Welcome back to Physics 211

1
Welcome back to Physics 211

• Impulse and Momentum
• Conservation of momentum
• Collisions

2
Current homework assignments

• WHW8
• In blue Tutorials in Physics homework book
• HW-53 1, HW-54 2, HW-56 2
• due Wednesday, Nov. 1st in recitation
• FHW5
• From end of chapters 8 and 9 in University
  Physics
• 8.70, 8.92, 8.94, 9.11, 9.83
• due Friday, Nov. 10th in recitation

3
Definitions of impulse and momentum
Impulse imparted to object 1 by object 2 I12
F12 ?t

• Momentum of an object
• p mv

4
Impulse-momentum theorem
Inet ?p

• The net impulse imparted to an object is equal to
  its change in its momentum.
• Note Unlike work and kinetic energy, impulse
  and momentum are vectors.

5
Two carts of different mass are accelerated from
rest on a low-friction track by the same force
for the same time interval. Cart B has greater
mass than cart A (mB gt mA). The final speed of
cart A is greater than that of cart B (vA gt vB).
After the force has stopped acting on the carts,
the kinetic energy of cart B is
1. less than the kinetic energy of cart A
(KB lt KA). 2. equal to the kinetic energy of cart
A (KB  KA). 3. greater than the kinetic energy
of cart A (KB gt KA). 4. Cant tell.
6

• Acceleration of two objects of different massby
  equal forces for equal times.
• Work done and final kinetic energies are
  different.
• Is there any combination of the quantities mass
  (m) and velocity (v) such as mv, m2v, mv3, etc.
  that is the same for both carts?
• FA FB
• ?tA ?tB

7
Suppose a tennis ball and a bowling ball are
rolling toward you. The tennis ball is moving
much faster, but both have the same momentum
(mv), and you exert the same force to stop each.
Which of the following statements is correct?

• 1. It takes equal distances to stop each ball.
• 2. It takes equal time intervals to stop each
  ball.
• 3. Both of the above.
• 4. Neither of the above.

8
Suppose a tennis ball and a bowling ball are
rolling toward you. Both have the same momentum
(mv), and you exert the same force to stop each.
It takes equal time intervals to stop each
ball. The distance taken for the bowling ball to
stop is the distance taken for the tennis ball
to stop.

• 1. less than.
• 2. equal to
• 3. greater than

9
Consider the change in momentum in these three
cases
A. A ball moving with speed v is brought to
rest. B. The same ball is projected from rest so
that it moves with speed v. C. The same ball
moving with speed v is brought to rest and
immediately projected backward with speed v.
In which case(s) does the ball undergo the
largest change in momentum?

• 1. Case A.
• 2. Case B.
• 3. Case C.
• 4. Cases A and B.

10
Throwing ball at student on cart
(Neglecting vertical forces for short time
interval while student catches ball.)
11
Notice

• By Newtons 3rd, law the force on the ball is
  equal and opposite to the force on the student
• Acts for same time interval ? equal and opposite
  changes in momentum

12
Newtons 3rd law and changes in momentum

• If all external forces (weight, normal, etc.)
  cancel

13
Conservation of momentum

• Assuming no net forces act on bodies there is no
  net impulse on composite system
• Therefore, no change in total momentum D(p1 p2)
  0

F
system
1
2
14
Conservation of momentum(for a system consisting
of two objects 1 and 2)

• If the net (external) force on a system is zero,
  the total momentum of the system is constant.
• Whenever two or more objects in an isolated
  system interact, the total momentum of the system
  remains constant

15
Conservation of momentum with carts

• Two carts initially at rest with compressed
  spring between them -- track with motion
  detectors
• Single cart with alcohol rocket

pi 0 pf
16
The fire extinguisher car is propelled by
ejecting large amounts of gas at high speed.
Could such a car operate outside of the Earths
atmosphere?

• 1. Yes
• 2. No
• 3. Not sure.

17
The New York Times, Jan.13, 1920, p. 12

• its flight would be neither accelerated nor
  maintained by the explosion of the charges To
  claim that it would be, is to deny a fundamental
  law of dynamics That Professor Goddard, with
  his chair in Clark College and the
  countenancing of the Smithsonian Institution,
  does not know the relation of action to reaction,
  and of the need to have something better than a
  vacuum against which to react to say that would
  be absurd.

18
The New York Times, July 17, 1969, p. 34

• an editorial feature of the New York Times
  dismissed the notion that a rocket could function
  in a vacuum and commented on the ideas of Robert
  H. Goddard.
• further investigation and experimentation have
  confirmed the findings of Isaac Newton in the
  17th century, and it is now definitely
  established that a rocket can function in a
  vacuum as well as in an atmosphere. The Times
  regrets the error.

19
Collisions

• If two objects collide and the net force exerted
  on the system (consisting of the two objects) is
  zero, the sum of their momenta is constant.

The sum of their kinetic energies may or may not
be constant.
20
Elastic and inelastic collisions

• If K is conserved collision is said to be
  elastic
• e.g. cue balls on a pool table
• KA,i KB,i KA,f KB,f
• Otherwise termed inelastic
• e.g. lump of putty thrown against wall
• KA,i KB,i KA,f KB,f
• Extreme case completely inelastic -- objects
  stick together after collision

21
A cart moving to the right at speed v collides
with an identical stationary cart on a
low-friction track. The two carts stick together
after the collision and move to the right. What
is their speed after colliding?

• 1. 0.25 v
• 2. 0.5 v
• 3. v
• 4. 2v

22
Cart A moving to the right at speed v collides
with an identical stationary cart (cart B) on a
low-friction track. This time the collision is
elastic (i.e. there is no loss of kinetic energy
of the system). What is each carts velocity
after colliding (considering velocities to the
right as positive)?
23
Check conservation of momentum and energy
24
Elastic collision of two masses
v1i
v1f
v2f
v2i 0
m1
m2
m1
m2
Momentum ? m1v1i 0 m1v1f m2v2f
Energy ? (1/2)m1v1i2 0 (1/2)m1v1f2
(1/2)m2v2f2
25
Special cases (i) m1 m2
v2f
v1i
v2i 0
v1f
m1
m2
m1
m2
26
Reading assignment

• Collisions, Extended objects, Center of Mass
• 8.3 - 8.5, 10.1 in textbook