Stuff you asked about:I thought I understood the concepts in the pre-lecture until they went over the three examples. I felt that it moved too fast especially when the video was showing manipulations of equations.I needed so much help with this. Please explain all of the checkpoint and lecture questions. Also, give more examples!!!I think work and energy is my favorite topic.I think i know the answers, but don't know why and how to explain why it is right.Well, the day I've been dreading has come. We have finished everything I've previously known about physics and the rest of the semester is new. Time to start learning.We should discuss calc 2 because it is much more difficult than this.This isnt that confusing to meMany of the concepts of work are very confusing. I hope to go over this in detail tomorrow1. This stuff is super confusing. Discuss all of it. 2. I think everyone will be glad to know the second I read about centrifugal force in my MCB lab manual, I dropped the class. DON'T THEY KNOW PHYSICS?!?!That was a lot to cover in one prelecture. How is dot product different from vector sum?

You are old enough & smart enough to see where the formulas come from now.

“It seems like work was defined differently to me in high school than it is here. Then again, I didn't pay much attention in high school”

“I really just don't understand work. Please try to cover this in a very understandable way. The pre-lecture just didn't do it for me! :)”

You aren't supposed to know everything after the prelecture

Physics 211Lecture 7

Today’s Concepts:Work & Kinetic Energy

Work-Kinetic Energy Theorem

2

1

r

r

W F dl

“Integrals are a little scary, but the concepts themselves don't seem to difficult.!”

The integral IS the concept !!

Work-Kinetic Energy Theorem

The work done by force F as it acts on an object that moves between positions r1 and r2 is equal to the change in the object’s kinetic energy:

W K2

1

r

r

W F dl

21

2K mv

TOT

TOT NET

“Doesn't work-kinetic energy theorem have anything to do with potential energy?."

Clicker Question

Does the work-kinetic energy theorem have anything to do with potential energy?

A) YESB) NO

W K

The Dot Product

“Direction and magnitude of the total work done is confusing..”

“the vector dot thing. what is the point of it? Will we have to use this in problems.”

Work-Kinetic Energy Theorem: 1-D Example

If the force is constant and the directions aren’t changing then this is very simple to evaluate:

In this case since cos(0)=1This is probably what you remember from High School.

F d

= Fd

2

1

r

r

W F dl F d

car

Clicker Question

A lighter car and a heavier van, each initially at rest, are pushed with the same constant force F. After both vehicles travel a distance d, which of the following statements is true? (Ignore friction)

A) They will have the same velocityB) They will have the same kinetic energyC) They will have the same momentum

F d

F d

car

van

W= Fdsame

DK= WSame too

2

1

r

r

F dl K

2

1

r

r

W F dl

A force pushing over some distancewill change the kinetic energy.

Concept – very important

Derivation – not so important2

1

r

r

F dl K

q

Work done by gravity near the Earth’s surface

mg

path

“May we please discuss the concepts of gravitational work?”

mg

dl1dy1

dx1

mg

dl1

dl2

dlN

Work done by gravity near the Earth’s surface

1 2 ...TOT NW W W W

1 2 ... Nmg dl mg dl mg dl

mg

dl1

dl2

dlN

Dy

Work done by gravity near the Earth’s surface

( ) g final initialW mg y y

1 2 ...TOT NW W W W 1 2 ... Nmg dl mg dl mg dl

1 2... Nmgdy mgdy mgdy mg y

2

1

( )r

r

W F r dr

2

1

2

r

e

r

GM mdr

r

2

1

r

e

r

GM m

r

2 1

1 1eGM m

r r

rdq

dr

Fg

dr

2 1

1 1g eW GM m

r r

1 2

1 2 2 1e

r rGM m

r r r r

Close to the Earth’s surface:

r1 ~ r2 ~ Re:

1 22e

e

GM mr r

R

mg -Dy

So: Wg = -mgDy

Work-Kinetic Energy Theorem

If there are several forces acting then W is the work done by the net (total) force:

You can just add up the work done by each force

NETW K

1 2 ...W W

NET TOTW W

H

Free Fall Frictionless incline String

Checkpoint

Three objects having the same mass begin at the same height, and all move down the same vertical distance H. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of a string.

In which case does the object have the biggest net work done on it by all forces during its motion?

A) Free Fall B) Incline C) String D) All the same

Clicker Question

Three objects having the same mass begin at the same height, and all move down the same vertical distance H. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of a string. What is the relationship between their speeds when they reach the bottom?

H

Free Fall Frictionless incline String

A) vf > vi > vp B) vf > vp > vi C) vf = vp = vi

Checkpoint

A car drives up a hill with constant speed. Which statement best describes the total work WTOT done on the car by all forces as it moves up the hill?

Less that 40% got this right…

A) WTOT > 0

B) WTOT = 0

C) WTOT < 0

v

v

Clicker Question

A car drives up a hill with constant speed. How does the kinetic energy of the car change as it moves up the hill?

A) It increasesB) It stays the sameC) It decreases

v

Clicker Question

A car drives up a hill with constant speed. The acceleration of the car:

A) Points up the hillB) Points down the hillC) Is zero

v

Clicker Question

A car drives up a hill with constant speed. The net force on the car:

A) Points up the hillB) Points down the hillC) Is zero

Reminder

W K2

1

r

r

W F dl

TOT

TOT NET

We know two expressions that involve WTOT

v

Checkpoint

A car drives up a hill with constant speed. Which statement best describes the total work WTOT done on the car by all forces as it moves up the hill?

A) The car moves upward, in the positive direction, therefore the force that caused it to move by a positive distance did positive work.B) change in kinetic energy is zero, total work done is zero.

C) the work is being done by gravity, which is in the negative direction..

TOT

A) WTOT > 0

B) WTOT = 0

C) WTOT < 0

“Question 1 in the prelecture is wrong. It asks for the work done and not the change in kinetic energy. Since the Apple is raised, there is work from the change in gravitational potential energy.”

Hand does positive work. Gravity does negative work. The sum of these is zero since Wtot = Whand + Wgravity = DK = 0

Checkpoint

A box sits on the horizontal bed of a moving truck. Static friction between the box and the truck keeps the box from sliding around as the truck drives.

S

a

The work done on the box by the static frictional force as the truck moves a distance D is:

A) Positive B) Negative C) Zero

Less that 40% got this right…

“How friction is related to work, and which direction work goes in various cases”

From Last Lecture

A box sits on the horizontal bed of a moving truck. Static friction between the box and the truck keeps the box from sliding around as the truck drives.

If the truck moves with constant accelerating to the left as shown, which of the following diagrams best describes the static frictional force acting on the box:

S

a

A B C

Checkpoint

The work done on the box by the static frictional force as the truck moves a distance D is:

A) Positive B) Zero C) Negative

D

A) since the static frictional force is acting in the same direction as the motion, i believe the work would be positive.B) Static means the box isn't moving, so the displacement is 0.

C) Friction always does negative work.

S

a

F

Work done by a Spring

“Can you clarify the directions of positive or negativity for springs when they are compressing and uncompressing?”

In this example the spring does negative work since F and Dx are in opposite direction. The axes don’t matter.

Use the formula to get the magnitude of the work

Use a picture to get the sign (look at directions)