it'd be located evenly around the donut. The
mass is, in other words, evenly distributed around the donut.
UB, Phy101: Chapter 7, Pg 25
Center of Mass
Ptot = MtotVcm
Fextt = Ptot = MtotVcm
So is Fext = 0 then Vcm is constant
Also: Fext = Mtotacm
Center of Mass of a system behaves in a SIMPLE way
- moves like a point particle!
- velocity of CM is unaffected by collision if Fext = 0
UB, Phy101: Chapter 7, Pg 26
UB, Phy101: Chapter 7, Pg 27
UB, Phy101: Chapter 7, Pg 28