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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?