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PHY131H1F - Class 11

Today:

• Conservative and

Nonconservative Forces

• Potential Energy

• Conservation of Energy

Clicker Question

A cart rolls up a frictionless incline. It starts

with speed vi, but stops near the top. As it rolls

up the ramp, its kinetic energy is transformed to

A. stopping energy.

B. gravitational potential energy.

C. energy of motion.

D. internal thermal energy.

E. energy of rest.

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Class 11 Preclass Quiz on MasteringPhysics

This was due this morning at 8:00am

72% of students got the first true/false question.

A nonconservative force permits a two-way conversion

between kinetic and potential energies. FALSE

A potential energy function can be specified for a

nonconservative force. FALSE

A conservative force permits a two-way conversion between

kinetic and potential energies. TRUE

The work done by a nonconservative force depends on the

path taken. TRUE

The work done by a conservative force depends on the path

taken. FALSE

A potential energy function can be specified for a

conservative force. TRUE

Class 11 Preclass Quiz on MasteringPhysics

This was due this morning at 8:00am

67% of students got the second true/false question.

The total mechanical energy of a system, at any one instant,

is either all kinetic or all potential energy. FALSE (although

it could be)

The total mechanical energy of a system is constant only if

conservative forces act. TRUE

The total mechanical energy of a system is equally divided

between kinetic and potential energy. FALSE (although

it could be)

Mechanical energy can be dissipated to nonmechanical

forms of energy. TRUE

The total mechanical energy of a system is constant only if

nonconservative forces act. FALSE (always false)

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Class 11 Preclass Quiz Student Comments

“FYI, the answer to the last question is posted online on

yahoo since two years ago.

https://ca.answers.yahoo.com/question/index?qid=20131003

213113AAT6UcS”

Yahoo!

Answers can

help you get

this part of

your mark. …but it’s not

going to help

you with this

part!

Class 11 Preclass Quiz Student Comments

“I say that Could you please differentiate between what

conservative and non-conservative forces are? Some

examples would be helpful perhaps :)”

Harlow answer: Yes will do!

“Do you believe in me?”

Harlow answer: Yes I do! You can do this!

(at 2:42 am) “I have a CHM138 midterm in about, let's see,

15 hours. Please wish me luck.”

Harlow answer: Good luck!

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Class 11 Preclass Quiz Student Comments

“i trust in physics, but i'd never tie a bowling ball to the end of

a string and let it go to see if it would hit me in an attempt to

test a theorem, just sayin'. my mom paid a lot of money for

my teeth”

Conservative and Nonconservative Forces

• A conservative force stores any work done against it, and

can “give back” the stored work as kinetic energy.

• For a conservative force, the work done in moving between

two points is independent of the path.

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• Because the work done by a

conservative force is path

independent, the work done in

going around any closed path is

zero:

𝐹 ∙ 𝑑 𝑟 = 0

Conservative and Nonconservative Forces

• A nonconservative force does not store work

done against it, the work done may depend on

path, and the work done going around a closed

path need not be zero.

Conservative and Nonconservative Forces

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• Examples of conservative forces include:

• Gravity

• The electric force

• The force of an ideal spring

• Nonconservative forces include:

• Kinetic Friction

• Pushing force of a human or animal

• Automobile engine

Conservative and Nonconservative Forces

Potential Energy

Consider two

particles A and B

that interact with

each other and

nothing else.

There are two ways

to define a system.

System 1 consists

only of the two

particles, the forces

are external, and the

work done by the

two forces change

the system’s kinetic

energy.

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Potential Energy

System 2 includes

the interaction

within the system.

Since Wext = 0, we

must define an

energy associated

with the interaction,

called the potential

energy, U.

When internal

forces in the system

do work, this

changes the

potential energy.

Potential Energy

• The change in potential energy is defined as

the negative of the work done by a

conservative force acting over any path

between two points:

– Potential energy change is independent of path.

– Only changes in potential energy matter.

– We’re free to set the zero of potential energy at

any convenient point.

B

ABA

U F dr

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Gravitational Potential Energy

• Gravitational potential energy stores the work

done against gravity:

– Gravitational potential energy increases linearly

with height y.

– This reflects the constant gravitational force near

Earth’s surface.

Gravitational Potential Energy

U mg y

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Last class at the end I asked:

• Which has more energy, a desk on the top floor

of a building, or a desk on the ground floor?

• Technically, neither (a desk is a desk)!!

• But, if you count the gravitational interaction

between the Earth and the desk, then the system

of the Earth+desk on top floor has more energy

than the system of the Earth+desk on bottom

floor.

• Potential energy is the interaction energy of at

least two things!

Clicker Question

A car starts with speed vi, but the driver puts on

the brakes and the car slows to a stop. As the

car is slowing down, its kinetic energy is

transformed to

A. stopping energy.

B. gravitational potential energy.

C. energy of motion.

D. internal thermal energy.

E. energy of rest.

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Kinetic Energy: The energy of motion

𝐾 =1

2𝑚𝑣2

Potential Energy: The

energy of position

𝑈 = 𝑚𝑔𝑦

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Internal Energy: The energy of

microscopic thermal vibrations

𝐸𝑖𝑛𝑡 ∝ 𝑇

Mechanical Energy

• Mechanical Energy is defined as the sum of the

kinetic plus potential energy:

Emech = K + U

• When the only forces doing work on an object are

all conservative, then the mechanical energy is

conserved.

Ef = Ei

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vi

v f

Another way of looking at freefall:

QUESTION:

I hold a ball at a distance of 5 m

above the ground and release it from

rest.

How fast is it going just before it

hits the ground?

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A small child slides down the four frictionless slides A–D.

Each has the same height, and the child always starts

from rest. Rank in order, from largest to smallest, her

speeds vA to vD at the bottom.

A. vC > vA = vB > vD

B. vC > vB > vA > vD

C. vD > vA > vB > vC

D. vA = vB = vC = vD

E. vD > vA = vB > vC

NOTE: The Zero of Potential Energy

You can place the origin of your coordinate system, and thus

the “zero of potential energy,” wherever you choose and be

assured of getting the correct answer to a problem.

The reason is that only ΔU has physical significance, not Ug

itself.

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QUESTION:

Zainab runs forward with her sled at

2.0 m/s. She hops at the top of a

very slippery slope. The slope is

7.0° below the horizontal, and

extends down a total vertical

distance of 5.0 m. What is her

speed at the bottom?

A. U → K

B. U → Eint

C. K → U

D. K → Eint

E. There is no transformation

because energy is conserved.

A child is sliding down a playground

slide at constant speed.

While sliding, the energy transformation

is

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Elastic Potential

Energy Consider a before-and-after

situation in which a spring launches

a ball

The compressed spring has

“stored energy,” which is then

transferred to the kinetic energy of

the ball

We define the elastic

potential energy U of

a spring to be:

U 1

2kx2

−𝑥i

𝑥f = 0

A spring-loaded gun shoots a plastic ball

with a speed of 4 m/s. If the spring is

compressed twice as far, the ball’s speed

will be

A. 1 m/s.

B. 2 m/s.

C. 4 m/s.

D. 8 m/s.

E.16 m/s.

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Before Class 12 on Monday

• Please finish reading Wolfson Chapter 7

• Something to think about:

• A red marble is balanced on the top of a smooth hill.

A blue marble sits at the bottom of a smooth valley.

Which marble is in equilibrium? What is the

difference between these two situations?