Clicker question (from a former midterm…) - U of T Physicsjharlow/teaching/phy131f15/lec10ToPost2.pdf · PHY131 Class 10 Notes 10/19/2015 14 Work and Kinetic Energy • If an object

PHY131 Class 10 Notes 10/19/2015

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PHY131H1F– Class 10

Today:

• Energy

• Work

• Work as an integral

• Kinetic Energy

• Power

Clicker question

(from a former midterm…)


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Class 10 Preclass Quiz on MasteringPhysics

This was due this morning at 8:00am

91% of students answered correctly: If a graph depicts force

versus position, the work done is equal to the area under

the curve.

82% of students answered correctly: A vector 𝐶 has a

magnitude 𝐶. Then the scalar product of the vector with

itself is 𝐶 ∙ 𝐶 = 𝐶2.

77% of students answered correctly: If the net work done on

an object is zero, the object’s kinetic energy remains the

same.

90% of students answered correctly: Person B does twice

the work of person A, and in one-half of the time. Person B

has four times the power output of person A.

Class 10 Preclass Quiz Student Comments

“The whole energy of the earth is increasing because of the

continuous sunlight, right?”

Harlow answer: Actually, no. The earth, just like the Sun,

radiates its energy out into space. The sun radiates visible

light, but the Earth, which is at a lower temperature, radiates

infrared light. But the Earth radiates exactly as much power

as it absorbs from the Sun. The whole energy of the Earth is

a constant.

About 100 comments such as: “none of us have had

integration yet”

Harlow answer: I understand this. But you must learn a bit

of integration for this course.


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Calculus in a nutshell

http://hyperphysics.phy-astr.gsu.edu/hbase/math/derint.html


“Is Work a scalar quantity or vector quantity?”

Harlow answer: Work, like all forms of energy, is a scalar

quantity. It has no direction associated with it. But it can be

positive or negative.

[lengthy description of confusion about the Power:Climbing

example on page 102, then] “... wait a minute... Do watts

always have 'per second' included within it?”

Harlow answer: correct. Watt is a short-form for

Joules/second

“Is there ever a time when you can use the equation for

work= F∆x without having to integrate?”

Harlow answer: Yes, if the force is constant!

“I had to do a lot of WORK in this chapter.. didn't like it but i

POWERED through it..”

“Brain is currently 待机-ing.... Please hold while it tries to

reboot.”

http://hyperphysics.phy-astr.gsu.edu/hbase/math/derint.html


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Last class I asked:“A pendulum bob swings back and forth on the end of a

string, describing a circular arc. Does the tension

force in the string to any work?”

Answer: NO!

The tension force always acts perpendicular to

infinitesimal displacement of the bob. In this case,

tension is not speeding the bob up or slowing down, it

is only turning it. So it does zero work.

Big Idea Chapters 6, 7 and 9 introduce the principles of

conservation of energy and conservation of

momentum. These concepts give us new useful ways

of analyzing motion.

Some quantities stay the same while other things

around them change.

For example, when a dish falls to the floor and

shatters, if you add up the mass of all the pieces, it will

be the same as the mass of the original dish. This is

“Conservation of Mass”: Mf = Mi.

Similarly, we have “Conservation of Energy” (Ef = Ei)

and “Conservation of Momentum” ( 𝑝𝑓 = 𝑝𝑖): two new

principles which we will use to solve problems.


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• Energy is a property of an object, like age or

height or mass.

• Every object that is moving has some Kinetic

Energy.

• Objects in a gravitational or electric field may

also have Potential Energy.

• Energy has units, and can be measured.

• Energy is relative; kinetic energy of car is

different for an observer in the car than it is for

an observer standing on the side of the road.

What is “energy”?

• involves force and distance.

• is force distance.

• in equation form: W F Δx

Two things occur whenever work is done:

• application of force

• movement of something by that force

SI Unit of work:

newton-meter (N·m)

or joule (J)

The most basic form

of energy: Work


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Work can be positive, zero or

negative

• When the force and the distance are in the same

direction, you are helping the motion with the

force, so the work done on the object is positive.

• The force is adding energy to the object +

environment.

F

Δx

• Maybe this force

is speeding the

object up.


negative

• When the force and the distance are at right

angles, you are not helping the motion with the

force, so the work is zero.

• This force is not changing the energy of the

object.

F• This force won’t

speed the object

up or slow it

down. Δx


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“If there is no displacement in the direction of your force,

there is ZERO work hahahahah.

“There is a term describing this saying a person is doing

efficient-less job called "无用功“


negative

• When the force and distance are in opposite

directions, you are hindering the motion with the

force, so the work done on the object is

negative.

• This force is reducing the energy of the object.

F• Maybe this

force is

slowing the

object down.

Δx


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• Justin is doing a bench press, and he slowly

pushes the bar up a distance of 0.30 m while

pushing upwards on the bar with a force of 200 N.

The bar moves with a constant velocity during this

time.

• During the upward push, how much work does

Justin do on the bar?

A. 60 J

B. 120 J

C. 0 J

D. -60 J

E. -120 J

Discussion Question


lowers the bar down a distance of 0.30 m while


The bar moves with a constant velocity during this

time.

• During the downward lowering, how much work

does Justin do on the bar?

A. 60 J

B. 120 J

C. 0 J

D. -60 J

E. -120 J

Discussion Question


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lowers the bar down a distance of 0.30 m while


He then pushes it up slowly the same distance of

0.30 m back to its starting position, also pushing

upwards on the bar with a force of 200 N.

