Post on 18-Aug-2018
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PHY131H1F - Class 19Today:
• Today, Chapter 12:
• Conditions for Static Equilibrium
• Center of Gravity
• Static Equilibrium Problems
• Stability
Suppose the girl on the left suddenly is handed a bag of apples weighing 50 N. Where should she sit order to balance, assuming the boy does not move?
A. 1 m from pivot
B. 1.5 m from pivot
C. 2 m from pivot
D. 2.5 m from pivot
Static Equilibirum
CHECK YOUR NEIGHBOR
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Class 19 Preclass Quiz on MasteringPhysics
This was due this morning at 8:00am
68% of students got: A heavy boy and a lightweight girl are
balanced on a massless seesaw. If they both move forward
so that they are one-half their original distance from the pivot
point, nothing will happen; the seesaw will still be
balanced.
72% of students got: A point of stable equilibrium is one at
which the potential energy is a minimum.
83% of students got: A body is in total equilibrium. The net
force and the net torque acting on the object are both
zero.
Class 17 Preclass Quiz Student Comments
“Is ‘static equilibrium’ the same as ‘total equilibrium’?”
Harlow answer: Yes.
“idk this is really random but do you watch star trek tos”
Harlow answer: yes. I have been watching that show since
I was 3 years old in fact.
“I enjoy physics because as difficult as it can be its so
rewarding when you solve a problem.”
“If there are two forces acting at on object on two different
point and these two force are equal and opposite, does it
count as 0 net force?”
Harlow answer: Yes.
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Class 17 Preclass Quiz Student Comments
“the last written question on the midterm, you calculate and
stated that "needed<max so it stay still". Confused. I thought
if the force you need to move is smaller than the force you
are getting, then you should be moving.”
30°
30°
My strategy:
• Assume block has stopped, and is
in equilibrium.
• Balance the forces on the f.b.d.
(spring, gravity and static friction)
• Solve for static friction.
• This is fs that is “needed” to keep
the block stationary.
• Compute fs,max = μs n.
• If fs,needed < fs, max, then it’s okay; it
doesn’t slip.
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Class 17 Preclass Quiz Student Comments
“So stable equilibrium is a local min of the potential energy
graph, and unstable equilibrium is a local max, right?”
Harlow answer: Yes.
“How much of an emphasis will be placed on chapter 10, 11,
and 12 on the final exam?”
Harlow answer: The final exam is comprehensive and will
include an even spread of material from chapters 1-14 plus
the Uncertainties Analysis. In practice, material from the
later chapters, 7-14, is a bit more likely to show up on the
final exam, since physics is cumulative, and these problems
actually involve material from multiple chapters.
“WHEN WILL THIS COURSE END”
Harlow answer: Thursday Dec. 17 at 11:00am. That’s
about 3½ weeks from now.
我想在上课的幻灯片上显示我的回复
Last day I asked
The supports to the diving board provide a vertical
force on the board so the diver will not fall. What
are the directions of the force on the board at point
1 and point 2: up or down? Why?
1 2100 N
400 N
300 N
4 m
1 m
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• Centre of mass is the average position of all the mass
that makes up the object.
• Centre of gravity (CG) is the average position of weight
distribution.
– Since here on Earth weight and mass are
proportional, centre of gravity and centre of mass
always refer to the same point of an object.
Gravitational Torque
• When calculating the torque due to gravity,
you may treat the object as if all its mass
were concentrated at the centre of mass.
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• A 4.00 m long, 500 kg steel beam is supported 1.20 m from the
right end. What is the gravitational torque about the support?
Equilibrium When Rotation is Possible• The condition for a rigid body to be in static equilibrium is that
there is no net force and no net torque.
• No matter which pivot point you choose, an object that is not
rotating is not rotating about that point.
• For a rigid body in total equilibrium, there is no net torque about
any point.
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Static Equilibrium Problems
• In equilibrium, an object has no net force and no net
torque.
• Draw an extended free-body diagram that shows
where each force acts on the object.
• Set up x and y axes, and choose a rotation axis. All
of these choices should be done to simplify your
calculations.
• Each force has an x and y component and a torque.
Sum all of these up.
• Three equations which you can use are:
Fx 0
Fy 0
0
Clicker Question.
An object could be in static equilibrium when
A. only one force is acting on it.
B. two or more forces are acting on it.
C. only one torque is acting on it.
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• A uniform steel beam of length L
and mass m1 is attached via a
hinge to the side of a building.
• The beam is supported by a steel
cable attached to the end of the
beam at an angle θ, as shown.
• Through the hinge, the wall
exerts an unknown force, 𝐹, on
the beam.
• A workman of mass m2 sits
eating lunch a distance d from
the building.
a. Find T, the tension in the cable.
b. Find Fx, the x-component of the
force exerted by the wall on the
beam ( 𝐹), using the axis shown.
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a. Find T, the tension in the cable.
b. Find Fx, the x-component of the
force exerted by the wall on the
beam ( 𝐹), using the axis shown.
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Centre of Gravity—Stability
The location of the centre of
gravity is important for
stability.
• If we draw a line straight down
from the centre of gravity and it
falls inside the base of the object,
it is in stable equilibrium; it will
balance.
• If it falls outside the base, it is
unstable.
Clicker question.
A
BC
D. All three of the trucks will tip over.
E. None of the three will tip over.
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• One block of length L is hanging off the edge of a table.
How far off the edge can it go without tipping?
Demo and example
• Two blocks have length L. The top one is hanging a distance L/2
off the one below it.
• How far off the edge can the bottom block be before the entire
stack topples over?
Demo and example
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• Three blocks have length L. The top one is hanging a distance
L/2 off the one below it. The one below that is hanging a distance
L/4 off the one below it.
• How far off the edge can the bottom block be before the entire
stack topples over?
Demo and example
• Three blocks have length L. The top one is hanging a distance
L/2 off the one below it. The one below that is hanging a distance
L/4 off the one below it. The one below that is hanging a distance
L/6 off the one below it.
• How far off the edge can the bottom block be before the entire
stack topples over?
Demo and example
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Stability• An equilibrium is stable if a slight disturbance from
equilibrium results in forces and/or torques that tend to
restore the equilibrium.
• An equilibrium is unstable if a slight disturbance causes
the system to move away from the original equilibrium.
Cone on its base is stable Cone on its tip is unstable
Kinds of Stability
What kind of equilibrium is this?
A.Stable
B.Neutrally stable
C.Unstable
D.Metastable
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Kinds of Stability
What kind of equilibrium is this?
A.Stable
B.Neutrally stable
C.Unstable
D.Metastable
Kinds of Stability
What kind of equilibrium is this?
A.Stable
B.Neutrally stable
C.Unstable
D.Metastable
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Kinds of Stability
What kind of equilibrium is this?
A.Stable
B.Neutrally stable
C.Unstable
D.Metastable
Before Class 20 on Wednesday
Please read sections 13.1 and 13.2 of chapter 13 on
oscillations and SHM.
The pre-class video for class 20 has an offer for $5 to the
first person who can explain a genuine conundrum I am
having..
The preclass quiz is due Wednesday morning at 8:00am.
Problem Set 8 on Chapters 10 and 11 is due tomorrow
evening at 11:59pm. Problem sets have Tuesday deadlines
now!
Something to think about over the weekend: A spring with a
mass attached to it is stretched and released. When the
spring returns to equilibrium, is the mass moving?