Physics 211 Lecture 18, Slide 1

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Physics 211 Lecture 18
Today's Concepts Static Equilibrium Potential
Energy Stability
Plus Ill work through a couple of the HW
problems
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Ladders on walls and tensions in ropes.
How to apply the concepts presented in
pre-lecutre in more word problems.
I just wanted to tell you how I experienced
physics this weekend. I was camping at Kickapoo
State Park, and I had hiked my way onto this
ledge overlooking a river
What is this footprint business? Thanks
go over the truck and box problem again.
i wish i did not leave this till 2 in the morning
None. This weather is making me too happy! I have
no problems in life!
It all seemed to make sense. Kudos to the
masterful prelecture.
How to determine if the torque is positive or
negative. I know the right hand rule as related
to the cross product, but some help would be
appreciated. Also, that was a very creative way
of saying the word "slip" to whoever does the
prelectures.
I'm starting to believe that you pick these
comments strictly at random because I've written
some pretty creative and funny comments (if I do
say so myself) in attempt to make it to the
almighty introduction lecture slide but to no
avail. However, I will never quit because
quitters never win, and winners never quit. I'll
cross my fingers and hope for the best.
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Act

• A (static) mobile hangs as shown below. The rods
  are massless and have lengths as indicated. The
  mass of the ball at the bottom right is 1kg.
• What is the total mass of the mobile?

A) 4 kg B) 5 kg C) 6
kg D) 7 kgE) 8 kg
1 m
2 m
1 kg
1 m
3 m
4
Act

• In which of the static cases shown below is the
  tension in the supporting wire bigger? In both
  cases M is the same, and the blue strut is
  massless.

A) case 1 B) case 2 C)
same
T1
T2
300
300
L
L/2
M
M
case 1
case 2
5

• Another way to see it

case 1
case 2
T1
T2
q
q
M
M
Balancing Forces in the y direction
Physics 211 Lecture 18, Slide 5
6

• Its the same. Why?

case 1
case 2
d1
T1
T2
d2
q
q
L
L/2
M
M
Balancing Torques
Physics 211 Lecture 18, Slide 6
7
Prelecture

• In which of the static cases shown below is the
  tension in the supporting wire bigger? In both
  cases the red strut has the same mass and length.

A) case 1 B) case 2 C)
same
T1
T2
300
300
L
L/2
case 1
case 2
55 got this right
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• In which of the static cases shown below is the
  tension in the supporting wire bigger? In both
  cases the red strut has the same mass and length.

T1

• case 1
• B) case 2
• C) same

T2
300
300
L
L/2
case 1
case 2

• Case 1 because the lever arm distance is the
  largest there
• Both cases must have the same torque. Since case
  1 has a longer length, it needs a smaller force
  than case 2, which has a shorter length.
• Both wires have to hold up a beam of the same
  mass.

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Lets work our way through a couple of HW problems
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Parts (a) and (b) are just like the problem we
did last lecture
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Parts (a) and (b) are just like the problem we
did last lecture
We also know T1 T2 Mg
2 equations, 2 unknowns Solve for T1 T2
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Act
Now find T2 right after you cut the wire on the
left.
T2
M
x cm
Mg
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Act
The free side of the beam will start to fall. Use
this fact to figure out how T2 compares to
weight of the beam?
T2
A) T2 Mg B) T2 gt Mg C) T2 lt Mg
M
x cm
Mg
Physics 211 Lecture 18, Slide 13
14
Find T2 right after you cut the wire on the left.

T2
M
x cm
d
Mg
Plug this into the expression for T2
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Just like the ladder problem in the prelecture
q
q
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Just like the ladder problem in the prelecture
q
q
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Just like the ladder problem in the prelecture
q
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Only difference iswhere q is defined
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General Case Ladder Example

• Bill (mass m) is climbing a ladder (length L,
  mass M) that leans against a smooth wall (no
  friction between wall and ladder). A frictional
  force f between the ladder and the floor keeps it
  from slipping. The angle between the ladder and
  the wall is f.
• How does f depend on the angle of the ladder and
  Bills distance up the ladder?

L
M
Bill
m
q
f
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• Balance forces
• x Fwall f
• y N Mg mg

Fwall
Balance torques
L/2
Mg
axis
d
mg
q
f
N
23
y
L/2
M
m
d
q
f
x
Physics 211 Lecture 18, Slide 23
24
Prelecture
In the two cases shown below identical ladders
are leaning against frictionless walls. In which
case is the force of friction between the ladder
and the ground the biggest? A) Case 1 B) Case
2 C) Same
Case 1
Case 2
70 got this right
Physics 211 Lecture 18, Slide 24
25
In the two cases shown below identical ladders
are leaning against frictionless walls. In which
case is the force of friction between the ladder
and the ground the biggest? A) Case 1 B)
Case 2 C) Same
Case 1
Case 2

• F(1/2) mg cot(theta)
• case 2 has a larger force of friction because a
  larger percentage of the center mass is in the
  vertical direction.
• The coefficient of friction and normal force are
  the same in both cases.

Physics 211 Lecture 18, Slide 25
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Box on Truck...
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Stability
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Prelecture

• Suppose you hang one end of a beam from the
  ceiling by a rope and the bottom of the beam
  rests on a frictionless sheet of ice. The center
  of mass of the beam is marked with an black spot.
  Which of the following configurations best
  represents the equilibrium condition of this
  setup?

A) B) C)
65 got this right
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• Which of the following configurations best
  represents the equilibrium condition of this
  setup?

A) B) C)

• The center of mass is inside the footprint of the
  object on the sheet of ice.
• The center of mass is directly below the point on
  the ceiling where the rope is attached.
• The ice is frictionless so it can't put a force
  on the beam that could make the string hang at an
  angle