• During the complete downward and upward

motion, how much total work does Justin do on

the bar? A. 60 J

B. 120 J

C. 0 J

D. -60 J

E. -120 J

Discussion Question

Simple Machines

• Devices for multiplying forces or changing the

direction of forces

• Cannot create energy but can transform energy

from one form to another, or transfer energy

from one location to another

• Cannot multiply work or energy


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• (Force distance)input (force distance)output

Principles of a simple machine:

• Conservation of energy concept:

Work input work output

• Input force input distance

Output force output distance

Simple Machines

Simplest machine:

• Lever

– rotates on a point of support called the

fulcrum

– allows small force over a large distance and

large force over a short distance


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Pulleys

This arrangement operates

like a lever with equal

arms— changes the

direction of the input force:

This arrangement

can allow a load to

be lifted with half the

input force:

Work as a scalar product

• The work done by a constant force is the

scalar-product of the force and the

displacement.

W = F r cosθ

𝑊 = 𝐹 ∙ 𝑟


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The Work Done by a Variable Force

To calculate the work done on an object by a force that is

not constant, we use an integral:

We must evaluate the integral either geometrically, by

finding the area under the cure, or by actually doing the

integration.

𝑊 = 𝑥1

𝑥2

𝐹𝑥𝑑𝑥

A particle moving along the x-axis experiences the force

shown in the graph.

How much work is done on the particle by this force as it

moves from x = 0 to x = 2 m?

A. 0.0 J

B. 1.0 J

C. 2.0 J

D. 4.0 J

E.−2.0 J


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Kinetic Energy• Energy of motion

• Depends on the mass of the object and square of

its speed:

If object speed is doubled kinetic energy is

quadrupled.

𝐾 =1

2𝑚𝑣2

Demonstration

• In terms of WORK and ENERGY,

describe what is happening to the ball

as it goes from A to B to C?

A spring-loaded toy gun is used to shoot a ball of mass m

straight up in the air. The spring has spring constant k. The

ball has speed vB at point B.


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Work and Kinetic Energy• If an object starts from rest and there is a net

force doing work on it, the work done will be

equal to the final kinetic energy of the object.

• In equation form:

𝐹𝑑 =1

2𝑚𝑣2

The Work – Kinetic Energy Theorem:

• The work done by the net force on an

object as it moves is called the “net work”,

Wnet.

• The the net work causes the object’s

kinetic energy to change by:

ΔK = Wnet.


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A particle moving along the x-axis experiences the force

shown in the graph. The particle starts at rest at x = 0.

What is the kinetic energy of the particle when it reaches

x = 2 m?

A. 0.0 J

B. 1.0 J

C. 2.0 J

D. 4.0 J

E.−2.0 J

Work-Energy Theorem• Applies to decreasing speed:

– reducing the speed of an object or bringing it to a halt

Example: Applying the brakes to slow a moving car, work is done on it (the friction force supplied by the brakes distance).


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(A) I did positive work on the box, friction did negative work on the

box, there was net positive work done on the box.

(B) I did positive work on the box, friction did negative work on the

box, there was net negative work done on the box.

(C) I did positive work on the box, friction did negative work on the

box, there was net zero work done on the box.

(D) I did zero work on the box, friction did negative work on the

box, there was net positive work done on the box.

(E) I did zero work on the box, friction did positive work on the box,

there was net zero work done on the box.

Clicker Question. (From 2013 final exam)

Yesterday in my office I pushed a box, initially at rest, across the

rough floor to the other side of my office, where it now rests. Which

statement below is true concerning this motion of the box?

Power• Measure of how fast work

is done

• In equation form:

Power =

work done

time interval

Unit of power

• joule per second, called the

watt after James Watt,

developer of the steam

engine

• 1 joule/second 1 watt

• 1 kilowatt 1000 watts


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Power

• 1 kWh is the amount of energy used by a

power of 1kW over 1 hour

• 1 kWh = 1000 J/s * 60 min/hour * 60 s/min

• 1 kWh = 3.6 million Joules

[Chart downloaded Oct.16 2015 from http://www.ontario-hydro.com/index.php?page=current_rates ]

• The unit of power is the

watt, which is defined as

1 watt = 1 W = 1 J/s

• Energy is measured by

Ontario Hydro in kWh

“kiloWatt hours”.

ExampleYour clothes dryer uses 5000 Watts and you need

to run it for 1 hour to dry your clothes. If you run it

during “on peak” time, such as between 7 and

11am on a weekday, the cost is 16 cents/kWh.

If you run it during “off peak” on the weekend the

price for Ontario Hydro electricity is 8 cents/kWh.

How much money do you save per load by doing

your laundry on the weekend?

http://www.ontario-hydro.com/index.php?page=current_rates


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Before Class 11 on Wednesday:

• Please read Chapter 7, sections 7.1-7.3

• Preclass quiz due Wednesday by 8:00am

• Complete MasteringPhysics.com Problem Set 4

due tonight at 11:59pm: Material: Uncertainties

and sections 5.1-5.3.

• Something to think about: Which has more

energy, a desk on the top floor of a building, or a

desk on the ground floor?

Documents

Clicker question (from a former midterm…) - U of T Physicsjharlow/teaching/phy131f15/lec10ToPost2.pdf · PHY131 Class 10 Notes 10/19/2015 14 Work and Kinetic Energy • If an object