Physics 151: Lecture 19 Todays Agenda

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Physics 151 Lecture 19Todays Agenda

• Topics
• Example problem (conservation of momentum)
• Impulse Ch. 9.2
• Center of Mass Ch. 9.6

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Conservation of Momentum
See text 9-2
video
See Figure 12-2
3
See text 9-2

• Example Problem
• A object of mass m0.200 kg is dropped from l
  30.0 cm height above a basket base (M0.200 kg)
  which is attached to the ceiling with a spring.
  If the spring is stretched by x 0.05 m
  before, find the maximum distance the spring will
  stretch ?

d 0.182 m
See Figure 12-2
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Force and Impulse
See text 9-2

• The diagram shows the force vs time for a typical
  collision. The impulse, I, of the force is a
  vector defined as the integral of the force
  during the collision.

F
Impulse I area under this curve !
t
?t
ti
tf
Impulse has units of Ns.
See Figure 12-2
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Force and Impulse
See text 9-2

• Using

the impulse becomes
F
t
?t
impulse change in momentum !
See Figure 12-2
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Force and Impulse
See text 9-2

• Two different collisions can have the same
  impulse since I dependsonly on the change in
  momentum,not the nature of the collision.

same area
F
t
?t
?t
?t big, F small
?t small, F big
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Force and Impulse
See text 9-2
soft spring
F
stiff spring
t
?t
?t
?t big, F small
Animation
?t small, F big
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Lecture 19, ACT 1Force Impulse

• Two boxes, one heavier than the other, are
  initially at rest on a horizontal frictionless
  surface. The same constant force F acts on each
  one for exactly 1 second.
• Which box has the most momentum after the force
  acts ?

(a) heavier (b) lighter
(c) same
F
F
heavy
light
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Lecture 19, ACT 2Force Impulse

• What is the average force that wall exerts on
  ball (0.40kg) if duration of wall-ball contact
  is 0.01 s ?

a) 20 N b) 200 N c) 2,000 N
d) 20,000 N
vi 30m/s
before collision
vf 20m/s
after collision
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Lecture 19, ACT 3

• A 0.20 kg stone you throw rises 20.3 m in the
  air. The magnitude of the impulse the stone
  received from your hand while being thrown is
• a. 0.27 Ns.
• b . 2.7 Ns.
• c . 4.0 Ns.
• d . 9.6 Ns.
• e . 34.3 Ns.

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System of Particles

• Until now, we have considered the behavior of
  very simple systems (one or two masses).
• But real life is usually much more interesting !
• For example, consider a simple rotating disk.

• An extended solid object (like a disk) can be
  thought of as a collection of parts. The motion
  of each little part depends on where it is in the
  object!

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System of Particles Center of Mass

• How do we describe the position of a system
  made up of many parts ?
• Define the Center of Mass (average position)
• For a collection of N individual pointlike
  particles whose masses and positions we know

(In this case, N 2)
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System of Particles Center of Mass

• If the system is made up of only two particles

(r1 - r2)
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System of Particles Center of Mass

• If the system is made up of only two particles

where M m1 m2
r2 - r1

m2
m1
RCM
r2
r1
y
x
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System of Particles Center of Mass

• The center of mass is where the system is
  balanced !

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Example Calculation
See text 9-6

• Consider the following mass distribution

(12,12)
2m
m
m
(0,0)
(24,0)
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System of Particles Center of Mass
See text 9-6

• For a continuous solid, we have to do an integral.

dm
r
y
where dm is an infinitesimal mass element.
x
video
See example 8-4, A Triangular Plate
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Example Astronauts Rope

• A male astronaut and a female astronaut are at
  rest in outer space and 20 meters apart. The male
  has 1.5 times the mass of the female. The female
  is right by the ship and the male is out in space
  a bit. The male wants to get back to the ship but
  his jet pack is broken. Conveniently, there is a
  rope connected between the two. So the guy starts
  pulling in the rope.
• Does he get back to the ship?
• Does he at least get to meet the woman?

-(
-)
m
M 1.5m
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Lecture 19, ACT 4Center of Mass Motion

• A woman weighs exactly as much as her 20 foot
  long boat.
• Initially she stands in the center of the
  motionless boat, a distance of 20 feet from
  shore. Next she walks toward the shore until she
  gets to the end of the boat.
• What is her new distance from the shore. (There
  is no horizontal force on the boat by the water).

20 ft
(a) 10 ft (b) 15 ft (c) 16.7
ft
before
20 ft
? ft
after
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Center of Mass Motion Review
See text 9.6

• We have the following law for CM motion
• This has several interesting implications
• It tell us that the CM of an extended object
  behaves like a simple point mass under the
  influence of external forces
• We can use it to relate F and A like we are used
  to doing.
• It tells us that if FEXT 0, the total momentum
  of the system does not change.
• As the woman moved forward in the boat, the boat
  went backward to keep the center of mass at the
  same place.

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Recap of todays lecture

• Chapter 9,
• Center of Mass
• Elastic Collisions
• Impulse