Physics 211 Lecture 10, Slide 1

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Physics 211 Lecture 10

• Today's Concept
• Center of Mass
• Finding it
• Using it

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Your Comments
Triple integrals.
This prelecture was very interesting because a
lot of calculus was involved. Although the triple
integral looked frightening at first, after the
explanation all the doubts were cleared
I think I understood most of it for once.
Pudding is so last week. How about some donuts?
why center of mass was not brought up earlier
when we were starting forces and why momentum was
not brought up in this prelecture.
why you have to make the concepts seem so hard
with the crazy equations and triple integrals
when they are actually understandable
I love how the astronaut in the prelecture had
the moon reflection on his helmet, even though he
was in the middle of space...
We need to discuss people's methods of getting on
to the powerpoint slides with thier responses.
Some people just seem too desperate.
Hmmm well go over the questions for the midterm.
How was your weekend?
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Inside Info Not much work energy on the
exam !
(certainly no center of mass stuff)
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Preflight
A yummy glazed doughnut is shown below. Where is
the center of mass of this fantastic culinary
delight?

• In the center of the hole.
• Anywhere along the blue dashed line going
  throughthe solid part of the dough.
• The center of mass is not defined in cases where
  there is missing mass.

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Three tiny equal-mass magnets are placed on a
horizontal frictionless surface at the corners of
an equilateral triangle. When the magnets are
released, they attract and quickly slide to a
single point. What are the coordinates of that
point?
Act
y
xCM yCM

• A) 0 0
• B) 0 H/2
• C) 0 H/3
• D) 0 H/4
• E) H/4 0

H
x
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Three tiny equal-mass magnets are placed on a
horizontal frictionless surface at the corners of
an equilateral triangle. When the magnets are
released, they attract and quickly slide to a
single point. What are the coordinates of that
point?
y
xCM yCM

• C) 0 H/3

H
x
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Act
The disk shown in Case 1 clearly has its CM at
the center. Suppose the disk is cut in half and
the pieces arranged as shown in Case 2 In which
case is the center of mass highest?
A) Case 1 B) Case 2 C)
same
XCM
Case 1
Case 2
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Act
The disk shown in Case 1 clearly has its CM at
the center. Suppose the disk is cut in half and
the pieces arranged as shown in Case 2 In which
case is the center of mass highest?
A) Case 1 B) Case 2 C)
same
X
X
XCM
X
Case 1
Case 2
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Act
Two pucks of equal mass, on a frictionless table,
are being pulled at different points with equal
forces. Which one gets to the end of the table
first?
(A) Puck 1 (B) Puck 2 (C) Same
(1)
T
M
F
(2)
M
T
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Two pucks of equal mass, on a frictionless table,
are being pulled at different points with equal
forces. Which one gets to the end of the table
first?
(C) Same
a1
(1)
T
M
F
a2
(2)
M
T
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Preflight
Two objects, one having twice the mass of the
other, are initially at rest. Two forces, one
twice as big as the other, act on the objects in
opposite directions as shown.
F
2F
2M
M
Which of the following statements about the
acceleration of the center of mass of the system
is true

• ACM F/M to the right
• ACM F/M to the left
• ACM F/3M to the right
• ACM F/3M to the left
• ACM 0

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Two objects, one having twice the mass of the
other, are initially at rest. Two forces, one
twice as big as the other, act on the objects in
opposite directions as shown.
F
2F
2M
M
Which of the following statements about the
acceleration of the center of mass of the system
is true
The net force on the center of mass is F to the
left (-2F F) and acts on the whole system of
3M, so the acceleration is -F/3M.
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Two guys who weight the same are holding onto a
massless pole while standing on horizontal
frictionless ice. If the guy on the left starts
to pull on the pole, where do they meet?
Preflight
-3 m
0 m
3 m

• A) -3 m B) 0 m C) 3 m

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A large skinny guy with mass 2M and a smaller guy
with mass M are holding onto a massless pole
while standing on frictionless ice, as shown
below. If the little guy pulls himself toward
the big guy, where would they meet?
Act

• A) -3 m
• B) -1 m
• C) 0 m
• D) 1 m
• E) 3 m

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A large skinny guy with mass 2M and a smaller guy
with mass M are holding onto a massless pole
while standing on frictionless ice, as shown
below. If the little guy pulls himself toward
the big guy, where would they meet?
A) -3 m B) -1 m C) 0 m D) 1 m E) 3 m
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